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Proton magnetic resonance spectroscopy of human brain : T1 and T2 relaxation and absolute concentrations… Brief, Elana Esther 2000

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P R O T O N M A G N E T I C RESONANCE SPECTROSCOPY OF H U M A N BRAIN: Ti AND T  2  R E L A X A T I O N AND A B S O L U T E CONCENTRATIONS OF  M E T A B O L I T E S IN P A T I E N T S A N D H E A L T H Y V O L U N T E E R S Elana Esther Brief B . Sc. (Physics) York University M . Sc. (Physics) University of British Columbia  A THESIS SUBMITTED IN PARTIAL FULFILLMENT OF THE REQUIREMENTS FOR THE DEGREE OF DOCTOR OF PHILOSOPHY  in THE FACULTY OF GRADUATE STUDIES DEPARTMENT OF PHYSICS AND ASTRONOMY  We accept this thesis as conforming to the required standard  THE UNIVERSITY OF BRITISH COLUMBIA September 2000  © Elana Esther Brief = - 2 0 0 0  In presenting this thesis in partial fulfilment of the requirements for an advanced degree at the University of British Columbia, I agree that the Library shall make it freely available for reference and study. I further agree that permission for extensive copying of this thesis for scholarly purposes may be granted by the head of my department or by his or her representatives.  It is understood that copying or publication of this thesis for financial gain  shall not be allowed without my written permission.  Department of Physics and Astronomy The University of British Columbia 1956 Main M a l l Vancouver, Canada  Date:  Sec-WW 2.^ , Zooo  Abstract  Absolute concentrations have been measured of the brain metabolites choline, creatine and N-Acetyl-Aspartate using non-invasive proton ( H) Magnetic Resonance Spectroscopy (MRS) 1  in vivo. The accuracy of H-MRS has been improved as a result of better metabolite T i X  and T2 relaxation time measurements and a novel technique for measuring brain tissue water concentration.  The precision of MRS has been measured for all major brain metabolites  including choline CHO, the methyl group of creatine CRE, the methylene group of creatine (CR), glutamine (GLU), glutamate (GLN), myo-inositol (INS) and N-Acetyl-Aspartate NAA. T i and T2 have been measured more precisely and accurately than previously reported studies because of improvements made to the saturation recovery and decay experiments. Contrary to previous results, metabolite T i relaxation was found to differ for all metabolites between and within three regions of normal human brain. In addition, T2 relaxation of CHO and NAA have been found to be shorter than previously reported. The T i and T2 times measured in previous studies are explained in terms of short-comings in their experimental design. Brain tissue water content has been measured using a T relaxation imaging sequence and 2  normalizing to an external standard. This determination of water content is a vast improvement over previous experiments which either quoted literature values for water content for pure tissues, or made erroneous assumptions regarding the magnetic resonance visibility of the protons associated with water. The concentrations of CHO and NAA exhibited a regional dependence in the parietal white and occipital grey regions examined whereas CRE did not. The concentrations measured here were found to be within the range of the concentrations quoted in the literature, however the slight differences can be explained in terms of the improved water content measurements and the T corrections. 2  ii  Clinical applications of the T i and absolute concentration studies are discussed. In particular, the T i times of NAA and CHO within multiple sclerosis lesions were reduced compared the the corresponding metabolites in healthy white matter. This may help explain confusing published observations such as the reversible decrease of NAA in M S lesions. Three separate studies are introduced which investigate the brain metabolite concentrations in patients with traumatic brain injury, patients with phenylketonuria and patients with chronic fatigue syndrome. This work represents the development and improvement of a new clinical tool which can be used in collaboration with radiologists, neurologists, endocrinologists and other specialists to investigate neurologic disease.  iii  Table of Contents  Abstract  ii  L i s t of Tables  ix  List of Figures  xii  Glossary  xiii  Acknowledgements  xv  1  Introduction: Overview of Magnetic Resonance Spectroscopy  1  2  Background  4  2.1  4  2.2  2.3  Qualitative NMR Physics 2.1.1  Localization  5  2.1.2  Relaxation  6  2.1.3. j Coupling  7  2.1.4  Solvent Suppression and MR Spectrum  7  2.1.5  Pulse Sequences  8  Neurohistology and Observed Chemicals  11  2.2.1  N-Acetyl-Asparate  13  2.2.2  Creatine  15  2.2.3  Choline-Containing Compounds  15  2.2.4  myo-Inositol  16  2.2.5  Glutamate and Glutamine  17  Materials and Methods  17 iv  3  Subject Selection and Voxel Placement  17  2.3.2  Spectral Fitting  2.3.3  Relaxation Fitting  21  2.3.4  Statistical Tests Used in the Studies  22  '.  18  2.4  Overview of Technical Contributions of Thesis  22  2.5  Previous Publications of Results in Thesis  23  Reproducibility  25  3.1  Methods  26  3.1.1  Subjects, Voxel Placement and Pulse Sequence  26  3.1.2  Spectral Fitting and Reproducibility Statistics  3.2  3.3 4  2.3.1  .  26  Results and Discussion  28  3.2.1  Reproducibility Results  28  3.2.2  Comparison with Literature  31  3.2.3  Use of Reproducibility Results  32  3.2.4  Improving Precision in MRS Experiments  33  Summary  34  T i Relaxation  35  4.1  Methods  36  4.1.1  Subjects, Voxel Placement and Pulse Sequence  36  4.1.2  Choice of T R Range  37  4.1.3  Spectral Fitting and T i Analysis  37  4.1.4  Temperature Dependence of T i in Metabolite Solutions  39  4.1.5  Simulations of Saturation Recovery Curves  39  4.2  Results  40  4.2.1  T i Results and Statistics  40  4.2.2  Temperature Dependence of T i in Metabolite Phantoms  42  v  5  Simulations  43  4.2.4  Biological Variation Compared with Data Noise for T i  45  4.2.5  Simple Theory for T i Mechanism  45  4.2.6  Comparison with Literature Values  48  4.2.7  Consequences of Omitting T i Corrections  48  4.3  Summary  49  T  Relaxation  50  Methods  52  5.1.1  Subjects, Voxel Placement and Pulse Sequence  52  5.1.2  Choice of T E Range  53  5.1.3  Spectral Fitting and T Analysis  53  5.1.4  Coupled Spins  55  5.1.5  Simulations of Decay Curves  56  2  5.1  5.2  5.3 6  4.2.3  2  Results and Discussion  56  5.2.1  T Results and Statistics  56  5.2.2  Simulations  58  5.2.3  Biological Variation compared with Data Noise for T  5.2.4  Comparison with Literature Values  59  5.2.5  Consequences of Omitting T Corrections  59  2  2  2  Summary  58  62  Quantification  63  6.1  Introduction  63  6.2  Methods  65  6.2.1  Subjects, Voxel Placement and M R S / M R I Pulse Sequence  65  6.2.2  Quantitative M R I Analysis  66  6.2.3  Spectral Fitting and Relaxation Corrections  67  vi  6.2.4 6.3  6.4 7  Results and Discussion  68  6.3.1  Quantification Results  68  6.3.2  Comparison with Literature  69  Summary  72 73  7.1  Methods  74  7.1.1  Subjects and Voxel Placement  74  7.1.2  Spectral Analysis and T i Measurement  77  7.3  9  67  T i o f M u l t i p l e Sclerosis L e s i o n s  7.2  8  Calculating Concentrations  Results and Discussion  . .  77  7.2.1  Lesion T i  77  7.2.2  Consequences of T i Differences Between Lesions and Normal  79  7.2.3  Comparison with Literature  80  7.2.4  Possible Explanation for T Reduction of NAA+NAAG and CHO in Lesions  80  x  Summary  81  Future W o r k  82  8.1  Relaxation Mechanisms  82  8.2  Technical Optimization  82  8.3  Future Medical Applications  83  8.3.1  Traumatic Brain Injury  • 84  8.3.2  Phenylketonuria  86  8.3.3  Chronic Fatigue Syndrome  87  Conclusions  89  Bibliography  91  vn  A  B  P h y s i c s of M R  108  A. l  The Physics of Magnetic Resonance  108  A.1.1  Basic Equations of Q M  108  A.1.2  The Zeeman Hamiltonian  110  A. 1.3  Dipolar Interactions and Motional Narrowing  Ill  A. 1.4  Relaxation  112  A. 1.5  Chemical Shift  115  A. 1.6  The Bloch Equations .  115  Accuracy and Precision  118  B. l  Propagation of Noise in Non-Linear Functions  118  B.2  Noise Plots  119  viii  L i s t o f Tables  3.1  Average C O V s for within-series, between-series and between-exam reproducibility 30  3.2  Upper and lower bounds in NAA concentration for 99.9% confidence interval . . .  4.1  Means and standard errors of metabolite T i (s) in vivo and phantom at 37°C. . . 41  4.2  L C M o d e l %SD Averaged over all Volunteers  45  5.1  Means and standard errors of metabolite T2 (ms) in vivo  56  6.1  Number of volunteers, concentrations and standard deviations (mM) for CHO, CRE and NAA  6.2  33  68  Number of volunteers, concentrations and standard deviations (mM) for CHO, CRE and NAA from literature  69  7.1  T i and standard deviations (s) for voxels A , B , C and D and controls  77  8.1  Concentrations and standard deviations (mM) for CHO, CRE and NAA in head injury patients and controls  B.l  85  Point number, bias and standard deviation for simulated T2  ix  fits  123  List of Figures  2.1  Chemical constituents of H-MRS spectrum acquired from phantoms  8  2.2  CHESS pulse sequence  9  2.3  PRESS pulse sequence  10  2.4  S T E A M pulse sequence  10  2.5  Chemical structure of NAA  13  2.6  Typical ^ - M R S output from LCModel  14  2.7  Chemical structure of creatine  15  2.8  Chemical structure of CHO  16  2.9  Chemical structure of INS  16  2.10 Chemical structure of GLN and GLU  17  2.11 Representative voxels on proton density images  19  3.1  Visual representation of the reproducibility studies  27  3.2  Three spectra from one volunteer for the within-series reproducibility study. . . .  27  3.3  Two spectra from one volunteer for the between-series reproducibility study. . . .  28  3.4  Seven spectra from one volunteer for the between-exam reproducibility study. . . 29  4.1  Fitted spectra stacked according to T R  4.2  A visual representation of the simulation used to calculate noisy T i times . . . . 40  4.3  T i fits to the average signal area for all parietal white matter volunteers  41  4.4  Single exponential recovery curves fit to 12 T R spectra  41  4.5  Arrhenius Plot: logarithm of T i plotted against 1/T (1/K) for templates  4.6  Simulated T i and standard deviation where true Ti=ls  x  38  . . . .  43 44  4.7  Signal at T R = o o against T i for simulations with 15% noise, true Ti=1.4s and true amplitude=l  4.8  44  T i weighted signal area ratios for each metabolite to CRE in occipital grey assuming T R = l s and unit concentration for each metabolite  49  5.1  Comparison of TE30ms and TE200ms spectra from healthy occipital grey matter. 50  5.2  Fitted spectra stacked according to T E  54  5.3  T2 fits to the average signal area over all occipital grey matter voxels  57  5.4  Distribution of T 2 times over all occipital grey matter voxels where the x-axis is volunteer number  57  5.5  Simulated T 2 for different T E values and ranges assuming true T2=300ms.  . . .  59  5.6  Amplitude against T2 for each of 1000 simulations at 15% noise and true T2=200ms. 60  5.7  Amplitude against T2 for each of 1000 simulations at 15% noise and true T2=400ms. 61  5.8  T2-weighting assuming unit signal area at TE=0ms  6.1  Placement of bottles in the 20mm thick, TE=10ms image of the modified C P M G  62  sequence  65  6.2  Logarithm of amplitude vs. T E in the modified C P M G data from an M R S voxel.  66  7.1  Voxel placement for each of the patients  75  7.2  Fitted spectra stacked according to T R for lesion  76  7.3  T i fit to CHO recovery for each M S lesion voxel  78  7.4  T i fit to CRE recovery for each M S lesion voxel  78  7.5  T i fit to INS recovery for each M S lesion voxel  78  7.6  T i fit to NAA+NAAG recovery for each M S lesion voxel  78  7.7  Relative uncorrected signal intensity against T R for NAA and CHO in lesions compared with normals  B.l  79  Simulated T 2 against noise for each point in a 5 T E decay curve, T2true=200ms.  xi  121  B.2  Simulated T  2  against noise for each point in a 5 T E decay curve, T2true=400ms.  xi 1  122  Glossary  Abbreviation 1 3  C  Meaning Carbon-13 Nucleus  CFS  Chronic Fatigue Syndrome  CHESS  Spectroscopy Pulse Sequence: CHEmical Shift Selective  CHO  Choline-Containing Compounds  COV  Coefficient of Variation  CNS  Central Nervous System  CR  Creatine; specifically the C H group on Creatine  CRE  Creatine; specifically the C H 3 group on Creatine  *H  Hydrogen Nucleus; Proton  INS  Inositol; specifically myo-Inositol  GE  General Electric Company  GLN  Glutamine  GLU  Glutamate  2  mM  milli-mol/litre  MRI  Magnetic Resonance Imaging  MRS  Magnetic Resonance Spectroscopy  MRSI  Magnetic Resonance Spectroscopy Imaging  MS  Multiple Sclerosis  NAA  N-Aceytl-Aspartate  NAAG  N-Aceytl-Aspartyl-Glutamate  NMR  Nuclear Magnetic Resonance  1 3  P  Phosphorous-31 Nucleus  xin  PHE  Phenylalanine  PKU  Phenylketonuria  PRESS  Spectroscopy Pulse Sequence: Point RESolved Spectrocopy  RF  Radiofrequency  % SD  Standard Deviation as Estimated by L C M o d e l  SNR  Signal to Noise Ratio  STEAM  Spectroscopy Pulse Sequence: STimulated Echo Acquisition Mode  T  Temperature (used as T=37°C)  T  Tesla (used as 1.5T or 2.0T)  Ti  Spin-Lattice Relaxation Time (s)  T  Spin-Spin Relaxation Time (s)  2  TE  Time to Echo (Echo Time)  TM  Mixing Time  TR  Time to Repeat (Repeat Time)  voxel  Volume Element: the volume from which the spectrum is collected  WC  Water Content  xiv  Acknowledgements  I like the person I am becoming — and for that I have a great number of people to thank. The distinction between family, friends and teachers has been blurred - the love, support and knowledge that has so generously been bestowed upon me has come from the same people taking on different roles in my life as needed. I must first thank my advisory committee: Profs. Alex MacKay (my supervisor), Myer Bloom, Elliott Burnell, David L i and Qing-San Xiang. They have taught me how to ask clear scientific questions and have provided me with the tools to answer those questions. Each has demonstrated to me how to conduct research with curiousity and joy. B y their example, I have learned to greatly respect others' expertise and to have humility when presented with complicated problems. I could not have learned from a better group of scientists and I am unspeakably grateful for having had this opportunity. I am also fortunate to have been immersed in an outstanding lab. M y colleagues (past and present) Sofia Chavez, X i n Chen, Keith Cover, Craig Jones, Bettina Jung, Corree Laule, Frank Linseisen, Jamie Lloyd-Smith, Burkard Madler and Irene Vavasour have provided me with an environment rich in questions and answers. I am honoured to be involved in their lives scientifically and personally. M y colleague deserving of the most praise for his extraordinary knowledge and patience is Ken Whittall. K e n has jarred me into clearer thinking through his questions, has provided me with analysis tools to understand my data, and has taught me how to develop analysis tools for myself. In the past five years, the U B C M R I technologists have shared their space and their knowledge with me. Their suggestions for how best to collect data have helped my studies enormously. They have patiently taught me how to use the M R I scanner, and have collected  xv  excellent data when I have been absent. I have to thank the excellent staff in the Department of Physics and Astronomy for their administrative talents. They have quickly resolved problems that took me months to establish. M y thesis was proof-read by three remarkable friends: Jamie Lloyd-Smith, Jenifer Thewalt and Ken Whittall. Their attention to content and flow enabled me to improve this document dramatically. Any errors in this thesis are mine alone, but I must share the credit for the fluidity of the document. I have developed many friendships in the past five years and each has deepened with time. BeAtrice Winsborrow was my first dear friend in Vancouver and it is with great joy that I am part of hers and her daughter, Robyn's lives. Jamie Lloyd-Smith has moved from Vancouver but remains deep in my heart. Yvette Cheong shares with me constantly, comfort and joy. K e n Whittall makes a space for me to discuss any concern. Kaspar Mossman, my boyfriend, has supported me over distance and time. M y first name Elana means little tree and I link my strengths to the fertile soil that house my roots. I must acknowledge my family for being constant in their love and support throughout my life. M y aunts, uncles and cousins: Helen, Paul, Laura, Simon and Rebecca; Nancy, Dov, Aimee, Karen and Deborah, Neal, Sloane, Rebecca and Joel. M y grandparents: Sam (Z"L) and Goldie Brief (Z"L) and Harry and Millie Stein. M y siblings: Sam and Rachel. And finally, but hardly finally because they are the source, I thank my parents Harold and Fredelle Brief who have taught me love and respect by example. The best of me is them.  This work could not have been done without the financial support of the Natural Science and Engineering Research Council of Canada (PGSB) and the Canadian Multiple Sclerosis Foundation.  xvi  Chapter 1 Introduction: Overview of Magnetic Resonance Spectroscopy  Magnetic Resonance Spectroscopy (MRS) in vivo is a relatively new technique in diagnostic medicine that provides information about the chemical constituents in a localized part of the human body. M R S is the in vivo application of Nuclear Magnetic Resonance ( N M R ) . The resonance phenomenon of a nuclear magnetic moment was discovered in 1938 by Isidor Isaac Rabi (Nobel Prize 1944) [1, 2]. N M R in condensed matter was first achieved in 1946 by two independent groups led by Felix Bloch [3, 4] and Edward Mills Purcell [5] (Nobel Prize 1952). The first N M R images were obtained in 1973 by Paul Lauterbur [6]. The application of Fourier analysis to N M R by Richard Ernst [7] (Nobel Prize 1991) dramatically improved the efficiency of data collection and made N M R imaging feasible. The first clinical N M R scanners came into hospitals in the early 1980s. A n M R S exam is conducted using a Magnetic Resonance Imaging (MRI) scanner. as M R I detects NMR-sensitive nuclei (e.g. H , 1  1 3  Just  C , P ) in different spatial positions, M R S 3 1  detects different molecules containing those nuclei in the same space. One of the first papers on in vivo M R S was published in 1983 by Cady et al. [8] on cerebral metabolism in infants with P - M R S . Before 1983 in vivo M R S examinations were conducted with only 3 1  3 1  P and  1 3  C  nuclei [9]. H - M R S in vivo was more challenging than the other nuclei because of the need for 1  solvent suppression: the concentration of water is five orders of magnitude larger than that of the M R S chemicals (metabolites) in vivo, therefore solvent suppression is essential for detecting the metabolites. The first published paper on H - M R S in human brain [10] appeared in 1985 1  in which the authors demonstrated that localized spectroscopy was possible in vivo. H - M R S 1  of human brain developed very quickly after the 1987 paper by Frahm et al. [11] in which the  1  Chapter 1. Introduction: Overview of Magnetic Resonance Spectroscopy  2  authors distinguished all the chemicals which made up the observed spectrum. In the past decade M R S of humans has expanded rapidly. M R S has been conducted on brain, skeletal muscle, heart and internal organs. Spectra have been measured from one voxel in each acquisition (single voxel M R S ) and from multiple spatially resolved voxels in one acquisition (MRS imaging, MRSI). M R S is being developed to be used both spatially and temporally: for example, chemical composition is determined for localized multiple sclerosis lesions compared to the surrounding normal-appearing tissue and dynamic spectroscopy exams monitor the uptake of  1 3  C labelled glucose to follow biochemical changes in real time. Brain H - M R S has been 1  applied to many neurological diseases including multiple sclerosis, schizophrenia, Alzheimer's, stroke and AIDS-related illnesses. In the 2000 I S M R M meeting [12] over 250 of 2200 abstracts dealt with M R S of humans in vivo. Despite the proliferation of M R S exams, some fundamental questions have not yet been answered in the literature. For instance, early studies measuring the T i and T 2 of the brain metabolites did so in a rudimentary manner and were never improved upon (more information in chapters 4 and 5). As we shall see (chapter 6), T i and T2 corrections are essential for accurate determination of concentration and neglecting them can lead to severe errors in concentration estimates.  In addition, T i measurements presented here may help explain confusing results  such as the reversible N A A decreases seen in multiple sclerosis lesions [13] (chapter 7). Finally, accurate determination of brain water content has not yet been achieved in the M R S literature and a novel method for its measurement is presented in chapter 6. M y intention for this P h D dissertation was to build and describe a clinical tool which can be used to accurately and precisely measure absolute concentrations of brain metabolites using 1  H - M R S . The thesis consists of the following: 1. Introduction: techniques used to acquire, analyze and understand the data 2. Reproducibility: results of a reproducibility study measuring the precision of the M R S signal area estimates  Chapter 1. Introduction: Overview of Magnetic Resonance Spectroscopy  3. T i Measurements: results of a T i study in three areas of healthy human brain 4. T2 Measurements: results of a T2 study in two areas of healthy human brain 5. Absolute Concentrations: results of a quantification study measuring absolute concentrations of brain metabolites 6. T i of Metabolites in MS: results of a T i study in multiple sclerosis lesions 7. Applications of M R S : descriptions of upcoming studies in various patient populations This document thus describes the development and application of a more precise and accurate tool than has previously been used in the literature.  3  Chapter 2  Background  In writing this chapter I have made the assumption that the reader is either very familiar with the physics behind magnetic resonance or is completely new to it. In this background section I will describe the physics of magnetic resonance qualitatively in order to make sense of how the data were acquired. For more detail please read appendix A and references therein.  2.1  Qualitative N M R Physics  A n NMR-sensitive nucleus has a non-zero nuclear spin. Almost every element in the periodic table has an isotope with a non-zero nuclear spin. However, in order to have a detectable signal with M R S we are limited to those isotopes with a high natural abundance (i.e. in a given sample the natural abundance is the percentage of the particular isotope). The natural abundances [14] are 99.985% for *H (the nucleus of hydrogen), 1.11% for  1 3  C and ~100% for P . Although there 3 1  are only a few nuclei which have high enough biological abundances for in vivo studies, they give information about a number of important chemicals. For instance, when using A D P and A T P can be examined and for C - M R S , 1 3  1 3  3 1  P-MRS,  C infused glucose can be mapped in the  body. We chose H - M R S because H has the highest natural abundances and because many 1  :  neurological conditions can change the concentrations of molecules visible with H - M R S . From 1  here on I will refer only to the proton, H , when describing the NMR-sensitive nucleus. 1  When placed in a magnetic field some protons align with the field and some against. The protons aligned with the field are at a lower energy than those aligned against and the energy difference, A E , is given by A E = TryB (section A.1.2) where B is the strength of the magnetic field, 7 is the gyromagnetic ratio and H is a constant. As described by Boltzmann statistics,  4  Chapter 2.  Background  5  for two million protons at room temperature in a 1.5T magnetic field, nine more nuclei align with the field.  To align more nuclei against the field, the nuclei must be irradiated with  electromagnetic waves with energy A E , or, said differently, with frequency u> = E / h . A t 1.5T, the frequency is u>/27r=64MHz and is in the radiofrequency ( R F ) range. Protons in a magnetic field precesses at the angular frequency, u, which is determined by the Larmor equation: u — 7B.  (2.1)  This means that when the field strength increases, the frequency of precession increases. If the field strength were to change by cr, the frequency would shift according to: u> = 7B(1 — a).  (2.2)  The a change (chemical shift) is on the order of parts per million of frequency (or field strength). The frequency position of individual signal resonances are measured in ppm (parts per million). In the semi-classical approach to the physics of magnetic resonance (section A.1.6), we speak of an ensemble of nuclei which makes up a magnetization vector. Instead of aligning discretely with or against the field, the magnetization vector could point in any direction with respect to the magnetic field. In this thesis, I refer to tipping the magnetization vector by 90° or 180° which means that R F is applied to the nuclei for the magnetization vector to subtend a 90° or 180° angle with respect to its original direction.  2.1.1  Localization  M R I and M R S detects the magnetization at a particular location in the body. Very simply, an M R I scanner is built such that the receiver coils (those which detect the magnetization) are orthogonal (90°) to the direction of the magnetic field. In order to detect the signal the magnetization vector must be tipped into the transverse plane, 90° to the magnetic field. Because of T relaxation factors (section 2.1.2) the magnetization should be detected as soon 2  as possible after excitation. The need for localization, however, increases the time necessary  Chapter 2. Background  6  to acquire the signal. Therefore in localized M R S there is a delay (>10ms) between excitation and detection. Nuclear signals can be spatially localized by applying non-uniform magnetic fields across the body in different directions. For instance, if a magnetic field gradient G(z) is imposed onto the static field B , then in the x — y plane at position Az the resonant frequencies are Q  Au = j(B  0  + G(A.z)).  In applying a radiofrequency pulse with bandwidth A w to the body,  only the nuclei in the slice will be excited. The bandwidth of the pulse determines the slice thickness. The simplest pulse shape is sine = sin(u)/u  which is the Fourier transform of a box  in position space. As an example of pulse parameters and their effect: a sine pulse with a small bandwidth will excite a thin, but sharply defined, slice. In M R S , localization is achieved by selecting three orthogonal slabs. Only the nuclei in the intersection of the three slabs will have their magnetization tipped such that it is detectible by the end of the sequence. The intersection of the slabs is referred to as the voxel. 2.1.2  Relaxation  As soon as the magnetization is tipped into the transverse plane it begins to relax. There are three relaxation processes of interest in M R I and they are characterized by T i , T and T * . 2  2  T i relaxation is the process by which the excited nuclei give up energy to the 'lattice' and return to their lower energy state. In metabolites in human brain the T i times (chapter 4) are about 1.4s. Initially when tipped into the transverse plane the nuclear ensemble precesses around the main magnetic field in phase. T relaxation occurs when the nuclei lose their phase coherence 2  with each other. The nuclei remain in their excited state, but undergo an irrecoverable loss of coherence due to randomly fluctuating nuclear interactions (section A . 1.4). In human brain, after T « 0.3s (chapter 5), 1/e (~67%) of the protons are still phase coherent with each other. 2  I mention T * for completeness. T * is similar to T in that it is a loss of phase coherence, 2  2  2  but T * is due to nuclear interactions and static interactions such as magnetic field inhomogeneities. 2  Chapter 2. Background  The relationship between T  7  2  and T * may be symbolically represented as 1/T * = 1/T 2  2  2  +  2 inhomogeneities •  In this thesis only T i and T relaxation will be considered. 2  2.1.3  j Coupling  When two protons are in close proximity, for instance when they are fewer than four bonds away from each other, they influence the field experienced by each other based on their orientation in the magnetic field. For example, if proton A is aligned against the field and proton B is aligned with the field, proton A will experience a slightly different magnetic field than if proton B were aligned against the field. In an ensemble, almost half of the protons will be aligned against the field, and half with the field. The ensemble of protons in the same position as proton A will generate signal at two frequencies instead of one. The difference in the two frequencies is called the j coupling constant; it is specific to the molecule and remains the same at all field strengths. The j coupling evolves over time and the split signals change phase with each other at the frequency of the j coupling constant. Because the j coupling splits the signal from a proton, at low signal to noise (SNR) the signals from those protons are harder to detect. Furthermore, at 1.5T (the magnetic field strength used for the experiments in this thesis) the split peaks overlap. At different T E times (section 2.1.5) the two peaks could constructively contribute to each others signal or can destructively cancel each other out.  2.1.4  Solvent S u p p r e s s i o n a n d M R S p e c t r u m  To detect the metabolite signal in ^ - M R S the water must be suppressed.  After successful  water suppression the H - M R S spectrum reveals a number of signals that do not arise from 1  the protons on water. Protons on different molecules (and at different positions on the same molecule) experience slightly different magnetic environments because the electrons from the surrounding atoms on the molecule shield the magnetic field. As a result the protons precess  Chapter 2.  Background  8  full spectrum CRE CHO INS NAA GLU 4.0  3.0  2.0  1.0  chemical shift (ppm)  Figure 2.1: Chemical constituents of H - M R S spectrum acquired from phantoms. 1  at different frequencies according to equation 2.2 and give rise to the signals in a H - M R S 1  spectrum (figure 2.1).  2.1.5  P u l s e Sequences  The spin gymnastics described above can be visualized with pulse-sequence timing diagrams. These diagrams are visual representations of what the M R I scanner is doing. There are two rows in the following diagrams: the top shows the radiofrequency pulses and the bottom shows the gradient timing. Figure 2.2 shows the timing diagram from the CHEmical Shift Selective (CHESS) watersuppression pulse sequence. Each of three radiofrequency pulses are followed by strong gradients. The bandwidth of the radiofrequency pulses is 75Hz centred on water. Each pulse tips the protons associated with water into the transverse plane. The gradient which follows dephases the magnetization so that when the spectroscopy sequences ( S T E A M or P R E S S discussed below) begin all of the signal from water is dephased. Figures 2.4 and 2.3 are the two spectroscopy sequences used. Figure 2.3 shows the Point REsolved Spectroscopy Sequence (PRESS) acquiring a spin echo and figure 2.4 depicts the STimulated Echo Acquisition Mode ( S T E A M ) sequence acquiring a stimulated  echo. The main  difference between the spin echo and the stimulated echo is that the signal from the spin echo has double the S N R of the stimulated echo. Unless the 'unsuppressed water' signal was collected,  Chapter 2.  Background  9  t_sup  tjsuptrtter  Usupirrter  t 03end  y  ^ — , i  ~4  W  pwrfsup  .  ^  ft ' ! ^ a, ;U  , .  *  p*_rfSUp  ~«  .  ^  pwjrfcup  AN •*—M—'  MM  MM pw gcaup  :  MM  MM  :  f w gc3Up  gc3up  Figure 2.2: C H E S S pulse sequence. the C H E S S sequence preceeded every S T E A M or P R E S S acquisition. One main difference between the sequences shown in figures 2.2, 2.4 and 2.3 are the 'spatially selective pulses' which appear i n the spectroscopy but not in the C H E S S sequences. The spatially selective pulses are the radiofrequency pulses which have a gradient beneath them and they excite the nuclei in only one plane. Nuclei tipped by all three radiofrequencies (i.e. at the intersection of the three planes) will give rise to a signal in the acquisition window. Those nuclei which do not see all three pulses, however, are dephased by the large gradients (called 'crushers') to the left and right of the radiofrequency pulses. The S T E A M sequence consists of three 90° pulses whereas the P R E S S sequence has one 90° followed by two 180° pulses. Each sequence has its advantages and disadvantages. Labelled on diagram 2.4 are the time between pulses, £12, £23 and £3,.. The times £12 + £3r is called the echo time (TE) and £i = £23. The mixing time ( T M ) is the time between the second and the 2  third pulses, £23. In contrast, P R E S S does not have a T M time. The entire time in figure 2.3 t\2 + ^23 + Hr is the T E . The time between repetitions of the entire pulse sequence (i.e. between  Chapter 2. Background  4  t_12  t_st1  1 23  I 3r  t rfinish  ^4  RF acq. window pw rf1 ^  \  ^ pw_rf2  ^—•—pw_rf3  n Grad  pw Bzs pw gc12  pw gxs  M »^ pw gc23a  •i*" pw gc23b pw gys  *-»—*-++-* pw gc3r  Figure 2.3: P R E S S pulse sequence.  RF  Grad  Figure 2.4: S T E A M pulse sequence.  tdaq  pw  Chapter 2. Background  11  the first 90° and the subsequent 'first' 90°) is called the repetition time ( T R ) . Each sequence is repeated to increase the S N R by averaging spectra. The number of acquisitions refers to the number of times the sequence was repeated and it is usually around 128. T  2  relaxation occurs over the T E time and follows the relationship: S(TE) =  S(0)exp~ ^ TE  2  where S(0) and S(TE) are the amounts of coherent magnetization at times t=0 and t = T E . To measure T2 (chapter 5), we collected spectra at various T E times and generated a decay curve of the signal area at each T E . Tx relaxation occurs over the entire repetition time, T R and follows the relationship S(TR) = S(oo)(l - exp~ / i) TR T  where S(TR) and S(oo) are the amounts of  magnetization at t = T R and at t=oo. For T i measurements (chapters 4 and 7), the T R was varied and a saturation recovery curve was generated.  The T M was kept constant for all  experiments in this work. The S T E A M sequence, historically, had a shorter minimum T E because of the arrangement of gradients for localization and dephasing. S T E A M also deposits less radiofrequency energy into the subject because it does not use 180° pulses. P R E S S has the advantage of double the signal of S T E A M because it collects a spin echo rather than a stimulated echo. However, P R E S S depends on the scanner generating two accurate 180° pulses which may be difficult depending on local homogeneity. For most of the experiments in this thesis S T E A M was used because of its lower minimum T E . There have been improvements in P R E S S spectroscopy such that its minimum T E is now the same as that of S T E A M (TE=30ms) in normal operation. However, when the shape of the localization gradients are altered the minimum S T E A M T E can be as low as T E = l l m s . When the need for better SNR was very important (chapter 5 and 7) P R E S S was used.  2.2  Neurohistology and Observed Chemicals  To appreciate the importance of each of the chemicals detected with ^ - M R S we must first consider what the brain is made of. Having a rough understanding of the cells in the central nervous system (CNS) will help develop a context for the location and function of the metabolites.  Chapter 2.  Background  12  W i t h i n this thesis, the words 'chemical', 'molecule' and 'metabolite' will be used interchangeably to refer to the sources of M R S signals not arising from water. The C N S consists of neurons and glial cells. B y volume they each constitute about half of the C N S . Neurons transmit electrochemical signals through the C N S while glial cells are considered the 'support cells' of the nervous system. The neuron can be thought of having three distinct parts: the cell body, the axon and the dendrites. The neuronal cell bodies make up the grey matter in the brain and the axons are long processes which project out from the cell body like tenticles. Signals coming from the neuronal cell body are transmitted along the axon which are up to one metre in length. In order to transmit the signal quickly and efficiently most axons are wrapped with layers of lipid called myelin and the tracts of myelinated axons make up the white matter in the brain and spinal cord. Finally, the dendrites are also processes projecting out of the cell body and they receive signals from axons via synapses. There are three types of CNS glial cells: astrocytes, oligodendrocytes and microglia. Astrocytes provide physical support to neurons, clean up dead neurons, control the chemicals surrounding the neurons and provide nourishment to the neurons.  Astrocytes are in greater number in  grey matter than white matter. Oligodendrocytes make the myelin sheath which surrounds the axons and provide physical support to the axons they are wrapping. The oligodendrocytes, therefore, are in higher number in white matter. Microglia are the smallest of the glial cells and clean up the C N S debris. 1  H - M R S is sensitive to the following chemicals in human brain: N-Acetyl-Asparate (NAA),  creatine, choline-containing compounds (CHO), myo-inositol (INS), glutamine (GLN) and glutamate (GLU).  There are many other chemicals which make up the signal, but measuring them  accurately is very difficult because of their low S N R as a result of their low concentration and substantial j coupling (they include alanine, G A B A , glucose, N-Acetyl-Aspartyl-Glutamate (NAAG) and taurine). Lactate is also detectible using H - M R S , but is only seen temporarily in 1  diseased tissue undergoing anaerobic respiration. The chemical signals in the ^ - M R S spectrum  Chapter 2.  Background  13  O  II  CH -C 3  HO-C-CH 'C—C-OH 2  Figure 2.5: Chemical structure of NAA. are shown in figure 2.1 from the top line they are: the full spectrum, the methyl (CH3) group of creatine (ORE), CHO, INS, NAA and GLN. The methylene ( C H ) group of creatine (CR) is not 2  shown in the diagram but is referred to later in the thesis. The following subsections give an overview of the most visible metabolites in vivo, indicating whether they are more prominantly in neurons or glia and describing what their function may be.  2.2.1  N-Acetyl-Asparate  NAA (figure 2.5) is the most prominent peak in the H spectrum at 2.01ppm (figure 2.6). It was 1  discovered in 1956 by Tallan [15] and it is confined to the fluid portion of the cytoplasm exclusive of organelles and membranes [16, 17]. A decrease in NAA can be seen after administration of neurotoxic agents [18]. While its function is unknown, NAA could be an osmolyte in the nerve cell [16, 19] and may be an acetyl donor for myelin synthesis [16, 20]. In fact, infants have very little NAA and its increase coincides with the onset of myelination [21]. It has been demonstated in rats that NAA exists in all regions of the nerve cell [22] and it is homogeneously distributed around the brain [23, 24]. M R S studies in vivo have estimated the concentration of NAA to be two times higher than found in gas chromotography [15][25] and high-resolution ^ - N M R [26, 27, 28] of biopsed human tissue and furthermore, M R S has estimated the NAA concentration to be lower in white than grey matter [29]. The concentration of NAA declines rapidly with time in monkey brain homogenates  Chapter 2.  Background  14  Data ot Radiology Research, LCModel (Version S.f-G) Gopyrght  S. W. Prcvencher.  The University of British Columbia,  Ret.: Magn. Reson. Med.  Vancouver  30:672-070(1893).  SunDsc  (9]  -  -  Or+Cro'  »  pajtaiM S D D M P  '  621:12.-01 1998  'ns'  -  s.O  5D&EAS -  ,TFHB.  F I L E R S - • / Msoaj Eft 51S / u n o o r r _ 030. B A S I S " B - I L B S O - ' ) M S O Q J L C n y o r by a 00S 1  F I L P S - ' / MO«iy IjC£l_*rcnr k / 9 90 S Oeccunl 1 1 » _ P 3 37 93 . p a ' 0 6ceuni 1 Chemical SHft (ppm)  DBI. TAT  -  33792. F M t '  0. 0004  Figure 2.6: Typical ^ - M R S output from L C M o d e l . (ground up tissue) but slowly i n whole pieces of excised tissue [30]. N A A is hydrolysed by amidohydrolase [31] and there is a three-fold higher hydrolase activity in white matter compared to grey matter [32]. The discrepancy between the in vitro and in vivo NAA concentrations has been attributed to the hydrolysis of NAA after excising the tissue and during the preparation for tests. On the 'left' shoulder of NAA in the spectrum is N-Acetyl-Aspartyl-Glutamate (NAAG) (at 2.1ppm). NAAG is also in all parts of the nerve cell [22] but varies regionally [23]. W i t h S N R at 1.5T it is possible to spectrally resolve NAA and NAAG, however when the S N R decreases the two chemicals cannot readily be distinguished and are reported as the total NAA (tNAA). A l l M R S studies which have measured NAAG values regionally have been conducted at 2.0T [23, 29] Because of its specificity to neurons, NAA is considered a 'marker of neuronal integrity' [33]. A decrease in the NAA signal has been seen i n many neurological disorders including multiple sclerosis (chapter 7), schizophrenia [34, 35, 36], acute head injury (chapter 8) and stroke.  Chapter 2.  Background  15  NH  ll  H N-C NCH, O 2  I  3  H 0 2  II  CH -C-OH 2  Figure 2.7: Chemical structure of creatine. 2.2.2  Creatine  The CRE signal arises from two chemicals creatine (figure 2.7) and phosphocreatine (PCR) [29] both contributing overlapping signals to the spectrum at 3.0 and 3.9ppm (figure 2.6). Creatine is essential in the anaerobic storage and production of energy in the cells during which creatine kinase catalyzes the reversible inorganic phosphate (Pj) transfer from PCR and A D P to creatine and A T P [37]. This creatine/PCR reaction sustains fast energy consumption in the cell and facilitates 'metabolic energy transport' (i.e. net A T P transfer from the mitochondria to the sites where A T P is used) in large cells with nonuniform mitochondrial distributions [38]. Regions with high amounts of creatine kinase enzymes also have high concentrations of both creatine and PCR [39, 40] and it has been found that there are higher concentrations of these chemicals in cell preparations of astrocytes and oligodendrocytes than in neurons [17]. The in vivo concentration estimates of creatine have been found to be below those from in vitro studies in enzymatic analysis [41] but similar to those from high-resolution proton spectroscopy of human biopsy [26, 27, 28].  3 1  P - M R S experiments [42, 43, 44, 45] have found  the PCR concentration to be consistent with ^ - M R S studies [29] if the creatine and PCR levels are equal as has been seen in rats and rabbits [46, 47].  2.2.3  Choline-Containing  Compounds  The CHO signal (at 3.2 ppm in figure 2.6) arises from small water-soluble or emulsifying compounds carrying choline moieties [29] and these include (in order of decreasing concentration) phosphorylcholine and glycero-phosphorylcholine (both playing important roles in phospholipid  Chapter 2.  Background  16  HOCH CH -N-CH 2  2  CH  3  OH ~  3  Figure 2.8: Chemical structure of CHO.  HO  OH  HO'  OH HO  OH  Figure 2.9: Chemical structure of INS. metabolism), acetylcholine (a neurotransmitter for which free choline is the immediate precursor) and free choline [46, 47, 48]. CHO shows the largest regional variation in concentration of all the brain metabolites [24] and it correlates with the degree of myelination: there is more choline in white matter than in grey [24, 29]. High-resolution proton spectroscopy of perchloric acid extracts of human biopsy material finds the same concentrations as in vivo results [26, 27, 28].  2.2.4  myo-Inositol  INS (figure 2.9) was first detected by ^ - N M R in brain extracts at 3.5 ppm (figure 2.6) in 1985 by Cerdan et al. [49]. It is not present in neurons and can be considered a glial cell marker [50]. INS exhibits a regional variation being lowest in white matter, slightly higher in cortical grey and highest in cerebellum [29, 51]. Because of its high degree of j coupling (section 2.1.3) and short T its signal decays rapidly after excitation and is difficult to measure. 2  INS plays a role in metabolism of membrane-bound inositol phospholipids [24] and in various neuronal signaling systems [24, 52]. In addition, it is an important osmolyte, particularly in cerebellum [24].  Chapter 2.  Background  17  O H N-C 2  H NH, O \ ^ II CH CH C 2  2  (a) glutamine  (b) glutamate  Figure 2.10: Chemical structure of GLN and GLU. 2.2.5  Glutamate and Glutamine  At 1.5T, GLU and GLN (figure 2.10) are difficult to distinguish from each other in the ^ - M R S spectrum because of their overlapping signals. One of the pathways in which GLU is made is from the precursor a-ketoglutarate in the citric acid cycle in mitochondria [37]; thus it is present in all cells. Because it is one of the major excitatory neurotransmitters in C N S GLU is found in higher concentrations in neurons than in glia [21]. Both in vivo [24, 29] and in vitro [28, 53, 54, 55] its concentration is found to be lower in white matter than grey matter, GLN is mostly present in astrocytes which contain GLN ligase and is higher in grey matter than white matter due to the larger population of astrocytes [29]. GLU is important in the liver for ammonia detoxification [37]. If the liver is compromised then ammonia detoxification can be conducted in astrocytes by the enzyme glutamine synthetase which incorporates ammonia and GLU to make GLN [56]. A n increase in GLU and GLN has been observed in patients with hepatic encephalopathy [57].  2.3  Materials and Methods  2.3.1  S u b j e c t Selection a n d V o x e l P l a c e m e n t  A l l M R I and M R S exams were conducted on a 1.5T G E Signa Horizon Echospeed M R Scanner with a quadrature bird-cage headcoil tuned to protons. Volunteers were selected from healthy normal adults ranging in age from 18-60 years old. Informed written consent was obtained before all examinations. A l l studies were conducted  Chapter 2.  Background  18  under the ethical approval of Vancouver Hospital Health Sciences Centre and the University of British Columbia. Depending on the experiment, the voxels were placed in occipital grey, parietal white or frontal white to maximize the grey or white contribution as seen on an image with negligible T i or T  2  weighting (proton density image). The white matter voxels were always placed in  the subject's dominant hemisphere based on handedness or the Modified Annette Handedness Questionnaire [58]. Figure 2.11 shows representative 7.2 mL voxels (19.3x19.3x20 mm ) selected for occipital 3  grey matter, parietal white matter and frontal white matter measurements.  In these proton  density images white matter appears darker than grey matter. From intensity histogram thresholding on the proton density images surrounding the voxel I determined that pure grey matter contributed to, on average, 78 ± 10% (range 63 to 91%) of the total H signal in the occipital grey matter voxel (the remaining approximately 15% was from X  occipital white matter and cerebrospinal fluid). The parietal white matter voxel had on average 96 ± 2% signal from white matter (range 92 to 99%). The frontal white matter voxel had 87 ± 2% of its signal from white matter (range 83 to 93%). The grey matter values are consistent with the literature, as Wang et al. [59] placed their grey matter voxel (20x 20 x 20mm ) in the 3  same region of the brain and found that gray matter made up 80% of the signal. In contrast, their white matter voxel, located in occipital white, contained 17% gray matter.  2.3.2  Spectral Fitting  Metabolite spectra were collected from phantoms (bottles containing solutions of single chemicals) and from humans in vivo.  In addition, the unsuppressed water signal was collected. Two  methods were used for finding the areas of the chemical signals. The first method was by numerical integration and the second, a template fitting method. The phantom spectra and the water signal had a very high S N R due to their concentration and had zero baseline. In contrast, the in vivo spectra had a low SNR, overlapping chemical  Chapter 2.  Background  (a) occipital grey  19  (b) parietal white  (c) frontal white  Figure 2.11: Representative voxels on proton density images. signals and a varying baseline. Numerical integration was conducted on the phantom and water spectra. However, to accurately measure the metabolite area in vivo, the spectrum had to be fit with templates (as discussed below) which simultaneously fit the overlapping chemical signals and the baseline.  O v e r v i e w of S p e c t r a l F i t t i n g M e t h o d s i n L i t e r a t u r e There are three different approaches to spectral fitting: integration of peaks; fitting to peaks with Lorentzian or Gaussian lineshapes; and prior knowledge fitting. The prior knowledge fitting method has a clear advantage over the other approaches, particularly at short T E when there is substantial signal overlap: the manual integration of peaks or the lineshape fits are unable to distinguish between the signals. Prior knowledge fitting has been conducted by Provencher [60] (commercially available as LCModel), Stanley et al. [61] and Bartha et al. [62]. The hardest problem in frequency domain fitting is determining the shape of the baseline. A n underestimated baseline could lead to overestimations in peak areas. Three methods of baseline fitting are common in the literature: manual determination of baseline in which a user chooses 'zero' points in the spectrum and a straight line, cubic spline or polynomial is fit  Chapter 2.  Background  20  through them [63]; automatic determination of baseline where 'zero' points are at predefined frequencies and a line is fit through them [51]; and automatic baseline fitting in which the baseline is fit with a smooth curve at the same time as the metabolites are fit (LCModel) [60]. The L C M o d e l baseline fitting is superior to the other methods since it fits those chemicals with low S N R and is less susceptible to fitting those resonances as the baseline. W i t h one exception [24] (who also used LCModel) all the studies discussed in this thesis have either used integration of peaks or lineshape fitting in the frequency domain with the first two methods of baseline determination.  P h a n t o m and Unsuppressed Water Spectral Fitting The phantom work discussed in chapter 4 and the unsuppressed water spectra discussed in chapter 4, 6 and 8 were analysed with in house software. The FIDS were automatically eddycurrent corrected [64] to compensate for the phase accumulated in the signal due to eddycurrents, Fourier transformed and manually phase-corrected. Signal areas were determined by numerical integration. The baseline offset (measured by finding the mean of the spectrum far from all peaks) was removed prior to measuring the signal areas.  In vivo S p e c t r a l F i t t i n g Metabolite areas in vivo were determined using L C M o d e l (version 5.2-1) [60], a user-independent fitting program that eddy-current corrects the spectrum with the unsuppressed water signal, automatically phases the spectrum and fits the spectrum with the sum of representative spectra (templates) of all the individual metabolites (figure 2.1). A n example of the L C M o d e l output can be seen in figure 2.6. L C M o d e l was designed to find the 'concentration' of a metabolite by fitting the spectrum with templates of known concentrations.  The values from the scanner tuning are used to  normalize the in vivo signal areas to the template areas. Because I required the signal areas at different T E and T R times, I altered the application  Chapter 2.  Background  21  of L C M o d e l in three significant ways. First, I collected templates at all of the T E values used in the experiments so that they would be influenced by the same j coupling modulation and unknown scanner effect as the in vivo spectra. Second, I normalized each of the templates to have unit area so that the in vivo metabolite area would not be convolved with the Ti or T  2  relaxation of the templates. Thirdly, I disabled the scanner tuning correction and used a water content measurement (section 6.2.2) in its place. L C M o d e l estimates the reliability of a 'concentration' measurement and returns a standard deviation for the concentration estimate of each metabolite. Standard deviations less than 20% are considered reliable [65]. The templates used in L C M o d e l were alanine, creatine ( C H and C H 3 peaks), choline, 2  G A B A , glucose, glutamine, glutamate, glycerophosphorylcholine, myo-inositol, lactate, N-AcetylThe creatine C H and C H 3 were fit  Aspartate, N-acetyl-aspartyl-glutamate and taurine.  2  independently of each other by two singlets (acetate). The templates were created from spectra of individual chemical solutions scanned with the same parameters as the in vivo spectra (which varied with experiment). The solutions had lOOmM concentration, were made within days of scanning from chemicals purchased from Sigma chemical and were titrated to p H 7.2. They were scanned at 21° C in a 300mL spherical glass flask at the centre of the headcoil.  2.3.3  Relaxation Fitting  M R S relaxation times of the metabolites were determined using a non-negative least squares (NNLS) algorithm [66] to fit the decay or recovery curves. For a mono-exponential fit, N N L S successively fits the data with a single component from a range of possible relaxation times and determines that relaxation time which minimizes the x misfit. For bi-exponential fits, N N L S 2  successively fits the data with all combinations of two relaxation times from a range of possible times. The combination of relaxation times is chosen to minimize x 2  The data in chapters  4 and 5 were fit with both the mono- and bi-exponential implementation of N N L S . For both T i and T  the ratio of the mono- to bi-exponential x  2  2  normalized by the degrees of freedom  Chapter 2.  Background  22  (F statistic) did not vary significantly from unity. Invoking Occam's Razor which states that given two solutions the simpler one is preferred, the mono-exponential fit was selected. More information on the exact application of N N L S is given i n chapters 4 and 5.  2.3.4  S t a t i s t i c a l Tests U s e d i n t h e S t u d i e s  Two statistical tests were used in this thesis: the Student's t test (t test) and the F test. A n F test determines whether the variances of two distributions are the same or different from the each other. Based on the results of the F test, the equal variance or unequal variance Student's t test is used. The Student's t test determines if the means of two samples are different. It is assumed that the data in the two samples arise from normal distributions. If the variances of the distributions are the same, then the equal variance t test can be used. Otherwise, the unequal variance t test is applied. When two datasets are acquired under the same conditions then the paired Student's t test can be used. For example, the paired t test was used to determine a difference in the means of T i times for NAA and CRE estimated from the same group of volunteers. The Student's t test returns a probability, p. Two-sided probabilities less than 0.05 (p<0.05) are considered significant. If 0.05<p<0.1, the two means show a trend towards being different. The means and standard deviations are often calculated over all volunteers. Sometimes the standard error is quoted in place of the standard deviation. The standard error is defined as the standard deviation divided by y/n, where n is the number of observations (or subjects).  2.4  O v e r v i e w of T e c h n i c a l C o n t r i b u t i o n s of T h e s i s  Existing techniques were used to acquire and analyse the data. The data was acquired with G E software from their P R O t o n Brain Exam ( P R O B E ) package. As listed in section 2.1.5, CHESS, S T E A M and P R E S S were used. No modifications were made of this existing software.  Chapter 2.  Background  23  L C M o d e l was purchased to measure the metabolite signal areas more precisely and accurately. I modified the application of the program to measure the exact quantities needed for measuring T i and T relaxation and absolute concentrations (section 2.3.2). 2  Modified-CPMG M R I methods had been developed to study water content and T relaxation 2  in 5mm thick slices of brain in vivo [66, 67]. The application of this technique to 20mm thick slices required modification in the data analysis. A s described in section 6.2.2 only the even echoes of the data were used to determine the T and signal at zero time. 2  2.5  Previous Publications of Results in Thesis  The work in chapters 3, 4, 5, 7 and 8 has been presented at posters in meetings. In reverse chronological order, the references are: 1. Brief, E . , Whittall, K . P., L i , D . K . B . and MacKay, A . L . Metabolite Tl in Multiple Sclerosis Lesions Differs from Normal. European Society for Magnetic Resonance in Medicine and Biology ( E S M R M B ) , 2000, Paris, France 2. Brief, E . , Whittall, K . P., L i , D . K . B . and MacKay, A . L . Absolute Quantification in MRS with an External Standard: There is no Invisible Water. E S M R M B , 2000, Paris, France 3. Brief, E . , Whittall, K . P., L i , D . K . B . and MacKay, A . L . Metabolite T Relaxation x  Differs Between and Within Regions in Normal Human Brain. E S M R M B , 2000, Paris, France 4. Brief, E . , Whittall, K . P., L i , D. K . B . and MacKay, A . L . In vivo Metabolite T Accurately 2  Measured with Large TE Range. E S M R M B , 2000, Paris, France 5. Brief, E . , Vernon-Wilkinson, R., Clement, J . , MacKay, A . , Scamvougeras, A . , Feldman, H., and Forster, B . H-MRS, MRI and Neuropsychological Testing of Patients with Traumatic l  Chapter 2.  Background  Brain Injury at Long Elapsed Time after Injury.  24  International Society for Magnetic  Resonance in Medicine (ISMRM), 2000, Denver, U S A 6. Brief, E . , Whittall, K . , MacKay, A . , and L i , D. Metabolite Tl Relaxation Differs Between and Within Regions in Normal Human Brain. I S M R M , 2000, Denver, U S A 7. Brief, E . , Whittall, K . , MacKay, A . , and L i , D . Precision of MRS Metabolite Peak Areas in Human Brain at Short TE. I S M R M , 1999, Philadelphia, U S A 8. Brief, E . , Whittall, K . , MacKay, A . , and L i , D.'Metabolite Tl Relaxation Differs Between and Within Regions in Normal Human Brain. I S M R M , 1999, Philadelphia, U S A 9. Brief, E . Multiple Sclerosis: What can we learn using Magnetic Resonance? Advanced Systems Institute, 1999, Vancouver, Canada 10. Brief, E . , Whittall, K . , MacKay, A . , and L i , D. Intra-Subject Reproducibility in Quantitative H-MRS.  1  Canada  Canadian Association of Medical Physics Annual Meeting, 1996, Vancouver,  Chapter 3  Reproducibility  As M R S is used increasingly in investigation of various brain diseases, it becomes very important to assess the inherent uncertainty in the measurement. B y measuring the reproducibility of the metabolite areas in healthy controls the precision can be calculated for each metabolite. The knowledge of precision can then be used in both study design and M R S interpretation to determine either the number of subjects which must be included in a study to see a specific metabolite concentration change, or to state a confidence interval for the differences seen between a set of patients and a set of controls. Standard deviations of other M R S parameters like metabolite relaxation times can be estimated by running simulations of 'noisy' data where the 'noise' is determined by the measurement precision for each metabolite. Most reproducibility studies have been conducted at long T E [68, 69, 70, 71] where the spectrum simplifies to the well-known singlets of CHO, CRE and NAA. One study conducted at TE=30ms [72] measured the precision for INS. To date, no studies have reported the reproducibility of measuring GLN or GLU at 1.5T. The first aim of the present work was to use short echo time spectroscopy (TE=30ms) and fit the spectrum with a template fitting method to assess the within-series, between-series and between-exam reproducibility of metabolite areas in healthy human brain in vivo for CHO, CR, CRE, GLN, GLU, INS, NAA and NAA+NAAG. The second aim was to provide a method for determining the confidence intervals for differences seen in concentrations of chemicals between patients and healthy volunteers.  25  Chapter 3.  3.1  Reproducibility  26  Methods  3.1.1  Subjects, Voxel Placement and Pulse Sequence  Single voxel spectra were acquired from in vivo healthy brain in 23 volunteers. M R spectra were recorded using a single-voxel S T E A M with TE=30ms, TR=1.5s, and TM=13.7ms, 128 acquisitions, 2048 complex points and a bandwidth of 2500Hz. For the within-series study the voxel was autoprescanned once and then three spectra were acquired in succession from the exact same location. The autoprescan automatically detected the water centre frequency (course adjustment), set the transmitter gain, conducted a localized shim on the voxel which optimized the magnetic field homogeneity, detected the water centre frequency (fine adjustment), set the receiver values and determined the flip angles for the water suppression pulses. Collectively, the autoprescan results are referred to as the scanner tuning. For the between-series study, the voxel was autoprescanned, one spectrum was acquired, and then the voxel was autoprescanned a second time and another spectrum was acquired. For the between-exams study, one volunteer was scanned seven times over the course of one year. The voxel location in the between-exam study was matched to previous films to ensure accuracy in its placement. For a visual representation of this study see figure 3.1.  3.1.2  Spectral Fitting and Reproducibility Statistics  The templates used in the L C M o d e l analysis (section 2.3.2) were scanned with S T E A M at TR=5s, TE=30 and TM=13.7ms to have the highest SNR. The TR=5s templates merely scale to fit the data collected at other T R values. In addition to metabolite areas, the area of the unsuppressed water was also measured by numerical integration as described in section 2.3.2. Voxels were placed either in occipital grey or parietal white (see figure 2.11 for location). The L C M o d e l signal areas were normalized to the unsuppressed water signal to cancel the multiplicative scaling factor introduced by scanner tuning. The normalization was particularily important in the between-series and between-exam studies because the scanner tuning differed  Chapter 3.  Reproducibility  27  Figure 3.1: Visual representation of the reproducibility studies.  (a) 1st s p e c t r u m  ( b )2 n d s p e c t r u m  (c) 3 r d spectrum  Figure 3.2: Three spectra from one volunteer for the within-series reproducibility study, for the spectra. The precision of the measurement was represented by the coefficient of variation (COV) where C O V = 100% x standard deviation/mean. For the within-series data three spectra were acquired from each of 19 volunteers. The mean and standard deviation of the normalized signal areas for each metabolite were calculated and the mean of the C O V over the volunteers gave the within-series reproducibility for each metabolite. Figure 3.2 shows three representative spectra from the within-series study. Two spectra were acquired from each of nine volunteers in the between-series study. Again,  Chapter 3. Reproducibility  (a) 1st spectrum  28  (b) 2 n d spectrum  Figure 3.3: Two spectra from one volunteer for the between-series reproducibility study. the mean and standard deviation of normalized signal area for each metabolite were calculated. The mean of the C O V over the volunteers gave the between-series reproducibility. Figure 3.3 shows two representative spectra from the between-series study. Finally, one volunteer was scanned seven times during one year. The normalized signal area was averaged over all the exams. The between-exam C O V was calculated from the mean signal area over the standard deviation for all exams. A l l seven spectra are shown in figure 3.4. For comparison, the L C M o d e l %SD (section 2.3.2) was averaged for each metabolite over all the spectra.  3.2 3.2.1  Results and Discussion Reproducibility Results  Table 3.1 provides a summary of the C O V s for each study. For all metabolites except C H O the between-exam C O V was slightly larger than the within-series and between-series C O V s . For all metabolites, the standard deviation of the mean C O V s for the within-series study was ~50% and for the between-series was ~70%. This uncertainty in C O V arose from the variation of C O V s between individual volunteers. For the between-exam study, the L C M o d e l %SD values were very close to the C O V s . This implies that users of L C M o d e l may be able to assess their uncertainty directly from the L C M o d e l output rather than conducting an exhaustive reproducibility study. The overlap of the L C M o d e l %SD and the reproducibility C O V s suggest that the limit of  Chapter 3.  Reproducibility  29  (a) 1st s p e c t r u m  ( b )2 n d s p e c t r u m  ( c )3 r d  spectrum  (d) 4 t h s p e c t r u m  (e)5th  spectrum  (f) 6 t h  spectrum  7th  spectrum  Figure 3.4: Seven spectra from one volunteer for the between-exam reproducibility study.  Chapter 3.  Reproducibility  30  metabolite area estimate precision is that of the L C M o d e l %SD. When discussing the C O V s below their units (%) will be assumed.  Metabolite  CHO CR CRE GLN GLU GLN+GLU INS NAA NAA+NAAG  Within-Series (%) (white n=9 grey n=10) 8 12 7 53 26 21 13 8 18  Between-Series (%) (white n=7 grey n=2) 3 9 5 49 32 31 15 5 12  Between-Exam (%) (all white n=7) 5 12 9 82 49 42 24 9 23  L C M o d e l %SD for Between-Exam (n=l, scanned 7 times) 9 13 9 333 45 38 16 11 25  Table 3.1: Average C O V s for within-series, between-series and between-exam reproducibility The between-series C O V s were slightly smaller than the within-series COVs. The spectra for the within-series study were collected within the context of another spectroscopy study which lasted one hour and the three spectra from each volunteer were acquired at random times between other spectroscopy acquisitions. The large variation in C O V s may be attributed to the fact that some volunteers may have moved between spectral acquisitions. In contrast, the between-series spectra were acquired within 15 minutes of each other and thus the lower C O V s may reflect a reduction in volunteer movement rather than a truly lower variation. The increase in the C O V for CHO in the within-series C O V compared with the C O V s from the between-series and between-exam (8, 3 and 5, respectively) was a result of the relative number of white or grey voxels in the studies. The signal area for CHO was smaller in grey voxels than white voxels and therefore, given the same standard deviation, the C O V would be greater in grey than white. The signal areas for the other metabolites are similar in grey and white matter so the C O V s should also be similar unless there is a change in standard deviation. The C O V s calculated separately for the within-series data led to differences in Cho  Chapter 3.  Reproducibility  31  (grey: C 0 V = 9 ; white: C 0 V = 6 ) and INS (grey: C 0 V = 7 ; white: COV=20).  3.2.2  Comparison with Literature  Brooks et al. [72] studied 10 volunteers using S T E A M TE=30ms, TR=2s in occipitopartietal white matter.  They conducted six successive acquisitions in one session, then again after  one hour and finally one month later.  The spectra were fitted with M R U I software using  Gaussian singlets for CHO, CRE, INS and NAA. They assessed a within-series and a betweenexam variability. The C O V s were calculated for each individual in each session (equivalent to the within-series C O V in this paper). The C O V s were as follows: CHO 5 (range: 2-11), CRE 4 (range: 1-10), INS 8 (range: 2-24) and NAA 3 (range: 0.2 - 7). Simmons et al. [68] scanned 8 volunteers with P R E S S TE=136ms, TR=2s in grey and white matter. They acquired five successive spectra in one session and scanned all eight subjects five times over three months. One subject was scanned 14 times over 2 years. They fit the spectra with a Levenberg-Marquardt fit using Lorentzian lines and normalized the metabolites to the water peak.  The C O V s were calculated for CHO, CRE and NAA as follows: within-  series (CHO 5, CRE 3, NAA 1), between-exam for all 8 volunteers (CHO 6, CRE 4, NAA 3) and for one volunteer (CHO 7, CRE 6, NAA 4). Due et al. [69] calculated C O V s in multiple regions in the brain using P R E S S spectra at TE=136ms and TR=6s. They collected spectra in 'sequential' and 'separate' runs for several regions (frontal, parietal, occipital, hippocampus and cerebellum). In general the sequential and separate runs had similar C O V s compared to my results. (Note: Due et al. list their standard deviations and means, here C O V s were calculated for comparison.) The C O V s for CHO, CRE and NAA were respectively 6, 2 and 1 in the different brain regions. Marshal et al. [70] found C O V s for within-series and between-exams on twelve volunteers with P R E S S TE=135ms, TR=1.6s in parietal white matter. They found that the C O V s within-series and between-exams were approximately the same: CHO 11, CRE 10 and NAA 7. They acquired the data with the same voxel size as other groups (20x 20x20mm ) but 3  with 64 acquisitions compared with 128 or 256. This reduction in acquisitions could lead to  Chapter 3.  Reproducibility  32  larger standard deviations. Finally, in a spectroscopic imaging study by Bertolino et al. [71] they investigated 10 volunteers who underwent two M R S I exams separated by 90 days. The TE=272ms, TR=2.2s data gave C O V s of 10-20 for metabolite ratios across brain structures. The C O V s presented in this chapter are larger than those stated in the literature. This could be due to the relative number of grey and white voxels in each study (as discussed above). The short T E and long T E studies [72, 68, 69] had the same C O V s for CHO, CRE and NAA. The compartively large C O V s presented in this chapter are likely due to the low number of spectra acquired for each volunteer compared to the higher number of spectra acquired in the other studies (since the standard deviation is proportional to  Using L C M o d e l , which  \/^fn.  distinguishes the overlapping chemicals at low T E , the previously unknown C O V s for GLN and GLU could be calculated.  3.2.3  Use of Reproducibility Results  Finding the confidence interval for a difference between two metabolite concentrations involves applying the following formulas and the C O V s listed in table 3.1 to any M R S study. The small sample (1 — a) 100% confidence interval for the difference between two means (\i\ and /J,2) with unknown but equal standard deviations is defined as [73]  (Xi - X ) 2  - t  a/2  S\ p  — + — < Pi pi  - H2 < {Xi - X ) + t / 2  a 2  '  ri2  S\ p  —  yni  + — n  (3.1)  2  where S i and x are the means of small independent samples of size n\ and n , respectively, from 2  2  approximate normal distributions, £ / is the value of the t distribution with v = ri\ + n — 2 Q  2  2  degrees of freedom, leaving area of a/2 to the right and s  p  is the pooled standard deviation  given by  V  n\  +  n  2  —  2  In terms of the variables presented in this paper, Sj is S i X C O V / 1 0 0 . As an example, if the NAA concentration were compared between a group of controls (ni=10, x\ NAA = lOmM and COV=9) and ten patients (n2=10,COV=9), the difference in true mean  Chapter 3.  Reproducibility  33  N A A concentrations (n\ — (j, ) for a range of possible x  2  2  would follow table 3.2 for upper and  lower bounds for the 99.9% confidence interval.  X2  X\ - x  2  lower bound on p,i - fi 0.87 1.87 2.87 3.87 4.87 5.87 2  10. 10. 10. 10. 10. 10.  9. 8. 7. 6. 5. 4.  1. 2. 3. 4. 5. 6.  upper bound Ml - M2 1.13 2.13 3.13 4.13 5.13 6.13  Table 3.2: Upper and lower bounds in N A A concentration for 99.9% confidence interval  3.2.4  Improving Precision in M R S Experiments  There are many factors which contribute to the precision of the M R S experiment: scanner tuning, shimming, gradient performance, field strength, signal averaging, subject motion, baseline fitting, and metabolite area fitting. The scanning tuning was optimized for each volunteer.  Because the uncertainty in the  between-series study (studying the effect of tuning) was not significantly larger than the withinseries study (independent of tuning) we can conclude that further improvements to the optimization of the 90° pulse would not drastically improve the overall precision of the measurement. If the result of the shim was a linewidth greater than ~7Hz, the spectrum was not collected. (Note: using the G E Signa scanner, the F W H M stated on the scanner console should be ~2Hz.) Thus, there was an exclusion criterion before data collection. The physical limit to the linewidth is due to the T 2 of the water. The minimum linewidth is l/nT , where T2=0.08s for water. 2  •Thus the best expected linewidth is ~4Hz. Better shimming with non-linear shims may improve the linewidth slightly, but it cannot improve it substantially. To improve gradient performance, better gradients would have to be installed. Improved  Chapter 3.  Reproducibility  34  gradients would lead to less eddy current effects and would result in improved water suppression. This would lead to fewer baseline problems and, as a result, better metabolite area fits. Precision of metabolite area fitting would be improved at higher field strength because of the intrinsically higher signal to noise (for spectra collected with the same parameters) and because of less chemical signal overlap. To increase the SNR, more signal averages can be acquired. This may be impractical in the clinical setting because it would further increase the time of the patient exam. The subjects were positioned into the M R I scanner by experienced technologists. Velcro straps were placed across the forehead and chin, and extra cushions were tucked around the head to prevent subject movement. Improvements to securing the head can include using more straps, or moulded plates around the head. However, the voxels investigated in these studies are approximately 20 x 20 x 20mm . 3  Subject motion on the sub-millimetre range should not  drastically affect the spectrum. Baseline and metabolite area fitting have been optimized using L C M o d e l .  3.3  Summary  This chapter addresses the question of reproducibility within-series, between-series and betweenexams. The between-exam reproducibility is slightly larger than the others since it accounts for both scanner tuning variations and repositioning errors. The L C M o d e l %SD was found to be in the range of the estimated reproducibility C O V s which demonstrates a limit to the precision of the measurements.  The C O V for between-exam reproducibility should be used  for comparing patient and control groups and for serial studies. A technique is presented for determining statistical significances of concentration differences in a clinical setting given the C O V s measured. The C O V s can be used to determine the precision and accuracy of T i and T2 estimates with noise simulations, as seen in chapters 4 and 5.  Chapter 4 T i Relaxation  Most M R S I studies, those which acquire multiple spatially resolved voxels, have used T R values between 1.0 and 3.0s [12] where metabolite signal areas are reduced by T i relaxation. Single voxel studies have been acquired at many T R values, most commonly between 1.5 and 6.0s. Ti-weighting complicates comparison of results acquired at different T R times and could be misinterpreted as changes in metabolite concentration. T i times depend on the local environment of the protons (section A.1.4). One would expect the amplitudes and frequencies of microscopic molecular motions involving the protons on the metabolites to depend upon intra- and inter-molecular structural and geometric factors. Since M R S is sensitive to a variety of metabolites in various regions of the brain, it is conceivable that the T i of metabolites could be different from each other and that the T i of the same metabolites could differ regionally. Early investigations of T i relaxation of major brain metabolites provided T i corrections to concentration estimates [51, 74, 75, 76, 77, 78, 79, 80]. Some studies reported that there were no significant differences in T i between metabolites or between the same metabolite in different brain regions [51, 78]; other studies made no comment on T i differences either within tissues or regionally. In most cases, the saturation recovery curves (section 2.1.5) were measured at only two T R values. Assuming that there was only one T i relaxation causing the saturation recovery, mathematically two unknowns would be measured: the signal amplitude at t=oo and the T i time. Two T R values are sufficient to measure these unknowns, but given that each signal area measurement has an error (chapter 3) the T i determination may be suspect. Three studies using more than 2 T R values were Frahm et al. [78] (3 T R ) , Narayana et al. [75] (7  35  Chapter 4. T i Relaxation  36  T R ) , Knight-Scott et al. [81] (6-11 T R ) . The aim of the present work was: 1. To assess the precision of T i estimates from saturation recovery curves comprised of varying numbers of T R points. 2. To accurately measure metabolite T i times in parietal white, frontal white and occipital grey matter in normal human brain. 3. To determine whether the same metabolites from different regions in normal brain have different T i times. 4. To determine whether different metabolites in the same region in normal brain have different T i times. 5. To compare in vivo metabolite T i times with those from metabolites in solution.  4.1  Methods  There were three sections for this study. The in vivo work reports on the T i times found in three brain regions in healthy volunteers, in vitro work measures T i as a function of temperature for each of the metabolites in solutions of lOOmM, and the simulation work demonstrates why the data collection described here is superior to previous methods.  4.1.1  S u b j e c t s , V o x e l P l a c e m e n t a n d P u l s e Sequence  Single voxel spectra were acquired from occipital grey (n=10, 5 male/5 female, mean age 28 ± 9 years), parietal white (n=10, 6 male/4 female, mean age 31 ± 13 years) and frontal white (n=10, 6 male/4 female, age 31 ± 8 years). Figure 2.11 shows the voxels chosen for occipital grey, parietal white and frontal white matter measurements.  Chapter 4. Ti  Relaxation  37  The spectra were recorded using a single-voxel S T E A M localization sequence.  The voxel  was prescanned for the first spectrum only and the tuning was kept constant for all subsequent spectra on the same volunteer. Seven spectra were collected at TE=30ms, TM=13.7ms and TR=547, 751, 1200, 1500, 2500, 3500, and 5000ms. The number of acquisitions were 512, 512, 256, 256, 128, 128, and 96, respectively. A l l spectra contained 2048 complex points except for one having 1024 points (at TR=751ms) and another with 512 points (at TR=547ms). Figure 4.1.1 shows the spectra from one volunteer stacked according to increasing T R . One volunteer was scanned with 12 T R times (TR=547, 751, 1200, 1500, 2500, 3500, 5000, 6000, 7000, 8000, 9000, 10000ms) to determine the exponential nature of the fits. As described in section 2.3.3 the data were fit with the assumptions of mono- or bi-exponential nature. A n F-statistic of the ratio of their variances (normalized to their degrees of freedom) verified the assumption of mono-exponential recovery.  4.1.2  Choice of T R Range  Because of the time to conduct localization and water suppression, the minimum T R is ~0.5s for acquiring 512 complex points.  For 1024 complex points, the minimum T R increases to  ~0.75s. We chose a maximum T R of 5s since it was ~ 3 T i and because the spectrum can be acquired in ~10 minutes. The entire Ti exam is 70 minutes long (compared with those in the literature which are ~20 minutes); if a longer T R point was acquired it would significantly increase the time for the entire exam. The intermediate T R values followed a geometric-like echo sampling.  4.1.3  Spectral Fitting and T i Analysis  The in vivo brain spectra at all T R times were fitted with L C M o d e l (section 2.3.2) using the templates collected at TE=30, TM=13.7 and TR5s. The metabolites for which the Ti values will be reported are the C H 2 and the C H 3 peak of creatine (CR and CRE, respectively), N-Acetyl-Aspartate (NAA), myo-inositol (INS) and choline + G P C (CHO).  The signals from  Chapter 4. T i Relaxation  38  5000 ms  3500 ms  2500 ms  1500 ms  200 ms  750 ms 530 ms Figure 4.1: Fitted spectra stacked according to T R .  Chapter 4. T i Relaxation  39  alanine, G A B A , glucose, glutamine, glutamate and taurine were too noisy to provide accurate T i fits. The T i of each metabolite was determined for every volunteer using a non-negative least squares algorithm [66] (see section 2.3.3) solving A  where  T  R  =  Aoo  *  (1  -  e  - ( T R - 3 E  +  T M ) /  T  l  )  (  4  1  )  is the signal area at an infinite T R and ATR is the measured signal area. Where the  L C M o d e l %SD exceeded 20% (section 2.3.2) the metabolite signal area was excluded from the T i recovery curve. If a curve had fewer than 5 T R points the T i was not determined. The T j mean and standard deviation over all volunteers were calculated for each metabolite in all tissues. In each tissue, either a paired or an unpaired Student's t test determined if the metabolites had different T i times. For each metabolite both unequal and equal variance t tests determined the probability that the T i was the same in the three different tissues. A n F test determined whether to use the equal or unequal variance t tests. Two-sided probabilities less than 0.05 were considered significant. More information on the statistical tests used is given in section 2.3.4.  4.1.4  Temperature Dependence of T i i n M e t a b o l i t e Solutions  T i measurements of metabolites in solution were performed using the same parameters as in vivo except with one quarter the number of averages to save time since the concentrations were an order of magnitude larger than in vivo. The experiments were done at three temperatures, 7, 21 and 37°C at p H 7.2. The metabolite areas at each T R were found by integration as described in section 2.3.2. The T i of each metabolite was calculated with equation 4.1.  4.1.5  Simulations of Saturation Recovery Curves  Simulations were conducted to determine the variance of T i for saturation recovery curves with two, three and seven T R times. A synthetic saturation recovery curve was generated for  Chapter 4. Ti Relaxation  40  Figure 4.2: A visual representation of the simulation used to calculate noisy IT times Ti=1.0s. Random noise was added with standard deviations of 5, 10, 15 and 20% based on the coefficient of variation for each metabolite as measured in the reproducibility study (chapter 3). The zero mean noise for each point was determined by a normal (Gaussian) random number generator multiplied by the standard deviation. T i was calculated by a mono-exponential fit to each of 1000 synthetic saturation recovery curves corrupted by noise. The mean and standard deviation of T j were calculated. A visual representation is given of the simulation in figure 4.2. The saturation recovery curves were composed of time points to conform to our data (7TR: 547, 751, 1200, 1500, 2500, 3500, and 5000ms), the data of Frahm et al. [78] (3TR: 1500, 3000 and 6000ms) and that of Kreis et al. [51](2TR: 1500 and 5000ms).  4.2 4.2.1  Results T i Results and Statistics  Table 4.1 lists the T i means and standard errors for the metabolites in occipital grey, parietal, frontal white matter and in solution (templates) at 37°C. Each metabolite T i was averaged over 10 volunteers, except for occipital INS (n=9), parietal INS (n=8) and frontal INS (n=7) due to the exclusion criteria of excluding points with %SD>20%. The 12 T R dataset verified that the fits were well modelled with a single exponential recovery curve as explained in section 2.3.2 (see figure 4.4 for fits). Figure 4.3 shows the typical T i fits using the mean value of the signal  Chapter 4. T\  Relaxation  41  NAA 0 12 3 4 5 TR (s)  0 12 3 4 5 TR (s)  Figure 4.3: T i fits to the average signal area for all parietal white matter volunteers.  1.720  4.03  4.35  0.988  2.25  2.43  0.256  0.47  0.51  0 2 4 6 810 TR ( s )  0 2 4 6 810 TR (s)  r,  Ins  0 2 4 6 810 TR (s)  0 2 4 6 810 TR ( s )  Figure 4.4: Single exponential recovery curves fit to 12 T R spectra areas from parietal white matter over all volunteers.  Metabolite T i Occipital T i Parietal T i Frontal T i Phantom  INS  CHO  NAA  CRE  CR  0.94 (0.09) 1.17 (0.21) 1.42 (0.13) 1.47  1.01 (0.05) 1.19 (0.03) 1.39 (0.07) 2.71  1.22 (0.07) 1.35 (0.06) 1.51 (0.07) 1.57  1.34 (0.05) 1.50 (0.05) 1.79 (0.10) 2.25  0.95 (0.07) 1.27 (0.20)  —  1.58  H 0 1.10 (0.01) 0.77 (0.04) 0.76 (0.02) 2  —  Table 4.1: Means and standard errors of metabolite T i (s) in vivo and phantom at 37°C. As measured by an F test, the variances of T i in occipital grey and parietal white were not significantly different from each other, whereas many metabolites in frontal white matter had significantly different variances from the other tissues. When reporting comparisons between frontal white and the other tissues, the unequal variance t test was used, however, for occipital grey compared to parietal white the equal variance t test was used.  Chapter 4. T i Relaxation  42  The paired t test was used to compare N A A , C R E and C H O to each other because all tissues had n=10 volunteers for each metabolite. Due to the exclusion criteria, INS had fewer than 10 volunteers in each tissue and therefore the unpaired t test was used for all calculations involving INS.  Within each tissue, the metabolites' T i times followed the same ascending order: INS < C H O < N A A < C R E . For occipital grey matter T i , INS was signficantly lower than N A A and C R E with p<0.03 and p<0.002, respectively. C H O was significantly lower than N A A and C R E , p<0.001 in both cases. A trend (as defined by 0.1>p>0.05) was noted for N A A and C R E (p<0.1). In parietal white matter the T i of C H O was significantly lower than that of N A A and C R E with p<0.03 and p<0.00004, respectively. A trend was seen for N A A compared to C R E (p<0.07). For frontal white matter T i times, C H O was lower than N A A and C R E with p<0.03 and p<0.001, respectively. For the same metabolites in different tissues, the T i times increased from occipital grey < parietal white < frontal white matter.  This is most dramatic in C H O , where the T i in  occipital grey was significantly lower than that of parietal white (p<0.008), parietal white was lower than frontal white (p<0.03), and occipital grey was lower than frontal white (p<0.0004). The ranking could also be seen in C R E , for which occipital grey was lower than parietal white (p<0.03), parietal white was lower than frontal white (p< 0.01) and occipital grey was lower than frontal white (p< 0.0005). Similarly for N A A , the occipital grey T i was shorter than frontal white (p<0.009). In addition, for occipital grey matter the T i of C R was significantly shorter than that of C R E (p<0.0001). The T i of water followed the opposite regional trend to the metabolites (table 4.1)  4.2.2  T e m p e r a t u r e D e p e n d e n c e of T i i n M e t a b o l i t e P h a n t o m s  T i times of metabolites in phantoms differed from each other and increased with temperature (figure 4.2.2).  The observation verifies that the metabolites are randomly tumbling in the  Chapter 4. T i Relaxation  43  o N A A (CH3) • Ins (CH)2 A Ins (CH)4 o C r e (CH2) x Cre (CH3) o C h o (CH3)3  31  32  33  34  35  36  1/T(1/K)* 10 5 A  Figure 4.5: Arrhenius Plot: logarithm of T i plotted against 1/T (1/K) for templates fast motion limit where  UJT  C  1 (section A.1.4) and following from this, in section 4.2.5 an  interpretation can be postulated in terms of the sources of the correlation times. The T i times of C R and C R E differed whereas those of the two main peaks of INS did not. The T i times for every metabolite were higher in solution at 37° C (body temperature) than in vivo. In phantoms compared to in vivo, the choline had the longest T i instead of being the second shortest. The T i times in phantoms had the following order: INS < N A A < C R E < C H O . This corresponds to the descending order of molecular weights for each metabolite: 180.2, 175.1, 131.1 and 121.1 g/mol, respectively.  4.2.3  Simulations  For all simulated data the standard deviation of the measured T i doubled with each additional 5% of noise. Furthermore, the standard deviation of the 3 T R data was roughly double that of the 7 T R data, the standard deviation of the 2 T R data was larger still (figure 4.6). Another representation of the data can be seen in figure 4.7 where the simulated fit (amplitude and T i ) are shown. The simulated amplitude (the signal area at TR=oo) is plotted against its T i for all three T R realizations with the true amplitude being unity, the true Ti=1.4s and 15% noise. The maximum T i in the application of N N L S was 8s. It is clear from the plots that the 2 T R  Chapter 4. T\  Relaxation  44  Percentage Noise  Figure 4.6: Simulated T i and standard deviation where true T i = l s .  0  (a) 2 T R  2 4 6 S'r-ulatec T1 "me (s) (b) 3 T R  2 4 6 Sinulatec Tl ~me (s) (c) 7 T R  Figure 4.7: Signal at TR=oo against T i for simulations with 15% noise, true T i = 1.4s and true amplitude=l. and 3 T R fits have more spread over T i than the 7 T R fit since the 7 T R does not come close to the maximum simulated T i . Given the magnitude of the standard deviations, to see subtle T i changes one must acquire more T R points or increase the number of subjects. At noise levels of >10% the estimates of T i were artificially high for all T i simulations, but particularly high for the 2 or 3 T R values. Because of this bias, increasing the number of subjects would not improve the accuracy of the measurement. Table 4.2 lists the %SD of the spectral fit (as calculated by L C M o d e l , section 2.3.2) averaged over all subjects for each metabolite in each tissue (provided that the metabolite passed the  Chapter 4. T\  Relaxation  45  exclusion criteria listed earlier). As a result of the large %SD there were too few points meeting  Metabolite T I Occipital T i Parietal T i Frontal  INS 13 15 14  CHO 14 9 10  NAA 10 10 13  CRE C R 8 15 9 15 10 —  Table 4.2: L C M o d e l %SD Averaged over all Volunteers the exclusion criteria to measure T i for C R in frontal white matter. Many of the standard deviations in this study are ~10%. According to figure 4.6, at this noise level the 7 T R data have less bias than the 2 or 3 T R data and therefore can better characterize the T i . Seven T R values afforded a more complete sampling of the T i recovery curve especially in the low T R (< 1500ms) range. Since the curve is changing most dramatically in that range, an unambiguous fit of T i should include those values. 4.2.4  B i o l o g i c a l V a r i a t i o n C o m p a r e d w i t h D a t a N o i s e for T i  The simulations for the 7 T R data at 5%, 10% and 15% noise demonstrated that the standard deviation of the T i estimates increased from 11% to 20% to 35%, respectively. The range in T i times over the volunteers is less, than that expected from the noise simulations. Thus, biological variation in T i is less than the experimental uncertainties.  4.2.5  S i m p l e T h e o r y for T M e c h a n i s m x  From the description of T i using spectral density functions, assuming rotational tumbling and assuming a single correlation time for the motions which lead to T i relaxation (section A . 1.4)  TT  K  I  +  +  i +  v  (  4  '  2  )  where r is the correlation time between field fluctuations sensed by the nucleus, and u> is the c  0  Larmor frequency. Because the curves in the Arrhenius plot shown in figure 4.2.2 had negative  Chapter 4. T i  Relaxation  46  slopes, the nuclei were tumbling rapidly in the weak collision limit such that  UT 0  C  <§; 1 which  leads to: ~  «  (4.3)  T. C  In vitro, the metabolites engage in rotational tumbling for which a correlation time may be approximated by the Stokes-Einstein relation: 4TT77 R  ,  3  J  = = ~WF'  <'>  T  4 4  where n is the microviscosity of the solvent in which the molecule is tumbling, k is the Boltzmann constant, T is the absolute temperature and R is the molecular radius. Assuming that the molecules can be modelled as tumbling spheres and the density of all molecules is the same, then R  3  is proportional to the molecular weight, M , of the molecules:  -5J-i  cx M .  (4.5)  Thus, an increase in molecular weight leads to a decrease in T i . This simple description is consistent with the trend that metabolites in phantoms with the highest molecular weight have the longest T i times. The order of T i times changes in vivo. The T i of C H O was ranked from having the longest T i to having the second shortest. This could be explained by the different chemicals which make up the choline signal (section 2.2.3). The ranking of phosphorylcholine (162.7 g/mol) based on molecular weight correctly predicts that the T i would be closer to that of INS. The significant difference between the T i times of C R and C R E calls into question the simplicity of describing T i as a result of only one relaxation mechanism. There are internal motions in the molecules which can contribute to relaxation.  For instance, the methylene  protons of creatine are in a relatively fixed position on the molecule whereas the methyl protons are rotating about the common C - C axis, the methyl rotor. In effect this rapid motion causes a reduction in the correlation time r and therefore increases the T i , which is what has been c  observed (table 4.1).  Investigation of T i mechanisms is an important topic and may help  Chapter 4. T\  Relaxation  47  elucidate the molecular environment in vivo. Unfortunately, a full study is beyond the scope of this thesis. Pragmatically, the fact that C R E and C R have different T i times has implications for the use of template fitting programs. The T i of C R E is longer than that C R in phantoms and in vivo and the T i times in phantoms are longer than those in vivo. Because the peaks exhibit different T i times, they will have different Ti-weightings. The template for creatine should be composed of two peaks which fit the CH2 and C H 3 signals independently of each other. If the template is the full creatine spectrum then signal area estimation errors are more likely to occur because the in vivo peaks will have different areas relative to each other than the template peaks. There are two possible explanations for the increase of all metabolite T i times from occipital grey to parietal white to frontal white. Both explanations are related to the local prevalence of paramagnetic materials: one involves the iron content of different tissues and the other considers cerebral blood volume. It is well known that iron concentrations vary throughout the brain [82] with deep grey matter structures having the highest concentration and white matter having the lowest. The effect of the proximity to iron on a proton is that the proton experiences a local fluctuating magnetic field at the Larmor frequency, thereby creating a potent T i relaxation mechanism. It would be expected that a decrease in iron concentration would lead to an increase in T i times. This is indeed what is seen, as metabolites in grey matter have lower T i times than in white matter. T i studies were conducted in the iron-rich putamen to verify this hypothesis but the data were too noisy (due to a reduced voxel size) to provide accurate fits. Cerebral blood volume in grey matter is higher than that in white matter. It is possible that the differences seen in T i times between grey and white are, in part, due to the increased amount of oxygen and/or hemoglobin in the voxel. Similar to the postulate on the effect of iron in vivo, an increase deoxygenated haemoglobin would cause fluctuating magnetic fields which would reduce T i . Cerebral blood oxygenation has an important effect on T2*. This effect has been exploited by functional M R I techniques [83].  Chapter 4. T\  4.2.6  Relaxation  48  Comparison w i t h Literature Values  By fitting T i recovery curves to results from only two T R times, previously published studies lacked the necessary resolution to see T i differences within and between regions. For different metabolites, the data of Frahm et al. [78], which used 3 T R times, followed the same ranking of T i times as our data in the occipital area (voxel size: 64mL) and thalamus (27mL). The differences between T i times did not reach statistical significance and Frahm et al. concluded that the T i times did not vary from each other, either regionally or within the tissues. Narayana et al. [75] used the same range of T R times to this study. The metabolite T i times from their 27mL voxel also exhibited the same ranking as our data. The authors, however, did not comment on the T i times.  4.2.7  Consequences o f O m i t t i n g T i C o r r e c t i o n s  CRE has the longest T i of all metabolites and exhibits significant variations between regions. Taking metabolite ratios to CRE at short T R leads to significant errors in signal area estimation within and between tissues. Figure 4.8 was generated by assuming T R = l s and taking the ratio of unit metabolite signal areas with Ti-weighting to Ti-weighted occipital creatine: (]_ _ e - i / T i m e t ) S  where S  m e t  m  e  t  =  (1 _ g - l / T j o c c i p i t a l C R E )  is the plotted signal and T i  m e  t are from table 4.1.  (  4  6  )  Some metabolites may be  overestimated by over 25% (in occipital grey) where others will be underestimated by as much as 35%. Within each tissue, the metabolite signal areas are in error by at least 10%. Figure 4.8 demonstrates that the common practice of conducting Ti-corrections with only one T i value can lead to signficant errors in concentration estimation. Any attempt to quantify M R S data must incorporate the Ti-weightings of each metabolite in each tissue. The alternative is to use long T R . W i t h TR=5s, the ranges for signal over- and under-estimates reduce to 2% and 4%.  Chapter 4. T i Relaxation  49  in  I] Cre • NAA • Cho Sins  Occipital Grey Parietal White Frontal White  Figure 4.8: T i weighted signal area ratios for each metabolite to CRE in occipital grey assuming T R = l s and unit concentration for each metabolite. 4.3  Summary  We have demonstrated that the T i of metabolites in occipital grey are significantly shorter than corresponding metabolite T i times in parietal white matter and frontal white matter. Metabolite T i times in single tissue differ and follow a ranking consistent with the physical understanding of a simple relaxation mechanism. The in vivo findings are supported by the phantom work. Due to voxel size, our grey and white matter samples were not pure. Correction to partial volume averaging should only strengthen our results, given that differences were found between each tissue. Simulations were conducted to determine how sensitive T i measurements are to number of T R acquisitions and to noise. The T i differences measured could not have been seen by most other investigators because of their choice of T R values. Given the sensitivity that metabolite T i times have to their environment, investigations should be conducted in diseased tissue, for instance multiple sclerosis lesions, to see if there are any further changes to T i . This may be fruitful in understanding local environments.  Chapter 5  T  1  2  Relaxation  H - M R S is conducted at either short T E (10ms to 30ms) with minimal T2-weighting or long  T E (135ms to 270ms) with greater T2-weighting. The short T E spectra have the advantage of greater S N R and reveal more metabolites than the long T E spectra. The long T E spectra, however, are easier to analyse because there is no metabolite signal area overlap, fewer baseline problems and no j coupling. Figure 5.1 plots a short T E (30ms) spectrum and a long T E (200ms) spectrum from the same voxel demonstrating the simplicity yet reduced information content of the long T E spectrum (note that these spectra are not scaled to each other). Long T E spectra, with their more severe T -weighting, require accurate T 2 corrections to 2  estimate the metabolite signal at TE=0ms in order to estimate absolute concentrations. They are highly susceptible to changes in T2 which may occur in diseased tissue. T2 times of metabolites are measured by collecting multiple spectra over a range of T E . The T2 is calculated from the change in signal area over T E times (section 2.1.5). Assuming a mono-exponential decay, the two unknown parameters in the fit are the T2 and the signal area at TE=0ms. Spectra collected at two T E times are sufficient for fitting the curve, but due to  (a) T E 30ms  (b) T E 200ms  Figure 5.1: Comparison of TE30ms and TE200ms spectra from healthy occipital grey matter.  50  Chapter 5. T  2  Relaxation  51  error in the signal area estimation, there could be severe errors in measuring T with very few 2  T E times (analagous to T i in chapter 4). Previous experiments in the early 1990s measured the T times of N A A , C R E and C H O 2  [51, 74, 75, 78, 84, 63, 85] finding large ranges in their estimated T  2  values: from 299ms to  483ms for N A A [84, 51], from 180ms to 252ms for C R E [85, 74, 63] and from 248ms to 401ms for CHO  [74, 51].  A l l of these T  2  experiments were fundamentally flawed: for all but one experiment the  longest T E was only 270ms, and the remaining experiment [75] had a maximum T E of 100ms. The decay curve for N A A (which, by the literature, has a minimum T  2  of 300ms) would still  have 37% (1/e) of its original signal (from equation 5.1). The decay curve, therefore, would only have sampled a 63% drop in signal area. For better sensitivity to the decay curve the maximum T E should be greater than the T . Augmenting the difficulty in the correct fitting 2  of a truncated decay curve is the noise in the data points (chapter 3). Spectra were collected at short T E (~30ms) for the initial points in the decay curve. In the early studies the spectra were fit either by Gaussian peaks or determined by numerical integration. A t short T E , though, the spectrum is complicated by metabolite signal overlap, varying baseline and j coupling.  Metabolite areas found with Gaussian fits or numerical  integration could be measured to be artificially elevated due to the overlapping resonances and incorrect baseline determination. There were no T  2  studies on normal brain after the early 1990s. The few T  2  subsequent  papers investigating T in diseased tissue, and their experiments were modelled after the earlier 2  publications. Investigators who work at long T E most often T correct with the values from a 2  6 T E method by Kreis et al. [51]. To more accurately and precisely measure T in vivo, the spectra have to be fit with a more 2  robust method (like LCModel) at short T E times and more spectra should be collected over a longer T E range. To expand the small range over which the decay curve was sampled, the T  2  experiments  Chapter 5. T  Relaxation  2  52  conducted here had a maximum T E of 800ms. Eight spectra were collected in that range. The spectra were fit by L C M o d e l (section 2.3.2) which fits to the complete spectrum better than earlier fitting approaches. The decay curves were generated from the singlets of N A A at ~2.0ppm, C R E at ~3.0ppm and C H O at ~3.2ppm in occipital grey and partietal white matter in vivo. The aims of the work were (as in chapter 4): 1. To accurately measure metabolite T times in parietal white and occipital grey matter in 2  normal human brain. 2. To determine whether the same metabolites from different regions in normal brain have different T  2  times.  3. To determine whether different metabolites in the same region in normal brain have different T2 times. 4. To assess the precision of T2 estimates from decay curves comprised of varying numbers • and ranges of T E points.  5.1  Methods  Similar to the T i study (chapter 4) both in vivo work and simulations were conducted.  5.1.1  Subjects, V o x e l P l a c e m e n t a n d P u l s e Sequence  Single voxel spectra were acquired from occipital grey (n=10, 4 male/6 female, mean age 28 ± 9 years) and parietal white (n=10, 6 male/4 female, mean age 31 ± 13 years). Figure 2.11 shows representative 7.2 mL voxels (19.3x19.3x20 mm ) selected for occipital grey and parietal 3  white matter measurements. The M R spectra were recorded using a single-voxel P R E S S localization sequence. The voxel was prescanned for the first spectrum only and the tuning was kept constant for all subsequent spectra on the same volunteer. Eight spectra were collected at TR=2000ms, and T E = 30, 60,  Chapter 5. T  2  Relaxation  53  100, 150, 200, 400, 600 and 800ms. Eight fitted spectra are plotted in figure 5.2 to demonstrate the variation in signal over the T E range. The number of acquisitions was 128 for spectra acquired at all T E times except for 256 for T E 400ms and 512 for T E 600 and 800ms. The spectral width was 2500Hz and 2048 complex points were acquired for each spectrum.  5.1.2  Choice of T E Range  Because of the time to conduct localization and water suppression, at TR=2s the maximum T E is ~800ms for acquiring 2048 complex points. We chose a minimum TE=30ms so that the gradient shapes did not have to change (section 2.1.5) The entire T exam is ~90 minutes 2  long (compared with those in the literature which are ~20 minutes); if a longer T E point was acquired the T R would have to be increased for all spectral acquistions which would significantly increase the time for the entire exam. The intermediate T E values followed an almost linear echo sampling.  5.1.3  Spectral Fitting and T  2  Analysis  The in vivo brain spectra were fitted with L C M o d e l (section 2.3.2) using the templates collected at the same T E as the spectrum so that the j coupling modulation on the spectrum was the same. The late T E spectra (400, 600, and 800ms) were fit with the TE200ms templates because the signals from the coupled peaks were gone and the remaining signal consisted of singlets only. In the T i study (chapter 4) one template was used (TE=30ms, TM=13.7ms and TR=5s) to fit all the spectra. This was effective because the different T R spectra merely scaled in size to each other. The different T E spectra, by contrast, do not scale to each other because the individual metabolite signal areas are modulated by j coupling. Each T E template can fit its corresponding T E spectrum, but the templates themselves have relaxed with T are scanned. B y normalizing the templates to have unit area, the T  2  2  when they  times of the templates  themselves could be ignored. For each template, the fractional signal area of the singlet peak was integrated. The metabolites for which the T  2  values are reported are the methyl group  Chapter 5. T  2  Relaxation  Figure 5.2: Fitted spectra stacked according to T E .  54  Chapter 5. T  2  Relaxation  55  of creatine (CRE), the methyl group of N-Acetyl-Aspartate (NAA), and the (0113)3 group of choline C H O because they are the only signals still present in the spectrum at late echo time (TE=800ms). The T 2 of each metabolite group was determined for every volunteer using a non-negative least squares algorithm [66] (section 2.3.3) solving ATE  -  A  0  e  ~  T E  / 2 T  (5.1)  where A is the singlet signal area at TE=0ms and A T E is the measured singlet signal area. Q  Where the L C M o d e l %SD exceeded 20% (section 2.3.2) the metabolite signal area was excluded from the T2 decay curve. If a curve had fewer than 3 acceptable T E points the T  2  was not determined. In practice the curves were composed of 5-8 data points. The  mean T2 and its standard deviation over the population were calculated for each  metabolite in all tissues.  5.1.4  C o u p l e d Spins  The singlet peaks of each of the metabolites were examined because their decay was completely due to T2 (i.e. there was no j coupling). To separate the singlet contribution from the rest of the template, each template was numerically integrated (section 2.3.2) and the fractional area of the singlet peak was measured for each template at each T E . After the spectrum was fit, the L C M o d e l metabolite area was multiplied by the appropriate 'fractional signal area'. The  signals from coupled spins are modulated by j coupling and over a range of T E their  areas vary with j coupling and T2 relaxation. As a result, it is difficult to fit a T2 decay curve to the data. This problem is compounded by the fact that the signal dies away quickly. For instance, a signal from INS does not appear prominently in the spectrum after T E 60ms. W i t h only three short T E points (TE=30, 60, 100ms), it was impossible to fit a T 2 decay curve for INS. G L U and G L N were even more difficult because their spectra overlap and their j coupling is more complex than that of INS.  Chapter 5. T  2  5.1.5  Relaxation  56  S i m u l a t i o n s of D e c a y C u r v e s  Simulations were conducted to determine the variance of T for decay curves made from different 2  T E times and T E ranges. Synthetic decay curves was generated for T  2  = 200ms and T  2  =  400ms. As for T i (chapter 4), noise standard deviations of 5, 10, 15 and 20% were chosen based on the coefficient of variation for each metabolite area as measured in the reproducibility study (chapter 3). The noise for each point was determined by a normal random number generator multiplied by the standard deviation. T  2  was calculated by a mono-exponential fit to each  of 1000 synthetic decay curves corrupted by noise (section 2.3.3). The mean and standard deviation of T  2  were calculated. A n illustration is shown in figure 4.2 for the T i simulations;  the T simulations were completely analogous. The decay curves were composed of time points 2  to conform to our data (8 T E : 30, 60, 100, 150, 200, 400, 600, 800ms), the data of Narayana et al. [75] (5TE: 20, 35, 50, 75, 100ms) Frahm et al. [78] (3TE: 50, 135, 270ms) and that of Kreis et al. [51] (6 T E : 30, 40, 60, 90, 135, 270ms).  5.2 5.2.1  Results and Discussion T  2  Results a n d Statistics  Table 5.1 lists the mean T2 and standard errors for the uncoupled metabolite peaks in the occipital grey matter and parietal white matter voxels. Figure 5.3 shows the T2 fits to the average signal area for each metabolite and figure 5.4 shows the distribution of T2 times for all occipital grey matter volunteers.  T T  2  2  Metabolite Occipital Grey (ms) Parietal White (ms)  C H O C R EN A A 302 (8) 156 (2) 308 (6) 279 (6) 169 (3) 359 (13)  Table 5.1: Means and standard errors of metabolite T2 (ms) in vivo  Chapter 5. T  2  Relaxation  Figure 5.3: T  2  57  fits to the average signal area over all occipital grey matter voxels.  0.50 CM h-  0.50  0.25  0.50  Cre.  0.2!  Cho  0.00 .  1—  0.00 (a)  (b)  Figure 5.4: Distribution of T volunteer number.  2  0.25 0.00 . (c)  times over all occipital grey matter voxels where the x-axis is  Chapter 5. T  Relaxation  2  58  According to the F test (section 2.3.4) the variances were unequal for N A A (occipital) compared to N A A (parietal) (p<0.003), C H O (parietal) to N A A (parietal) (p<0.03), C R E (parietal) to N A A parietal (p<0.0003), C H O (occipital) to C R E (occipital) (p<0.0006) and C R E (occipital) to N A A (occipital) (p<0.01). Thus the unequal t test was conducted. The C R E T  2  was significantly higher in parietal white than occipital grey (p<0.03) and  the T 2 times of C H O and N A A were significantly different in parietal white than occipital grey (p<0.004 and p<0.003, respectively). W i t h i n parietal white, each metabolite T 2 was different from each other (p<0.0001 for all t tests). W i t h i n occipital grey, the T2 times of N A A and C H O were not different from each other, but both were larger than the T 2 of C R E (p< 10~ ). 8  5.2.2  Simulations  Figure 5.5 clearly demonstrates that the 5 T E data (with maximum TE=100ms) exhibits a strong T 2 bias at high noise levels. The other simulations show some bias at higher noise and the 8 T E data shows the least bias. For the T2=200ms simulation, all but the 5 T E data fit the decay curves relatively well and measured the T 2 to be approximately 200ms. The standard deviation was lowest for the 8 T E data set and highest for the 3 T E data set. Figure 5.6 shows the distribution of T2 times for each T E data set, assuming a 15% noise level. In the case of the T2=400ms simulation, the T  2  was over-estimated by all the T E data  sets, but the over-estimation was minimal for the 8 T E data compared to the others.  The  distribution of T2 times is shown in figure 5.7. These simulations show that when the maximum T E W T 2 , there is a bias in the T 2 estimate..  5.2.3  B i o l o g i c a l V a r i a t i o n c o m p a r e d w i t h D a t a N o i s e for T 2  The simulations for our 8 T E data at 5%, 10% and 15% noise demonstrated that the standard deviations of the T2 estimates were 5%, 10% and 15%, respectively. The standard deviation in T2 times over the volunteers was around 10% (table 5.1) which is equal to that expected from  Chapter 5. T  2  Relaxation  59  Noise Simulation with True T2 = 0.3s  II  - r U l - t 0.05  1  m 0.1  1  i  0.15  0.2  Percentage Noise in Simulated Curves  Figure 5.5: Simulated T2 for different T E values and ranges assuming true T2=300ms. the noise simulations since the L C M o d e l %SD for the fits was around 10%. Similar to T i , the biological variation is less than the error in measurement of T times in normals. 2  5.2.4  Comparison w i t h Literature Values  Consistent with all studies in the literature, both C H O and N A A were longer than C R E . The literature quotes broad ranges for the T2 times of these metabolites, but this can be explained by the noise simulation described above. The T2 times found for C H O and N A A are shorter than the average T 2 times in the literature. The elevation of literature T 2 times is consistent with the finding that there is a long T2 bias when T2 times are measured with a maximum T E « T 2 This bias is further investigated in appendix B .  5.2.5  Consequences of O m i t t i n g T2 C o r r e c t i o n s  Figure 5.8 shows that in the absence of T2 corrections the signal areas at long echo times could be severely underestimated in both relative and absolute metabolite concentrations. Even at short echo times, there are errors in the relative metabolite concentrations. Given the range in literature T 2 times, signal areas corrected with previously published T 2 values could be highly overestimated. The need for T  2  corrections demonstrated in chapter 4.  corrections is completely analogous to the need for T i  Chapter 5. T  2  0.0  Relaxation  0.2  60  0.4  Simulated  0.6  0.8  T1 T i m e  (s)  (a) 3 T E  Simulated  1.0  0.0  0.2  0.4  Simulated  0.6  0.8  T2 Time  (s)  1.0  (b) 5 T E  T2 T i m e  (c) 6 T E  (s)  Simulated  T2 Time  (s)  (d) 8 T E  Figure 5.6: Amplitude against T for each of 1000 simulations at 15% noise and true T2=200ms. 2  Chapter 5. T  2  Relaxation  61  1 2 3 Simulated T2 Time (s  4  (b) 5 T E  (a) 3 T E  0  1 2 3 Simulated T2 Time (s)  1 2 3 Simulated T2 Time (s) (c) 6 T E  1 2 3. Simulated T2 Time (s) (d) 8 T E  Figure 5.7: Amplitude against T for each of 1000 simulations at 15% noise and true T2=400ms. 2  Chapter 5. T Relaxation  62  2  TE=30ms  TE=144 ms TE=272 ms  Figure 5.8: T2-weighting assuming unit signal area at TE=Oms. 5.3  Summary  It has been demonstrated that the measured T 2 of metabolites is affected by the range of T E values used in the experiment.  Previous experiments using a maximum T E of 272ms have  overestimated the T times. B y choosing a maximum T E of 800ms this problem has been 2  minimized. This work constitutes the first study which has examined T2 times using a large range of T E values. Based on simulations, the measurement appears to robustly measure in vivo T  2  times.  Metabolite T2 times differ between and within occipital grey and parietal white matter. Further investigation is necessary to measure other brain regions. These T 2 values can be used in corrections for normal human brain, but caution should be exercised when considering diseased tissue where metabolite T 2 times may differ from normal.  Chapter 6  Quantification  6.1  Introduction  Magnetic resonance spectroscopy (MRS) provides a unique non-invasive method for determining the chemical composition of localized parts of the body. However, the absolute concentration of the metabolites have been difficult to measure because of the many complicated factors affecting the signal. The signal area of the metabolite is proportional to its concentration, but the spectral singlet area at a given T R and T E is reduced by T i and T2 relaxation. For each subject the scanner tuning is optimized for the 90° pulse, and thus a given signal area in one subject does not necessarily represent the same concentration as the same signal area in another. The process of quantification can be broken into four parts: (1) spectral fitting to determine the signal areas; (2) accurate T\ and T2 corrections; (3) measurement of a signal or scanner variable which can be used as a standard regardless of scanner tuning; and, (4) estimation of water content to estimate metabolite concentration with respect to tissue water. Various spectral fitting methods were used by the groups cited in this chapter. W i t h the exception of Pouwels et al. [24] all the studies discussed have either used integration of peaks or lineshape fitting in the frequency domain with the manual baseline subtraction conducted before the fitting. The problem with the fitting approaches (section 2.3.2) is that they are susceptible to overestimating the signal areas because they cannot discriminate between overlapped metabolite signals. In addition, the baseline may be over- or under-estimated since it is not being fit in concert with the metabolites. Most studies [24, 29, 51, 69, 74, 75, 78, 84, 63, 85, 86] report on spectra collected at long  63  Chapter 6.  Quantification  64  T R (>3s) to minimize Ti-weighting of the spectrum. To minimize T2-weighting, short T E (2030ms) have been used in all studies with the exception of TE=135ms [63, 69]. Short T E studies have many overlapping signals in the spectrum; a robust fitting algorithm such as L C M o d e l must be used to accurately measure the signal areas. Many investigators have conducted T  2  and T i measurements on spectra [51, 69, 75, 78,  84, 63, 85]. Chapters 4 and 5 showed that their experimental designs were not adequate to accurately determine relaxation times. The impact of the T i relaxation errors to concentration estimates is minimal for the long T R spectra (figure 4.8), but the T  2  relaxation errors are  non-negligible in the short T E data and even more significant for long T E spectra (figure 5.8). There are many methods for defining a signal standard to be used in quantification. Early studies by Frahm et al. [78] used creatine as an internal standard of lOmM. Other studies normalized to the relaxation corrected water signal and used literature values for water content [74, 84, 85]. Investigators also used external standards, either during the spectral acquisition [29, 51, 75, 86, 63] or after the spectral acquisition [24, 69]. Finally, some investigators also standardized with the amplitude of a nonselective 90° pulse [29] or the amplitude of a modified water-suppression pulse [86]. In this study the metabolite signals areas were fit with L C M o d e l (section 2.3.2) instead of numerical integration or Gaussian fitting. Accurate relaxation corrections were based on the results of chapters 4 and 5 which investigated the same brain regions as those investigated here. Instead of assuming a water content based on literature values, here the water content was measured in vivo from quantitative images of the brain and external water bottles. The metabolite signals were normalized to the relaxation corrected unsuppressed water signal and were corrected for the water content. The concentrations of N A A , C R E and C H O are presented and discussed in the context of previous studies.  Figure 6.1: Placement of bottles in the 20mm thick, TE=10ms image of the modified C P M G sequence. 6.2  Methods  6.2.1  S u b j e c t s , V o x e l P l a c e m e n t a n d M R S / M R I P u l s e Sequence  Thirty-nine healthy volunteers underwent H M R S and quantitative M R I exams. Voxels were !  placed in occipital grey or parietal white matter (figure 2.11). The M R spectra were recorded using a single-voxel S T E A M localization sequence with parameters TE=30ms, TM=13.7ms, TR=5s, 96 acquisitions, 2048 complex points and bandwidth of 2500Hz. The quantitative M R I used a 32 echo modified C P M G sequence [67] with minimum TE=10ms and ATE=10ms (to a maximum of TE=320ms). The modified C P M G sampled the T decay 2  of a 20mm slice including the M R S voxel and water bottles placed alongside the head to serve as external standards (figure 6.1). The ratio of the T - and Ti-corrected voxel water signal to 2  the T2-corrected water bottle signal gave the water content (WC) for the voxel. Ti-correction was not conducted on the water bottles because the T i value was not determined. The entire exam was under 20 minutes because the spectrum was acquired (with positioning and autoprescanning) in ~12 minutes and the C P M G with one average required ~7 minutes.  Chapter 6.  Quantification  66  O.O  0.2 Measurement Time TE [s)  Figure 6.2: Logarithm of amplitude vs. T E in the modified C P M G data from an M R S voxel. 6.2.2  Quantitative M R I Analysis  To measure the water content of the voxel, the water signal amplitude from the voxel was plotted against T E for each of the 32 images from the modified C P M G (see figure 6.2). Different from our group's previously published decay curves from 5mm slices [67], the signal amplitude at each T E from 20mm slices alternate for the even and odd echoes. This is due to the wide radiofrequency distribution over the 20mm slice, accentuated by the data being acquired at a distance from the headcoiFs centre (typically 40mm from iso-centre). The wide R F distribution leads to a variation in the accuracy of the 90° and 180° pulses. T  2  decay curves from the brain  and water bottles were fitted to the even echoes with N N L S (section 2.3.3) because the even echoes are better rephased [87]. The water signal areas, both in vivo and for the water bottle at TE=0ms were calculated from the fit to yield T2-corrected signal areas. The ratio of the T2-corrected signal from the voxel to that from the bottle gave the water content of the voxel. In exams where there was more than one water bottle present, the average water content was calculated. The standard deviation of the water content for exams with more than one bottle was around 3% which is less than the standard deviation of the metabolite signal area estimates in chapter 3.  Chapter 6.  6.2.3  Quantification  67  Spectral Fitting and Relaxation Corrections  The in vivo brain spectra were fitted with L C M o d e l (section 2.3.2) using the templates collected with S T E A M at TE=30ms, TM13.7ms and TR5s. The area of the unsuppressed water -Awater was measured according to section 2.3.2. The  ^4  m e  t  and  ^4 ater W  were T i and T2-corrected. The T i corrections were made according  to Aoo = A R / ( l - e - (  T R  T  where  -™ ™)/^)  (6.1)  +  is the signal area in the limit that T R is infinity and A T R is the measured signal  area. For both . A  and A ,  m e t  the T i values from chapter 4 (table 4.1) were used.  w3jtei  The T2 corrections for A  m e t  followed _ 11  A  0  where A  Q  = A /e  2  T  TE  (6.2)  is the singlet signal area at TE=0ms and A T E is the measured singlet signal area,  the fractional signal area of the peak which includes only the singlet. The T2 corrections were made using the chapter 5 values (table 5.1). The metabolites for which the singlets were measured were C H O , C R E and N A A . The ^ w a t e r (TEO)  > the relaxation corrected water signal area in vivo, was found by comparing  the signal from spectroscopy to the modified C P M G signal as follows  where CPMG  ^  w a  w a t e r  ter(TE30) (TE30ms)  ^-water ( T E O ) _  CPMG  Avater ( T E 3 0 )  CPMG  w a t e r  w a t e r  (TEO)  ^  (TE30)  is the known water signal area measured by M R S , and C P M G a  r  e  ^  w a t e r  (TEO)  a n  d  the known water areas from the fit to the modified C P M G signal at  TE=0ms and TE=30ms, respectively. 6.2.4  Calculating Concentrations  After measuring all the variables, the concentration of the metabolite [met] was found by r  ,•,  [met] =  Anet(TEOTRoo)  i  np  w a t e r  '— x  Avater ( T E O T R o o )  rrnnn  A K  x W C x 55000mM n  Pmet  in  A\  (6.4)  Chapter 6.  where A  met  Quantification  (TEOTROO)  68  is the known metabolite area after T i - and T2-corrections, -<4  is the known unsuppressed water area both T i - and T2-corrected, n p  m e t  water  (TEOTROO)  and n p ^ ^ , . are the  numbers of protons contributing to the singlet signal (CHO:9, C R E : 3 , N A A : 3 , water:2), W C is the water content and 55000mM is the concentration of water if the W C were unity. Phantom studies have confirmed that this method gives accurate and precise results.  6.3 6.3.1  Results and Discussion Quantification Results  Table 6.1 lists the mean and standard deviations of the concentrations of C H O , C R E and N A A . The average water content was found to be 0.73 g / m L (standard deviation=0.03 g/mL) in parietal white voxels and 0.76 (0.05) g / m L in occipital grey voxels as measured by the modified C P M G in each M R S voxel. The C H O and N A A concentrations were both at a lower concentration in grey than white matter (p<0.00001 and p<0.01, respectively) according to the two-tailed Student's t test with unequal variance. W i t h i n each voxel, the two-tailed paired Student's t test showed that C R E had a lower concentration than N A A in parietal white (p<0.0004), but not in occipital grey where they were not significantly different. The C H O concentration was much lower than the N A A and C R E concentrations in both tissues.  n Parietal White 20 Occipital Grey 19  CHO  CRE  2.0 (0.2) 1.2 (0.2)  8.0 (1.6) 8.4 (1.4)  NAA  10.0 (1.7) 8.7 (1.5)  Table 6.1: Number of volunteers, concentrations and standard deviations (mM) for C H O , C R E and N A A .  Chapter 6.  6.3.2  Quantisation  69  Comparison with Literature  Six studies have investigated the same brain regions as studied here [24, 29, 51, 69, 86, 63]. Their results are listed in Table 6.2. The finding here of a higher C H O concentration in the white voxels compared to the grey is consistent with all reports which investigated the two tissues [24, 69, 86, 51]. The concentrations found in this study fit into the range of concentrations listed. However, taken study by study, the inconsistencies can be explained and the range of literature concentrations narrows as described in the next section.  n CHO Parietal White Our results 20 2.0 (0.2) Hennig[63] 32 1.5 (0.5) Kreis[51] 10 2.4 (0.02) Michaelis[29] 26 1.8 (0.3) Danielsen[86] 10 1.3 (0.1) Due [69] 28 2.4 Pouwels[24] 20 1.7 (0.3) Occipital Grey Our results 19 1.2 (0.2) Kreis[51] 10 1.9 (0.1) Danielsen[86] 10 1.0 (0.1) Duc[69] 28 1.2 Pouwels[24] 20 0.9 (0.1)  CRE  8.0 5.3 9.8 6.1 5.8 8.3 5.7  NAA  (1.6) (2.5) (0.2) (0.8) (0.7) (0.6)  8.4 (1.4) 11.1 (0.4) 8.0 (0.5) 6.6 6.9 (0.7)  10.0 (1.7) 8.2 (2.2) 13.6 (0.3) 8.8 (1.0) 8.7 (1.1) 12.6 8.0 (1.0) 8.7 (1.5) 12.7 (0.3) 10. (0.8) 13.7 9.2 (0.9)  Table 6.2: Number of volunteers, concentrations and standard deviations (mM) for C H O , C R E and N A A from literature.  Spectral fitting and  T  2  Hennig et al. [63] (table 6.2) found lower concentrations for each of the metabolite compared to our work. They collected heavily T2-weighted spectra at TE135ms. In all cases, the T 2 times were longer than ours ( C H O : 372ms vs. 302ms; C R E 252ms vs. 156ms; N A A 352ms vs. 308ms). Longer T 2 times lead to smaller T2-corrected signals. B y using our T 2 corrections,  Chapter 6.  Quantification  70  their concentrations would increase from C H O : 1.5mM, C R E : 5.3mM and N A A : 8.2mM, to C H O : 1.6mM, C R E : 7.4mM and N A A : 8.6mM. The different concentrations found by Due et al. [69] may also be due to problems with T corrections, but the authors do not list their T 2  2  times.  Pouwels et al. [24] used L C M o d e l to measure the spectral areas with TE=20, TR=6s. They did not conduct relaxation corrections on their data. At TE=20ms, however, the signals from C H O , N A A and C R E are reduced by 6, 7, and 12%, respectively. This T  2  correction increases  their concentrations in occipital grey matter (for instance) from C H O : 0.9mM, C R E : 6.9mM and N A A : 9.2mM, to C H O : l.OmM, C R E : 7.8mM and N A A : 9.8mM which are closer to our values for  C H O  and  C R E  but not  NAA.  Kreis et al. [51] reported much higher concentrations than any other study. Their T  2  times  were higher than ours, but since they already conducted T corrections at TE=30ms the relative 2  T correction would be minimal. Like all others except for Pouwels et al. [24], they fit the spectra 2  with numerical integration or Lorentzian lines. It is possible that their baseline correction (a frequency-independent D C baseline calculated from two data points) underestimated the baseline contribution in the spectrum and thus overestimated the signals: there is significant spectral overlap at TE=30ms (1.5T field strength) from macromolecules [88], G L N + G L U . Other studies working at field strength 2.0T [29, 86] may have been less susceptible to the problem of spectral overlap, and those working at TE=135ms [69, 63] were completely immune to the problem because of j coupling and T relaxation of those chemicals. 2  Water Content Whittall et al. measured the W C values of pure white and grey matter regions as 0.71 g / m L and 0.83 g/mL, respectively [89]. The white matter M R S voxels measured here (0.73 g/mL) had a lower W C than the grey matter voxels (0.76 g/mL). The M R S voxels, though, were not pure white or grey tissue and as a result the white W C was slightly higher than a pure white voxel and the grey, lower. The two groups who report water content measurements [51, 86] used different variations  Chapter 6.  Quantification  71  of the method developed by Ernst et al. [90]. Ernst measured a quantity called B W + M , which is a measured brain water (BW) and an estimated "missing signal" (M). The B W is measured by fitting the water area of ten unsuppressed spectra collected at TE=30, 45, 67.5, 100, 200, 500 and 1500ms, TR=30s with two T2 components and finding the component of the smaller T2 at TEOms (the longer T2 component is attributed to cerebrospinal fluid, C S F ) [90]. M is calculated to be the difference between the B W + C S F component and the signal which would arise from the voxel being pure water (according to an external standard). Water content is defined as the ratio of the B W to B W + M , the so-called total brain water. In our method, by contrast, the W C is the ratio of the relaxation corrected brain water signal to the relaxation corrected external standard. It is unclear why their denominator is the brain water signal added to, essentially, the external standard signal. The low metabolite concentrations of Danielsen et al. [86] (table ?? relative to our values (table 6.1) can be explained in terms of the water content that they used. Their metabolite signal areas were scaled inversely with the B W + M which they found. The total B W + M should be equivalent to our W C because it represents the water content of the voxel. However, the B W + M for the white matter voxel was reported as 0.92 g / m L and for the grey matter voxel, 0.94 g/mL. This overestimation of water content would lead to an underestimation of metabolite concentration. Kreis et al. [51] used the same method for measuring the water in the voxel as Danielsen et al. however their concentrations were scaled by the B W component reported as 0.65 g / m L (white) and 0.72 g / m L (grey). This underestimation of water content leads to the overestimation of metabolite concentration. The low estimations for the B W component are likely because their low T E range was TE=30, 45, 67.5, 100 and 200ms to measure a T2~80ms (brain tissue water). They may have underestimated their short decaying component because they had too few points to resolve it. In contrast, we measured TE=20, 40, 60, 80, 100, 120, 140, 160, 180 and 200ms in the same range and thus had more data to resolve this component.  Chapter 6.  6.4  Quantification  72  Summary  This is the first study which has combined quantitative M R I in conjunction with M R S and we have been able to fully quantify C H O , C R E and N A A concentrations in vivo. The modified C P M G sequence accurately determined the voxel water content which is a great improvement over previous methods. L C M o d e l yielded accurate measurements of the overlapping metabolite areas so that the contribution from the singlets could be measured. Relaxation corrections were conducted based on studies that improved the accuracy of T i and T2 estimation. Differences between our values and those reported by others could be explained in terms of T2-weighting or estimations of water content. Investigations can now be conducted in patient populations to determine metabolite concentrations in different disease states.  Chapter 7  T i o f M u l t i p l e Sclerosis L e s i o n s  There is a large array of literature in which Multiple Sclerosis (MS) has been investigated with M R S . In the papers in the early 1990s, investigators reported on the ratios (relative signal areas) of the metaobolites. Reductions in the and chronic lesions [93, 94]. The A n increase in the  CHO/CRE  NAA/CRE  NAA/CRE  ratio were reported in both acute [48, 91, 92]  reduction was thought to be due to axonal loss [92].  ratio was also reported [93] and was thought to be linked to an  increased membrane turnover associated with inflammatory cellular infiltration [95]. Elevations in  INS/CRE  were also reported [92, 95, 96] and were later postulated to be due to gliosis in the  lesion [97]. These early papers sought to distinguish between remitting relapsing M S (RRMS) and secondary progressive M S (SPMS) and how they differed from healthy tissue. Recent papers have reported a decreased N A A concentration in lesions and normal appearing white matter ( N A W M ) in M S patients compared to controls [98] (for absolute concentrations) [99] (for ratios). The estimated N A A concentration in N A W M was lower for S P M S and R R M S than for controls, but the decrease was found to be even lower for the S P M S group [100]. Leary et al. [101] found reductions in N A A concentrations in both lesions and N A W M for primary progressive patients compared to controls and Brex et al. [102] reported N A A concentration reductions in lesions but not N A W M in patients presenting with MS-like symptoms, but before diagnosis. M S patients have also been monitored longitudinally and it was found that the N A W M N A A concentration decreased for R R M S patients over time and the decrease in concentration was even more evident for patients who had clinically relevant relapses over the 30 month period of the study [103]. Reversible decreases of N A A were reported in M S patients studied serially [13].  73  Chapter 7. T\ of Multiple Sclerosis Lesions  74  A very interesting study which correlated M R S and histopathology found in 15 serial stereotactic needle biopsy specimens that the decreased M R S N A A concentration correlated with a reduction of axonal density, and the increased M R S C H O and I N S concentrations correlated with an increase in glial proliferation [104]. The results of these many investigations are encouragingly consistent, especially since they were conducted at a variety of T E and T R times.  However, to best distinguish between  metabolites in different tissues and disease states the M R S data must be fully quantified. To date no T i studies have been conducted in M S lesions. There is reason to believe that T i would change in lesions since T i is sensitive to the local environment of the metabolite (chapter 4). It is known that the protons associated with water in a lesion undergo characteristic relaxation changes [67] which suggests that the metabolite environment may be different from normal. A change in T i may necessitate re-interpretation of the results from studies conducted at short T R . In this study the T i times of  INS,  lesions from three patients. The total  CHO,  C R E  and  N A A + N A A G  N A A (NAA+NAAG)  the signal to noise was too low to separate the signal of  have been measured in four  was measured instead of N A A because NAAG  from that of  NAA.  As in chapter  4 we assume that there is one T i describing the relaxation of the entire molecule.  7.1 7.1.1  Methods Subjects a n d V o x e l P l a c e m e n t  Three patients with clinically definite multiple sclerosis underwent proton M R S and M R I . The M R S voxels were placed so that they were within large lesions in parietal white matter. Figure 7.1 shows the voxel placement for all three patients. The voxels ranged in volume from 2.43.4mL and contained from 52-72% lesion based on image segmentation. One patient (A) had two voxels examined on separate days. Gadolinium-contrast scans conducted immediately after M R S confirmed that none of the lesions studied changed their signal area. Gadolinium-contrast is a solution with heavy metal ions which is injected intravenously. In normal brain functioning,  Chapter 7. T\ of Multiple Sclerosis Lesions  (a) 3.5mL 57% lesion  (b) 3.5mL lesion  52%  75  (c) 2.6mL 58% lesion  (d) 2.5mL lesion  72%  Figure 7.1: Voxel placement for each of the patients. large ions cannot pass into the brain due to the blood brain barrier. In active M S lesions, the blood brain barrier breaks down and allows gadolinium to pass through.  The gadolinium  changes the T i and T of the water in the lesion, so a comparison of pre- and post-gadolinium 2  scans show whether the blood brain barrier is intact or not. Lesions whose signal area changes after administration of the contrast agent are considered enhancing lesions otherwise they are referred as chronic lesions. A l l lesions in this study were chronic. Voxels A and B were acquired using S T E A M and voxels C and D were acquired with P R E S S to contrast the two acquisition methods. Seven spectra were collected with the same parameters as those in chapter 4 with TE=30ms, TM=13.7ms and TR=547, 751, 1200, 1500, 2500, 3500, and 5000ms generating the series of spectra seen in figure 7.2. The number of acquisitions was 512, 512, 256, 256, 128, 128, and 96, respectively. A l l spectra contained 2048 complex points except for one having 1024 points (at TR=751ms) and another with 512 points (at TR=547ms). The voxel was prescanned for the first spectrum only and the tuning was kept constant for all subsequent spectra on the same patient.  Chapter 7. T i of Multiple Sclerosis Lesions  76  730 ms 530 ms  Figure 7.2: Fitted spectra stacked according to T R for lesion.  Chapter 7. T\ of Multiple Sclerosis Lesions  7.1.2  77  Spectral Analysis and T i Measurement  Chapter 4 details the spectral analysis and T i measurement. Again, where the L C M o d e l %SD exceeded 20% (see section 2.3.2) the metabolite signal area was excluded from the T i recovery curve. If a curve had fewer than 5 T R points the T i was not determined. The corresponding P R E S S or S T E A M templates with TE=30ms and TR=5s were used in L C M o d e l (section 2.3.2) for the P R E S S and S T E A M voxels. In addition to the metabolite T i times the water T i was also measured, as described in sections 2.3.2 and 2.3.3.  7.2  Results and Discussion  7.2.1  Lesion T  x  W i t h the exception of  INS  (subjects B and D) and  (B) (because of the exclusion  N A A + N A A G  criteria), the metabolites T i were fit for all voxels. Table 7.1 lists the T i times of water, C H O , CRE, INS  and  N A A + N A A G  for each voxel in each patient and also for healthy volunteers scanned  previously (chapter 4). The corresponding recovery curves for each voxel is shown in figures 7.3  ( C H O ) 7.4  (Cre)  A B C D Control  7.5  ( I N S ) and  7.6  (NAA+NAAG).  CHO  CRE  INS  N A A + N A A G  0.99 1.07 0.92 0.90 1.19 (0.10)  1.01 1.40 1.42 1.11 1.50 (0.15)  1.78  0.85  -  -  1.11  1.27 0.76 1.68 (0.28)  1.17 (0.60)  Water 0.87 1.01 1.30 1.08 0.76 (0.04)  Table 7.1: T i and standard deviations (s) for voxels A , B , C and D and controls.  According to a two-sided unequal variance t test, with p<0.05 defined as signficant, the average T i times of C H O and N A A were significantly lower in lesions than normal parietal white  Chapter 7. T i of Multiple Sclerosis Lesions  A  78  B  C  D  Figure 7.3: T i fit to C H O recovery for each M S lesion voxel.  A  B  C  0  Figure 7.4: T i fit to C R E recovery for each M S lesion voxel.  A  T  ' ' '  f.  'ns  c  1.050  T  |  0.621  0.192  /  Ins  Figure 7.5: T i fit to INS recovery for each M S lesion voxel.  Figure 7.6: T i fit to  NAA+NAAG  recovery for each M S lesion voxel.  Chapter 7. T i of Multiple Sclerosis Lesions  0  1  2  79  3  4  5  6  TR (s)  Figure 7.7: Relative uncorrected signal intensity against T R for N A A and C H O in lesions compared with normals. (p<0.003 and p<0.02).  Neither the T i of C R E (p< 0.08) nor the T  x  of INS (p<0.6) were  significantly different from normal parietal white. The T i of water in lesions was significantly higher than the water T i in healthy parietal white matter (p<0.04).  7.2.2  Consequences o f T i Differences B e t w e e n L e s i o n s a n d N o r m a l  A reduction in T i leads to reduced Ti-weighting at a given T R . This means that in an experiment comparing the  NAA+NAAG  signal from lesions and controls, the  NAA+NAAG  signal  would be over-estimated in the lesion for a Ti-weighted spectrum. The degree of the overestimation would depend on the T R used. For example, at TR=1.5s, given a lesion Ti=0.96s and normal Ti=1.68s, the relative signal intensity (assuming that they had the same concentration and T2) would be lesion/normal = 1.34. The relative signal areas without Ti-correction are plotted against T R for N A A and C H O in figure 7.7. The reversible decrease observed in N A A by De Stephano et al. [13] can be explained by T i effects. Initially, the N A A reduction could have been due to a loss in the number of axons, but then over time a shortening of the N A A T i could have given an apparent increase in the N A A concentration. At their TR=2s [13] the N A A areas would have been susceptible to this effect.  Chapter 7. T\ of Multiple Sclerosis Lesions  7.2.3  80  Comparison with Literature  The only reference to metabolite T i times in M S was made by Sarchielli et al. [100]. They investigated normal appearing white matter ( N A W M ) in 40 patients using with S T E A M TR=4s. To ensure that they had minimal Ti-weighting, they conducted a second M R S exam on four patients at TR=6s.  They found that the maximum variation in metabolite concentrations  was lower than 2.1%. According to our data, the  NAA+NAAG  signal in lesions should have  increased by ~6% at TR=6s compared to TR=4s. It is possible that metabolites in N A W M have different T i times than metabolites in lesions which would lead to further erroneous concentration estimates for spectra collected at short T R .  7.2.4  P o s s i b l e E x p l a n a t i o n for T i R e d u c t i o n o f  NAA+NAAG  Statistically significant reductions in the T i times of N A A + N A A G and  and  CHO  C H O were  i n Lesions observed in M S  lesions as compared to normal parietal white matter. In section 4.2.5 it was assumed that a single correlation time for the motions which led to T i relaxation and that the correlation time was approximated by the Stokes-Einstein relation:  Tc  =  (7.1)  where 77 is the viscosity, k is the Boltzmann constant, T is the absolute temperature and R is the molecular radius. In the weak collision limit (section A.1.4) T i is proportional to the inverse of T : C  J-i  ocr  c  (7.2)  If we are looking at the T i of one molecule in normal parietal white matter and in M S lesions, then we can assume that neither T nor R are changing in equation 7.1. The only possible variable is 77, the microviscosity of the solvent surrounding the molecule. If this is indeed the relevent relaxation mechanism, then it is possible that the reduction in T i times is due to a local increase in effective viscosity in the axons (where most, if not  Chapter 7. T\ of Multiple Sclerosis Lesions  all, of the  N A A + N A A G  81  concentration is thought to be found [33]). This is possibly an effect  of demyelination and the associated adjustments within an axon as it tries to remain viable without myelin. The main metabolites contributing to the C H O signal are phosphocholine and glycerophosphocholine which are both involved in the metabolism of membrane lipids [24]. The reduction in the C H O T i may reflect the altered environment in which cell membranes are being synthesized. The T i of C R E did not change in lesions relative to healthy white matter. This may indicate that the possible effective viscosity changes would not influence the C R E because of its location. There are two few data to comment on the T i of I N S .  7.3  Summary  The T i of  N A A + N A A G  was found to be significantly lower in lesions than it was in controls. To  avoid the complications of Ti-weighting, M R S should be conducted at long T R (>6s). As well, the T i of C H O is lower in lesions than in healthy tissue. Since the difference in C H O T i times between lesions and normal is not as great as that of  NAA+NAAG,  M R S conducted at T R « 5 s  will make the concentration of C H O apparently 7% higher due to Ti-weighting. It is interesting that the T i of C R E is the same in lesions as in controls. This suggests that the environment surrounding  C R E  is unchanged in a diseased state compared to healthy, but that for  NAA+NAAG  and C H O is changing. This study provides a preliminary look at the effect of disease on T i and serves as a warning to those investigators who acquire their data at short T R . T i investigations should be conducted on N A W M and different M S lesions to look for possible local environment alternation in those tissues.  Chapter 8  Future Work  8.1  Relaxation Mechanisms  The T i and T times in chapters 4 and 5 have shown intra- and inter-regional variations 2  due to improvements in data acquisition and analysis. This presents a unique opportunity to investigate the mechanisms for T i and T relaxation. B y applying the ideas of the spectral 2  density functions and correlation times (appendix A) we will likely gain insight into the intraand inter-molecular motions which can lead to a clearer understanding of healthy and diseased tissue. In particular, the mechanisms for T have not been addressed in this thesis. T relaxation 2  2  differs significantly from T i relaxation because of the J(0) term in equation A-21. J(0) is sensitive to slow motions (much slower than the Larmor frequency) such as molecular (surface) interactions. Intra- and inter-regional investigations may prove fruitful in understanding the location and function of the metabolites.  8.2  Technical Optimization  T i and T times estimates (chapters 4 and 5) may be improved by acquiring the spectra at 2  geometrically-spaced T R or T E times [105]. Investigations of metabolite T i and T  2  in disease processes could yield very interesting  insights into the metabolite environments.  On a practical level, these measurements can  direct investigators to choose T E and T R times to minimize the T i - and T -weighting in 2  the spectra. However, because of the length of time to acquire the data (>70 minutes) it is impractical to routinely conduct relaxation measurements on patients. W i t h improved echo 82  Chapter 8. Future Work  83  sampling techniques it may take less time to acquire a sufficient number of points to accurately characterize the relaxtion times. Future work should include the determination of best echo sampling schemes. A n introduction to this question is provided in appendix B . The influence of water suppression on metabolite signal areas has not been fully investigated. Further work can be conducted on the effect of intra-molecular magnetization transfer. The water content measurement can be optimized by also including a map of the B i field to correct for differences in signal intensity across the brain. Other than for creatine, intra-molecular T i differences in the templates have been ignored. Investigations of the effect of different T i times from different proton environments (methyl vs. methylene) on the same metabolite should be considered.  8.3  Future Medical Applications  The measurement of absolute concentrations of metabolites in human brain in vivo can be used to study any disease having a neurological component.  We have begun collaborations with  neurologists, psychiatrists, endocrinologists and specialists in infectious diseases to investigate whether M R S can provide clinically relevant information. The projects described have been designed by a group of investigators; in each section is a list of the contributors. The data for the first project on traumatic brain injury have been collected and are currently being analysed. The two other projects, on phenylketonuria and chronic fatigue syndrome, have recently passed ethics review and the data collection is forthcoming. It must be cautioned that there are limits to the applicability of the water content method to investigating disease. Implicit in the method is the assumption that the water content is the same in the intra- and extracellular spaces.  In oedemous tissue the extracellular water  content increases and the intracellular component may remain normal.  In this case, the  intracellular water content would be overestimated and the metabolite concentration would be underestimated.  Chapter 8. Future Work  8.3.1  84  Traumatic B r a i n Injury  This study was designed and conducted by myself, J . Clement (Radiology), R. Vernon-Wilkinson (Psychology), A . L . MacKay (Radiology/Physics), A . Scamvougeras (Psychology), H . Feldman (Neurology) and B . Forster (Principal Investigator, Radiology). The purpose of this study was to determine retrospective ^ - M R S predictors for the severity of traumatic brain injury (TBI). That is, we wished to develop a technique that could objectively determine the severity of T B I many years after the injury. A previous M R S study [106] conducted on patients soon after T B I reported that initial metabolite levels (primarily N A A ) correlated with G O S (Glasgow Outcome Score), a rating which ranks the patient's disability from 1 (death) to 5 (good outcome). No strong correlations were found between initial metabolite levels and G C S (Glasgow Coma Scale) which ranks the patient's level of consciousness immediately after a T B I . Follow-up M R S studies (up to one year after injury) did not distinguish between patients with good or poor outcomes. We sought to examine patients one to six years after T B I and investigate correlations between M R S findings, M R I findings and neuropsychological tests from a multidisciplinary clinical assessment. Twenty-one patients (14 male, 7 female, age 31 ± 10 years) with a history of significant T B I (defined by a non-zero head injury rating - see below) and twenty-one age-matched healthy controls (with no history of head injury) underwent H - M R S exams and quantitative M R I 1  (section 6.2). The voxels were placed in normal appearing occipital grey and parietal white matter (see figure 2.11) and acquired with S T E A M (96 acqs, TE=30ms, TM=13.7ms, and TR=5s). Clinical M R I included axial conventional SE, and T2* weighted G R E sequences in the coronal and axial planes to optimise detection of hemorrhagic diffuse axonal injury. No morpholog abnormalities were noted with M R I in the brain regions used for voxel placement for M R S . Each patient was initially assigned a G C S rating at the time of T B I . For the purposes of this study, a head injury rating was devised which rated the severity of the original T B I  Chapter 8. Future Work  Parietal White (patient) (control) Occipital Grey (patient) (control)  85  CHO  CRE  NAA  1.9 (0.5) 2.0 (0.2)  8.5 (1.2) 8.0 (1.6)  9.3 (2.2) 10.0 (1.7)  1.2 (0.3) 1.2 (0.2)  9.2 (2.0) 8.4 (1.4)  9.5 (1.5) 8.7 (1.5)  Table 8.1: Concentrations and standard deviations (mM) for C H O , C R E and N A A in head injury patients and controls. from 0 (none) to 6 (very severe) based on G C S and Post-Traumatic Amnesia (PTA) (for nonpenetrating brain injury). There were also two patients with severe penetrating injury for whom the P T A could not be assessed. During the clinical assessment, 1-6 years after T B I and within one week of the M R I and M R S exams, patients were assessed for their cognitive deficits, organic personality disorder, executive deficits and mood using standard neuropsychological tests and multidisciplinary clinical assessment.  Alcohol use and medications were also recorded.  In  addition, a G O S was estimated. The absolute concentrations of C H O , C R E and N A A were found according to chapter 6. Listed in table 8.1 are the concentrations for the head injury patients and those for the healthy volunteers as listed in table 6.1.  Using a two-tailed t test, there were no significant (p<0.05) differences found between average metabolite concentrations for T B I patients and controls in grey or white matter (table 8.1).  No correlations have been determined between neuropsychological testing and M R I  findings.  The data is continuing to be analysed to distinguish any correlations between the  results of neuropsychological tests and M R S and also the M R I findings and M R S .  Chapter 8. Future Work  8.3.2  86  Phenylketonuria  This study was designed and will be conducted by Sandra Sirrs (Principal Investigator, Endrocrinology), Alex MacKay (Physics/Radiology), David L i (Radiology), Michelle Mezei (Neurology), Margaret Toms (Endrocrinology), Bettina Jung (Medical Student) and myself. The following description was modified from the U B C Ethics Review form written by Sandra Sirrs. Phenylketonuria (PKU) is a genetic disorder of phenylalanine (PHE) metabolism. Patients with high blood P H E levels have a number of neurological symptoms which may include tremor, ataxia, hyper-reflexia, psychiatric disorders and cognitive impairment. Treatment of P K U involves rigid dietary restriction of P H E intake along with nutritional supplementation through the use of an expensive PHE-free formula. Treatment is difficult and compliance is poor in adults. Therefore, it would be desirable to have a non-invasive way of quantifying risk on patients to develop neurological effects from P K U , to target patients for whom aggressive therapy is indicated, as well as those for whom treatment would be expected to provide little benefit. Standard M R I techniques usually reveal widespread white matter changes in patients with P K U . These M R I changes are thought to represent the formation of structurally altered and less stable myelin (a condition referred to as 'dysmyelination') [107].  Unfortunately, these  changes correlate poorly with serum indicies of metabolic control and neurological findings in adults [107]. Further, some of these changes are reversible with improved metabolic control [108, 109, 110] unlike the white matter changes seen in other neurological conditions. M R I is not useful as a procedure to identify patients who have neurological damage from their P K U . • ^ - M R S in large voxels can detect the phenylalanine peak [107, 111, 112, 113, 114, 115, 116, 117, 118, 119, 120]. Preliminary studies [107, 117, 118] have suggested that levels of P H E in brain differ among P K U patients, but not all studies confirm a direct relationship of brain P H E concentration to neurological outcome. Furthermore, most studies [111, 114, 113, 116, 117, 120] compared the P H E area in the spectrum to C R E which was assumed to be normal. Patients will undergo a series of M R I , M R S and neurological exams. Absolute concentrations  Chapter 8. Future Work  87  of N A A , C H O , C R E and P H E will be measured according to chapter 6. The M R S data will be acquired from a large (60x 60x 20mm ) periventricular voxel with S T E A M TE=30ms, TM=13.7, 3  TR=5s and 96 acquisitions. In addition, quantitative M R I will be conducted on the 20mm slice surrounding the M R S voxel and on a 5mm slice in a lower region. A second M R I slice (5mm thick) will be used to measure the myelin content of various grey and white tissue structures [67]. In addition, patients will be examined by a neurologist who will rate their degree of neurological involvement using standard rating scales, which will consider cognitive performance and extent of abnormal physical findings such as cerebellar ataxia and tremor. Ultimately we would like to create a clinical tool that can determine the degree of risk for neurological damage assumed by patients when they are not following their diets. For this study we hypothesize that brain myelin content will correlate with neurological findings in adult patients with P K U and we will verify whether C R E can be used as an internal standard in this patient population. In addition we will investigate whether the concentration of P H E in the large voxel correlates with myelin content.  8.3.3  Chronic Fatigue Syndrome  This study was designed and will be conducted by Grant Stiver (Principal Investigator, Infectious Diseases), Tony Chow (Infectious Diseases), Kenna Sleigh (Infectious Diseases), Bruce Forster (Radiology), Saul Isserow (Cardiology), Alex MacKay (Physics/Radiology), Burkhard Madler (Physics) and myself. The following description was modified from the U B C Ethics Review form written by Grant Stiver. Chronic Fatigue Syndrome (CFS) is a poorly understood disorder characterized by a severe but unexplained fatigue and a number of other symptoms including muscle pain, joint pain, headaches and tiredness lasting more than 24 hours after exercise. No diagnostic test is available and C F S must be diagnosed by meeting officially-set criteria and excluding other illnesses that may account for symptoms. Differentiating C F S from other clinical conditions, like depression, is difficult.  Chapter 8. Future Work  88  CNS abnormalities have been detected in C F S patients. Neuroimaging techniques include M R I [121, 122, 123, 124, 125, 126], positron emission tomography ( P E T ) and single-photon emission computer tomography ( S P E C T ) [127, 122, 128, 129, 130, 131, 132, 133] which have demostrated cerebral disturbances which may be specific to C F S .  3 1  P - M R S has been conducted  on muscle [134, 135, 136] but only one ^ - M R S study has been reported. The H - M R S was a 1  long T E (T2-weighted) case study of the brains of three children with C F S [137]. They reported elevations of the  C H O / C R E  ratio in frontal white matter.  C F S patients seem intolerant of physiological stress and report a severe worsening of their symptoms following activity. In this study we will compare the brain metabolite and blood plasma responses of C F S patients and normal controls after strenuous physical exertion. Each patient (and control) will have a baseline M R S (according to chapter 6) with the voxel placed in basal ganglia. Basal ganglia was chosen based on abnormalities as seen in P E T studies. The patients will have blood drawn to measure levels of heat shock proteins (whose concentrations are indicative of physiologic stress). The patients will then exercise on a treadmill under the supervision of a cardiologist. Immediately post-treadmill the patients will have another M R S exam (in basal ganglia). The patients will be called back the next day for a final M R S . This study will look for metabolic differences (both blood work and M R S metabolite concentrations) between patients with C F S and controls, and within C F S patients pre- and post-exertion, will determine if self-reported symptoms correlate with these measurements.  Chapter 9  Conclusions  This thesis consists of a series of independent and interesting studies which have been brought together to form a cohesive description and method for application of M R S in vivo. The measurement of absolute metabolite concentrations in vivo (chapter 6), would not have been possible without the T i and T2 relaxation studies (chapters 4 and 5) which, in turn, were aided in establishing their reliability by the reproducibility study (chapter 3). In the process of measuring all the parameters necessary to estimate absolute concentrations, new and intriguingrelaxation results were discovered. Metabolite T i relaxation differed between and within each brain regions. In each tissue, the T i times ranked in the same order such that INS < CHO < NAA < CRE (table 4.1). The same ranking was found for metabolites in vitro, with the exception of CHO whose T i was the longest. The in vitro metabolite T i times ranked inversely with molecular weight. Free choline was measured in phantoms and its molecular weight is less than that of phosphocholine and glycerophosphocholine which make up the in vivo signal. The T i of CRE was longer than that of CR which could be understood if more than one correlation time is leading to T i relaxation and the effect of intramolecular motions is considered.  For each metabolite, the T i times  increased from occipital grey < parietal white < frontal white. The reason for this remains unknown, but it is proposed that there are differences in iron content or vascularity (and thus more haemoglobin) in these regions which can affect T i relaxation. Previous measurements of metabolite T i times did not detect the between- and within- region ranking of the T i times. It was shown through a simulation that because of their study design, particularly the number and range of T R values used, they lacked the necessary resolution to measure the T i differences  89  Chapter 9. Conclusions  90  presented here. The metabolite T2 times of C H O , C R E and N A A were found to be shorter than those previously measured in the literature. The T2 of C H O was lower in parietal white than occipital grey, and the T2 times of N A A and C R E were higher in parietal white than occipital grey (table 5.1). A simulation demonstrated that the literature T E times and ranges (i.e. T E  m a x  i  m u m  < 270ms)  caused severe overestimations of metabolite T 2 times, whereas the T2 measurement from the T E times and ranges chosen here was much less affected. The measurement of absolute metabolite concentrations was possible because of a newly applied technique to measure brain water content (section 6.2.2). The metabolite signals were T i and T2 corrected and normalized to in vivo water.  The absolute concentrations (table  6.1) were found by correcting the normalized signals for the water content as measured by quantitative M R I . Discrepancies between the concentrations measured here and those from other groups were explained in terms of the differences between their T2 corrections and water content and those presented here (section 6.3.2). As was my intention for this work, the techniques for relaxation measurements and absolute concentrations were applied to clinical work. It was found in chapter 7 that the T i times of N A A and C H O were lower in multiple sclerosis (MS) lesions than in normal white matter. This has implications for understanding serial studies which have reported increases in N A A concentrations over time, and it will also affect the future study design for M R S of MS lesions. Three studies were presented in chapter 8 which described three patient populations (patients with head injury, patients with phenylketonuria and patients with chronic fatigue syndrome) and the possibilities for better understanding the disease processes by finding absolute concentrations of brain metabolites. Through its novel in vivo relaxation and absolute concentration measurements, this work has improved upon the accuracy and precision of previous experiments. The discrepancies between the T i , T2 and concentrations reported here and those previously published have been explained. These techniques are now ready to serve as tools for researching neurologic diseases.  Bibliography  [1] 1.1. Rabi, J . R. Zacharias, S. Millman, and P. Kusch. A new method of measuring nuclear magnetic moments. Phys. Rev. 53, 318 (1938). [2] I. I. Rabi, S. Millman, P. Kusch, and J . R. Zacharias. The molecular beam resonance method for measuring nuclear magnetic moments. Phys. Rev. 55, 526-535 (1939). [3] F . Bloch, W . W . Hansend, and M . Packard. Nuclear induction. Phys. Rev. 69, 127 (1946). [4] F. Bloch. Nuclear induction. Phys. Rev. 70, 460 (1946). [5] E . M . Purcell, H . C . Torrey, and R. V . Pound. Resonance absorption by nuclear magnetic moments in a solid. Phys. Rev. 69, 37 (1946). [6] P. C. Lauterbur. Image formation by induced local interactions: examples employing nuclear magnetic resonance. Nature 242, 190-191 (1973). [7] R. R. Ernst and W . A . Anderson. Application of Fourier transform spectroscopy to magnetic resonance. Rev. Sci. Instr. 37, 93-102 (1965). [8] E . B . Cady, A . M . Costello, M . J . Dawson, D . T. Delpy, P. L . Hope, E . O. Reynolds, P. S. Tofts, and D . R. Wilkie. Non-invasive investigation of cerebral metabolism in newborn infants by phosphorus nuclear magnetic resonance spectroscopy.  Lancet 1, 1059-1062  (1983). [9] R. L . Nunnally.  In vivo monitoring of metabolism with nuclear magnetic resonance  spectroscopy. Seminars in Nuclear Medicine 13, 377-382 (1983).  91  Bibliography  92  [10] P. A . Bottomley, W . A . Edelstein, F . T. H . , and W . A . Adams. In vivo solvent-suppressed localized hydrogen nuclear magnetic resonance spectroscopy: a window to metabolism? Proceedings of the National Academy of Sciences of the United States of America 8 2 , 2148-2152 (1985). [11] J . Frahm, K . D . Merboldt, and W . Hanicke.  Localized proton spectroscopy using  stimulated echoes. J. Magn. Reson. 7 2 , 502-508 (1987). [12] Proceedings of the International Society for Magnetic Resonance in Medicine (2000). [13] N . De Stefano, P. M . Matthews, and D . L . Arnold.  Reversible decreases in N -  acetylaspartate after acute brain injury. Mag. Res. Med. 3 4 , 721-727 (1995). [14] M . A . Foster. Magnetic Resonance in Medicine and Biology. Pergamon Press, New York (1984). [15] H . H . Tallan. Studies of the distribution of N-Acetyl-L-Aspartic acid in brain. J. Biol. Chem. 2 2 4 , 41-45 (1956). [16] D. L . Birken and W . H . Oldendorf. N-Acetyl-L-Aspartic acid: a literature review of a compound prominent in the H - N M R spectroscopic studies of brain. Neurosci. Biobehav. 1  Rev. 1 3 , 23-31 (1989). [17] J. Urenjak, S. R. Williams, D. G . Gadian, and M . Nobel.  Proton nuclear magnetic  resonance spectroscopy unambiguously identifies different neural cell types. Neuroscience 13, 981-989 (1993). [18] K . J . Koller, R. Zaczek, and J . Coyle. N-Acetyl-Apartyl-Glutamate: regional levels in rat brain and the effects of brain lesions as determined by a new H P L C method.  J.  Neurochem. 4 3 , 1136-1142 (1984). [19] J .  R.  Moffett  and  acetylaspartylglutamate  M . A . A . Namboodiri. and N-aceytlaspartate  Differential  distribution of N -  immunoreactivities in rat forebrain.  Bibliography  93  Journal of Neurocytology 24, 409-433 (1995). [20] T . B . Patel and J . B . Clarke. Lipogenesis in the brain of suckling rats. Studies on the mechansim of mitochondrial-cytosolic carbon transfer. Biochemical Journal 188, 163-168 (1990). [21] S. R. Williams. In vivo proton spectroscopy: experimental aspects and potential, pp. 55-72 (1992). [22] J . R. Moffett, M . A . A . Namboodiri, and J . H . Neale. fixation  for immunohistochemistry:  Enhanced carbodiimide  application to the comparative distributions of  N-acetylaspartylglutamate and N-acetylaspartate immunoreactivities in rat brain.  J  Histochem Cytochem 41, 559-570 (1993). [23] P. J . W . Pouwels and J . Frahm. Differential distribution of N A A and N A A G in human brain as determined by quantitative localized proton M R S . NMR Biomed 10, 73-78 (1997). [24] P. J . W . Pouwels and J . Frahm. Regional metabolite concentrations in human brain as determined by quantitative localized proton M R S . Magn Reson Med 39, 53-60 (1998). [25] J . V . Nadler and J . R. Cooper. N-acetyl-L-aspartic acid content of human neural tumours and bovine peripheral nervous tissues. Journal of Neurochemistry 19, 313-319 (1972). [26] O. A . C. Petroff, D . D . Spencer, J . R. Alger, and J. W . Prichard. High-field proton magnetic resonance spectroscopy of human cerebrum obtained during surgery for epilepsy. Neurobiology 39, 1197-1202 (1989). [27] S. S. G i l l , D. G . T. Thomas, N . van Bruggen, D. G . Gadian, C. J . Peden, J . D. Bell, I. J . Cox, D . K . Menon, R. A . lies, D. J . Bryant, and G . A . Coutts. Proton M R Spectroscopy of intracranial tumours: in vivo and in vitro studies. Tomography 14, 497-504 (1990).  Journal of Computer Assisted  Bibliography  [28] J . Peeling and G . Sutherland.  94  High-resolution studies of extracts of human cerebral  neoplasms. Mag. Res. Med. 24, 123-136 (1989). [29] T . Michaelis, K . - D . Merboldt, H . Bruhn, W . Hanicke, and J. Frahm.  Absolute  concentrations of metabolites in the adult human brain in vivo: quantification of localized proton M R spectra. Radiology 187, 219-227 (1993). [30] F . H . Bruns, H . Reinauer, and W . Stork. Analyticsche und biologische studien liber den gehalt an N-acetyl-L-aspartat im gehirn. Hoppe-Seyler's Z Physiol Chem 348, 512-518 (1967). [31] F. B . Goldstein. Amidohydrolases of brain: enzymatic hydrolysis of N-acetyl-L-aspartate and other N-acetyl-L-amino acids. Journal of Neurochemistry 26, 45-49 (1979). [32] A . F . d'Adamo, J. C. Smith, and C. Woiler.  The occurrence of N-acetylaspartate  amidohydrolase (amionoacylase II) in the developing rat.  Journal of Neurochemistry  20, 1275-1278 (1973). [33] D. L . Arnold, P. M . Matthews, G . Francis, and J . Antel. Proton magnetic resonance spectroscopy of human brain in vivo in the evaluation of muliple sclerosis: assessment of the load of disease. Mag. Res. Med. 14, 154-159 (1990). [34] P. C. Williamson, D. J . Drost, J . A . Stanley, T. J . Carr, S. Morrison, and H . Merskey. Localized phosphorus 31 magnetic resonance spectroscopy in chronic schizophrenic patients and normal controls. Arch Gen Psychiatry 48, 578 (1991). [35] J . A . Stanley, P. C. Williamson, D. J . Drost, T. J . Carr, R. J . Rylett, A . Malla, and R. T. Thompson. A n in vivo study of the prefrontal cortex of schizophrenic patients at different stages of illness via phosphorus magnetic resonance spectroscopy. Arch Gen Psychiatry 52, 399-406 (1995). [36] J . A . Stanley, P. C. Williamson, D . J. Drost, R. J. Rylett, T. J. Carr, A . Malla, and R. T.  Bibliography  95  Thompson. A n in vivo proton magnetic resonance spectroscopy study of schizophrenia patients. Schizophr Bull 22, 597-609 (1996). [37] A . L . Lehninger, D . L . Nelson, and M . M . Cox. Principles of biochemistry. New York : Worth Publishers, 2 edition (1993). [38] R. A . Meyer, H . L . Sweeney, and M . J . Kushmerick.  A simple analysis of the  "phosphocreatine shuttle". American Journal of Physiology 246, C365-C377 (1984). [39] P. Kaldis, W . Hemmer, E . Zanolla, D . Holtzman, and T. Wallimann.  'Hot spots'  of creatine kinase localization in brain: cerebellum, hippocampus and choroid plexus. Developmental Neuroscience 18, 542-554 (1996). [40] S. E . Ilyin, G . Sonti, G . Molloy, and C . R. Plata-Salaman. Creatine kinase-B-mRNA levels in brain regions from male and female rats. Molecular Brain Research 41, 50-56 (1996). [41] O. H . Lowry, S. J . Berger, M . M . Y . C h i , J . G . Carter, H . Blackshaw, and W . Outlaw. Diversity of metabolic patterns in human brain tumours. I. High energy phosphate compounds and basic composition. Journal of Neurochemistry 29, 959-977 (1977). [42] P. A . Bottomley, C. J . Hardy, J . P. Cousins, M . Armstrong, and W . A . Wagle. AIDS dementia complex: brain high-energy phosphate metabolite deficits. Radiology 179, 407411 (1989). [43] K . Roth, B . Hubesch, and D . J . Meyerhoff. Noninvasive quantitation of phosphorus metabolites in human tissue by N M R spectroscopy. J. Magn. Reson. 81, 299-311 (1989). [44] P. R. Luyten, J . P. Groen, J . W . A . H . Vermeulen, and J . A . den Hollander. Experimental approaches to image localized human (1989).  3 1  P N M R spectroscopy. Mag. Res. Med. 11, 1-21  Bibliography  96  [45] P. A . Bottomley, , J . P. Cousins, and D . L . Pendrey. Alzheimer dementia: quantification of energy metabolism and mobile phosphoesters with P-31 N M R spectroscopy. Radiology 1 8 3 , 695-699 (1992). [46] K . Dross and H . Kewitz. Concentration and origin of choline in the rat brain. Naunyn Schmiedebergs Arch Pharmacol 2 7 4 , 91-106 (1972). [47] B . Tunggal, K . Hofmann, and W . Stoffel.  In vivo  1 3  C nuclear magnetic resonance  investigations of choline metabolism in rabbit brain. Mag. Res. Med. 1 3 , 90-102 (1990). [48] D . H . Miller, S. J . Austin, A . Connelly, B . D. Youl, D. G . Gadian, and W . I. McDonald. Proton magnetic resonance spectroscopy of an acute and chronic lesion in muliple sclerosis. Lancet 3 3 7 , 58-59 (1991). [49] S. Cerdan, R. Parrilla, J . Santoro, and M . Rico.  :  H N M R detection of cerebral myo-  inositol. FEBS Letters 1 8 7 , 167-172 (1985). [50] A . Brand, C. Richter-Landsberg, and D. Leibfritz.  Multinuclear N M R studies on the  energy metabolism of glial and neuronal cells. Developmental Neuroscience 1 5 , 289-298 (1993). [51] R. Kreis, T. Ernst, and B . D . Ross. Absolute quantitation of water and metabolites in the human brain. II Metabolite concentrations. Journal of Magnetic Resonance, Series B 1 0 2 , 9-19 (1993). [52] M . J . Berridge and R. F . Irvine. Inositol phosphates and cell signalling. Nature 3 4 1 , 197-205 (1989). [53] R. Knorle, D. Assmann, G . B . Landwehrmeyer, R. Scheremet, K . Muller, and T. J . Feuerstein. Aspartate, glutamate, glutamine, glycine and 7-aminobutyric acid in human bioptic neocortical areas: comparison to autoptic tissue. Neuroscience Letters 2 2 1 , 167172 (1997).  Bibliography  97  [54] T . L . Perry, S. Hansen, K . Berry, C . Mok, and D . Lesk. Free amino acids and related compounds in biopsies of human brain. Journal of Neurochemistry 18, 521-528 (1971). [55] T. L . Perry, S. Hansen, and S. S. Gandham. Postmortem changes of amino compounds in human and rat brain. Journal of Neurochemistry 36, 407-412 (1981). [56] A . Martinez-Hernandez, K . P. Bell, and M . D . Norenberg. Glutamine synthetase: glial localization in brain. Science 195, 1356-1358 (1977). [57] B . D . Ross, E . R. Danielsen, and S. Bluml. Proton magnetic resonance spectroscopy: the new gold standard for diagnosis of clinical and subclinical hepatic encephalopathy? Dig Dis. 14 S u p p l 1, 30-39 (1996). [58] M . Annett. The binomial distribution of right, mixed and left handedness.  Q J Exp  Psychol 19, 327-333 (1967). [59] Y . Wang and S.-J. L i . Differentiation of metabolic concentrations between gray matter and white matter of human brain by in vivo magnetic resonance spectroscopy.  Magn  Reson Med 39, 28-33 (1998). [60] S. W . Provencher. Estimation of metabolite concentrations from localized in vivo proton N M R spectra. Magn Reson Med 30(6), 672-9 (1993). [61] J . A . Stanley, D . J . Drost, P. C. Williamson, and R. T. Thompson. The use of a priori knowledge to quantify short echo in vivo H M R spectra. Magn Reson Med 34, 17-24 1  (1995). [62] R. Bartha, D . J . Drost, and P. C. Williamson. Factors affecting the quantification of short echo in-vivo *H M R spectra: prior knowledge, peak elimination, and filtering. NMR Biomed 12, 205-216 (1999). [63] J . Hennig, H . Pfister, T. Ernst, and D. Ott. Direct absolute quantification of metabolites  Bibliography  98  in the human brain with in vivo localized proton spectroscopy. NMR Biomed 5(4), 193199 (1992). [64] U . Klose. In vivo proton spectroscopy in the presence of eddy currents. Mag. Res. Med. 14, 26-30 (1990). [65] S. W . Provencher. LCModel and LCMgui user's manual (2000). [66] K . P. Whittall and A . L . MacKay. Quantitative interpretation of N M R relaxation data. Journal of Magnetic Resonance 84, 134-152 (1989). [67] A . L . MacKay, K . Whittall, J . Adler, D . L i , D . Paty, and D . Graeb. In vivo visualization of myelin water in brain by magnetic resonance.. Magn Reson Med 31(6), 673-677 (1994). [68] A . Simmons, M . Smail, E . Moore, and S. C. R. Williams. Serial precision of metabolite peak area ratios and water referenced metabolite peak areas in proton M R spectroscopy of the human brain. Magn Reson Imaging 16(3), 319-330 (1998). [69] C. O. Due, O. M . Weber, A . H . Trabesinger, D . Meier, and P. Boesiger. Quantitative H 1  M R S of the human brain in vivo based on the simulation phantom calibration strategy. Magn Res Med 39(3), 491-496 (1998). [70] I. Marshall, J. Wardlaw, J. Cannon, J. Slattery, and R. J. Sellar. Reproducibility of metabolite peak areas in H M R S of brain. Magn Reson Imaging 14(3), 281-292 (1996). 1  [71] A . Berolino, J . H . Callicott, S. Nawroz, V . S. Mattay, J. H . Duyn, G . Tedeschi, J . A . Frank, and D. R. Weinberger. Reproducibility of proton magnetic resonance spectroscopic imaging inpatients with schizophrenia. Neuropsychopharmacology 18(1), 1-9 (1998). [72] W . M . Brooks, S. D . Friedman, and C . A . Stidley. Reproducibility of ^ - M R S in vivo. Magn Res Med 41(1), 193-197 (1999). [73] R. E . Walpole. Introduction to statistics, chapter 8, pp. 166-167. MacMillan Publishing Co., Inc. (1974).  Bibliography  99  [74] P. Christiansen, P. Toft, H . B . Larsson, M . Stubgaard, and O. Henriksen.  The  concentration of N-acetyl aspartate, creatine + phosphocreatine, and choline in different parts of the brain in adulthood and senium. Magn Reson Medicine 11(6), 799-806 (1993). [75] P. A . Narayana, D . Johnston, and D . P. Flamig.  In vivo proton magnetic resonance  spectroscopy studies of human brain. Magn Reson Imaging 9(3), 303-8 (1991). [76] P. B . Toft, P. Christiansen, 0 . Pryds, H . C. Lou, and 0 . Henriksen. T l , T2, and concentrations of brain metabolites in neonates and adolescents estimated with 1H M R spectroscopy. J Magn Reson Imaging 4(1), 1-5 (1994). [77] P. Gideon and O. Henriksen. In vivo relaxation of N-acetyl-aspartate, creatine plus phosphocreatine, and choline containing compounds during the course of brain infarction: a proton M R S study. Magn Reson Imaging 10(6), 983-8 (1992). [78] J. Frahm, H . Bruhn, M . L . Gyngell, K . D. Merboldt, W . Hanicke, and R. Sauter. Localized proton N M R spectroscopy in different regions of the human brain in vivo. Relaxation times and concentrations of cerebral metabolites. Magn Reson Med 11(1), 47-63 (1989). [79] K . Kamada, K . Houkin, K . Hida, H . Matsuzawa, Y . Iwasaki, H . Abe, and T. Nakada. Localized proton spectroscopy of focal brain pathology in humans: significant effects of edema on spin-spin relaxation time. Magn Reson Med 31(5), 537-40 (1994). [80] R. Longo, A . Bampo, V . Rossella, S. Magnaldi, and A . Giorgini. Absolute quantitation of brain l h nuclear magnetic resonance spectra comparison of different approaches. Investigative Radiology 30, 199-203 (1995). [81] J . Knight-Scott and S.-J. L i . Application of homospoil saturation recovery to the measurement of longitudinal relaxation times of 1H metabolites in the occipital lobe of human brain. In Proceedings of the International Society for Magnetic Resonance in Medicine (1997).  Bibliography  100  [82] B . Hallgren and P. Sourander. The effect of age on the non-haemin iron concentration in the human brain. J. Neurochem 3, 41-51 (1958). [83] S. Ogawa, D . W . Tank, R. Menon, J . M . Ellermann, S. G . K i m , H . Merkle, and K . Ugurbil. Intrinsic signal changes accompanying sensory stimulation: functional brain mapping with magnetic resonance imaging. Proc. Nat. Acad. Sci. USA 89, 5951-5955 (1992). [84] P. Christiansen, 0 . Henriksen, M . Stubgaard, P. Gideon, and H . B . W . Larsson. In vivo quantification of brain metabolites by H - M R S using water as an internal standard. Mag. 1  Res. Imag. 11, 107-118 (1993). [85] P. B . Barker, B . J . Soher, S. J . Blackband, J . C . Chatham, V . P. Mathews, and R. N . Bryan. Quantitation of proton N M R spectra of the human brain using tissue water as an internal concentration reference. NMR Biomed 6, 89-94 (1993). [86] E . R. Danielsen, T . Michaelis, and B . D . Ross.  Three methods of calibration in  quantitative proton mr spectroscopy. J. Magn. Reson. 106, 287-291 (1995). [87] C. Slichter. Principles of magnetic resonance. Berlin ; New York : Springer-Verlag, 2 edition (1978). [88] K . L . Behar, D . L . Rothman, D. D. Spencer, and O. A . C. Petroff.  Analysis of  macromolecule resonances in rl N M R spectra of human brain. Mag. Res. Med. 32, l  294-303 (1994). [89] K . P. Whittall, A . L . MacKay, D. A . Graeb, R. A . Nugent, D . K . B . L i , and D . W . Paty. In vivo measurement of T distributions and water contents of normal human brain. Mag. 2  Res. Med. 37, 34-43 (1997). [90] T. Ernst, R. Kreis, and B . D . Ross. Absolute quantitation of water and metabolites in the human brain. I. Compartments and water. J. Magn. Reson. 102, 1-8 (1993).  Bibliography  101  [91] D . L . Arnold, P. M . Matthews, G . S. Francis, J . O'Connor, and J . Antel. Proton magnetic resonance spectroscopic imaging for metabolic characterization of demyelinating plaques. Ann. Neurol. 31, 235-241 (1992). [92] H . Bruhn, J . Frahm, K . D . Merboldt, F . Hanefeld, H . J . Christen, B . Kruse, and H . J . Bauer. Muliple sclerosis in children: cerebral metabolic alterations monitored by localized proton magnetic resonance spectroscopy in vivo. Ann. Neurol. 32, 140-150 (1992). [93] P. M . Matthews, G . Francis, J . Antel, and D. L . Arnold. Proton magnetic resonance spectroscopy for metabolic characterization of plaques in muliple sclerosis. Neurol. 41, 1251-1256 (1991). [94] P. Van Hecke, G . Marchal, K . Johannik, P. Demaerel, G . Wilms, H . Carton, and A . L . Baert. Human brain proton localized N M R spectroscopy in multiple sclerosis. Mag. Res. Med. 18, 199-206 (1991). [95] C. A . Davie, C. P. Hawkins, G . J . Barker, A . Brennan, P. S. Tofts, D . H . Miller, and W . I. McDonald. Serial proton magnetic resonance spectroscopy in acute multiple sclerosis lesions. Brain 117, 49-58 (1994). [96] R. A . Koopmans, D . K . B . L i , G . Zhu, P. S. Allen, A . Penn, and D . W . Paty. Magnetic resonance spectrsocopy of multiple sclerosis:  in vivo detection of myelin breakdown  products. Lancet 341, 631-632 (1993). [97] P. A . Brex, G . J . M . Parker, S. M . Leary, P. D. Molyneux, G . J. Barker, C. A . Davie, A . J. Thompson, and D . H . Miller. Lesion heterogeneity in multiple sclerosis: a study on the relations between appearances on T i weighted images, T j relaxation times, and metabolite concentrations. J Neurol Neurosurg Psychiatry 68, 627-632 (2000). [98] J . Foong, L . Rozewicz, C. A . Davie, A . J. Thompson, D . H . Miller, and M . A . Ron. Correlates of executive function in multiple sclerosis: the use of magnetic resonance  Bibliography  102  spectroscopy as an index of focal pathology.  J Neuropsychiatry  Clin Neurosci  1 1 ( 1 ) ,  45-50 (1999). . [99] A . Tourbah, J . L . Stievenart, O. Gout, B . Fontaine, R. Liblau, C. Lubetzki, A . Cabanis, and O. Lyon-Caen.  Localized proton magnetic resonance spectroscopy in relapsing  remitting versus secondary progressive multiple sclerosis. Neurology 53(5), 1091-1098 (1999). [100] S. Sarchielli, O. Presciutti, G . P. Pelliccioli, R. Tarducci, G . Gobbi, P. Chiarini, F . Alberti, A.and Vicinanza, and V . Gallai. Absolute quantification of brain metabolites by proton magnetic resonance spectroscopy in normal-appearing white matter of multiple sclerosis patients. Brain 1 2 2 , 513-521 (1999). [101] S. M . Leary, C . A . Davie, G . J . M . Parker, V . L . Stevenson, L . Wang, G . J . Barker, D. H . Miller, and A . J . Thompson.  1  H Magnetic resonance spectroscopy of normal appearing  whtie matter in primary progressive multiple sclerosis. J Neurol 2 4 6 , 1023-1026 (1999). [102] P. A . Brex, B . Gomez-Anson, G . J. M . Parker, P. D . Molyneux, K . A . Miszkiel, G . J . Barker, D. G . MacManus, C. A . Davie, G . T. Plant, and D. H . Miller.  Proton M R  spectroscopy in clinical isolated syndromes suggestive of multiple sclerosis. Journal of the Neurological Sciences 1 6 6 , 16-22 (1999). [103] N . De Stefano, P. M . Matthews, L . Fu, S. Narayanan, J . Stanley, G . S. Francis, J. P. Antel, and D. L . Arnold. Axonal damage correlates with disability in patients with relapsingremitting multiple sclerosis. Results of a longitudinal magnetic resonance spectroscopy study. Brain 1 2 2 , 1469-1477 (1999). [104] A . Bitsch, H . Bruhn, V . Vougioukas, A . Stringaris, H . Lassman, J . Frahm, and W . Briick. Inflammatory C N S demyelination: histopathologic correlation with in vivo quantitative proton mr spectroscopy. Am. J. Neuroradiol. 2 0 , 1619-1627 (1999).  Bibliography  103  [105] C . Labadie, D . Gounot, Y . Mauss, and B . Dumitreso. Data sampling in M R relaxation. MAGMA  2 , 383-385 (1994).  [106] S. D . Friedman, W . M . Brooks, R . E . Jung, S. J . Chiulli, J . H . Sloan, B . T. Montoya, B . L . Hart, and R. A . Yeo. Quantitative proton M R S predicts outcome after traumatic brain injury. Neurology 52(7), 1384-1391 (1999). [107] J . Pietz, R. Kreis, H . Schmidt, U . K . Meyding-Lamade, A . Rupp, and C . Boesch. Phenylketonuria: findings at M R imaging and localized in vivo H-1 M R spectroscopy of the brain in patients with early treatment. Radiology 2 0 1 , 413-420 (1996). [108] J . H . Walter. Late effects of phenylketonuria. Arch Dis Child 7 3 , 485-486 (1995). [109] J . H . Walter, F . White, J . E . Wraith, J . P. Jenkins, and B . P. Wilson. Complete reversal of moderate/severe brain M R I abnormalities in a patient with classical phenylketonuria. J Inherit Metab Dis 2 0 , 367-369 (1997). [110] M . A . Cleary, J. H . Walter, J . E . Wraith, F . White, K . Tyler, and J . P. Jenkins. Magnetic resonance imaging in phenylketonuria: reversal of cerebral white matter change. J Pediatr 1 2 7 , 251-255 (1995). [ I l l ] U . Bick, K . Ullrich, U . Stober, H . Moller, G . Schuierer, A . C. Ludolph, C. Oberwittler, J. Weglage, and U . Wendel. hyperphenylalaninaemia:  White matter abnormalities in patients with treated  magnetic resonance relaxometry and proton spectroscopy  findings. Eur J Pediatr 1 5 2 , 1012-1020 (1993). [112] R. Kreis, J . Pietz, J . Penzien, N . Herschkowitz, and B . C. Identification and quantitation of phenylalanine in the brain of patients with phenylketonuria by means of localized in vivo 1H magnetic-resonance spectroscopy. J Magn Reson B 1 0 7 , 242-251 (1995). [113] H . E . Moller, P. Vermathen, K . Ullrich, J . Weglage, H . G . Koch, and P. E . Peters. In-vivo N M R spectroscopy in patients with phenylketonuria: changes of cerebral phenylalanine levels under dietary treatment. Neuropediatrics 2 6 , 199-202 (1995).  Bibliography  104  [114] E . J . J . Novotny, M . J . Avison, N . Herschkowitz, O. Petroff, J . W . Prichard, M . R. Seashore, and D. L . Rothman. In vivo measurement of phenylalanine in human brain by proton nuclear magnetic resonance spectroscopy. Pediatr Res 37, 244-249 (1995). [115] M . Dezortova, L . Hejcmanova, and M . Hajek. phenylketonuria? MAGMA  Decreasing choline signal-a marker of  4, 181-186 (1996).  [116] H . E . Moller, J . Weglage, D . Wiedermann, P. Vermathen, U . Bick, and K . Ullrich. Kinetics of phenylalanine transport at the human blood-brain barrier investigated in vivo. Brain Res 778, 329-337 (1997). [117] H . E . Moller, J . Weglage, D . Wiedermann, and K . Ullrich.  Blood-brain barrier  phenylalanine transport and individual vulnerability in phenylketonuria. J Cereb Blood Flow Metab 18, 1184-1191 (1998). [118] J . Weglage, H . E . Moller, D. Wiedermann, S. Cipcic-Schmidt, J . Zschocke, and K . Ullrich. In vivo N M R spectroscopy in patients with phenylketonuria: interindividual differences in brain phenylalanine concentrations.  clinical significance of J Inherit Metab Dis  21, 81-82 (1998). [119] J . Pietz and R. Kreis. Large neutral amino acids block phenylalanine transport into brain tissue in patients with P K U . J Clin Investigation 103, 1169-1178 (1999). [120] R. A . Moats, R. Koch, K . Moseley, P. Guldberg, F. Guttler, R. G . Boles, and M . D. J. Nelson. Brain phenylalanine concentration in the management of adults with phenylketonuria. J Inherit Metab Dis 23, 7-14 (2000). [121] B . H . Natelson, J . M . Cohen, I. Brassloff, and H . J . Lee. A controlled study of brain magnetic resonance imaging in patients with the chronic fatigue syndrome. J Neurol Sci 120, 213-217 (1993). [122] R. B . Schwartz, B . M . Garada, A . L . Komaroff, H . M . Tice, M . Gleit, F . A . Jolesz, and B. L . Holman. Detection of intracranial abnormalities in patients with chronic fatigue  Bibliography  105  syndrome: comparison of M R imaging and S P E C T .  Am J Roentgenol 162,  935-941  (1994). [123] H . Cope, A . Pernet, B . Kendall, and A . David.  Cognitive functioning and magnetic  resonance imaging in chronic fatigue. Br J Psychiatry 167, 86-94 (1995). [124] A . Greco, C . Tannock, J . Brostoff, and D . C . Costa.  Brain M R in chronic fatigue  syndrome. Am. J. Neuroradiol. 18, 1265-1269 (1997). [125] P. A . Keenan. Brain M R I abnormalities exist in chronic fatigue syndrome. J Neurol Sci 171, 1-2 (1999). [126] G . Lange, J . DeLuca, J . A . Maldjian, H . Lee, L . Tiersky, and B . H . Natelson. Brain M R I abnormalities exist in a subset of patients with chronic fatigue syndrome. J Neurol Sci 171, 3-7 (1999). [127] M . Ichise, I. E . Salit, S. E . Abbey, D . G . Chung, B . Gray, J . C. Kirsh, and M . Freedman. Assessment of regional cerebral perfusion by 99Tcm-HMPAO S P E C T in chronic fatigue syndrome. Nucl Med Commun 13, 767-772 (1992). [128] R. B . Schwartz, B . M . Garada, A . L . Komaroff, H . M . Tice, M . Gleit, F . A . Jolesz, and B. L . Holman. Detection of intracranial abnormalities in patients with chronic fatigue syndrome: comparison of M R imaging and S P E C T .  Am J Roentgenol 162,  935-941  (1994). [129] B : Fischler, H . D'Haenen, R. Cluydts, V . Michiels, K . Demets, A . Bossuyt, L . Kaufman, and K . De Meirleir.  Comparison of 99m T c H M P A O S P E C T scan between chronic  fatigue syndrome, major depression and healthy controls: an exploratory study of clinical correlates of regional cerebral blood flow. Neuropsychobiology 34, 175-183 (1996). [130] H . Cope and A . S. David. Neuroimaging in chronic fatigue syndrome. J Neurol Neurosurg Psychiatry 60, 471-473 (1996).  Bibliography  106  [131] H . H . Abu-Judeh, S. Levine, M . Kumar, H . el Zeftawy, S. Naddaf, J . Q. Lou, and H . M . Abdel-Dayem. Comparison of S P E C T brain perfusion and 18F-FDG brain metabolism in patients with chronic fatigue syndrome. Nucl Med Commun 19, 1065-1071 (1998). [132] G . Lange, S. Wang, J . DeLuca, and B . H . Natelson. Neuroimaging in chronic fatigue syndrome. Am J Med 1 0 5 ( 3 A ) , 50S-53S (1998). [133] U . Tirelli, F . Chierichetti, M . Tavio, C . Simonelli, G . Bianchin, P. Zanco, and G . Ferlin. Brain positron emission tomography ( P E T ) in chronic fatigue syndrome: preliminary data. Am J Med 1 0 5 ( 3 A ) , 54S-58S (1998). [134] W . Block, F. Traber, C. K . K u h l , E . Keller, R. Lamerichs, J . Karitzky, H . Rink, and H . H . Schild.  31P-MR spectroscopy of peripheral skeletal musculature under load:  demonstration of normal energy metabolites compared with metabolic muscle diseases. Rofo Fortschr Geb Rontgenstr Neuen Bildgeb Verfahr 168, 250-257 (1998). [135] R. J. Lane, M . C. Barrett, D. J . Taylor, G . J . Kemp, and R. Lodi. Heterogeneity in chronic fatigue syndrome: evidence from magnetic resonance spectroscopy of muscle. Neuromuscul Disord 8, 204-209 (1998). [136] K . K . McCully and B . H . Natelson. Impaired oxygen delivery to muscle in chronic fatigue syndrome. Clin Sci (Colch) 97, 603-608 (1999). [137] A . Tomoda, T . Miike, E . Yamada, H . Honda, T. Moroi, M . Ogawa, Y . Ohtani, and S. Morishita. Chronic fatigue syndrome in childhood. Brain Dev 2 2 , 60-64 (2000). [138] R. L . Dixon and K . E . Ekstrand. The physics of proton N M R . Medical Physics 8, 807-818 (1982). [139] W . S. Hinshaw and A . H . Lent. A n introduction to N M R imaging: from the Bloch Equation to the Imaging Equation. IEEE 71, 338-350 (1983).  Bibliography  107  [140] A . Abragam. The principles of nuclear magnetism.  Oxford [Oxfordshire] : Clarendon  Press ; New York : Oxford University Press (1983). [141] E . Fukushima and S. B . W . Roeder. Experimental pulse NMR : a nuts and bolts approach. Reading, Mass. : Addison-Wesley Pub. Co., Advanced Book Program (1981). [142] Bloembergen, Purcell, and Pound. Relaxation Effects in Nuclear Magnetic Resonance Absorption. Phys. Rev. 7 3 , 679-712 (1948). [143] L . C. Hebel and C. P. Slichter. Nuclear Spin Relaxation in Normal and Superconducting Aluminum. Phys. Rev. 1 1 3 , 1504-1519 (1959). [144] R. K . Harris.  Nuclear Magnetic Resonance Spectroscopy - A Physiochemical  View.  Pitman Books L t d . (1983). [145] R. M . Silverstein, G . C. Bassler, and T . C. Morrill. Spectometric Identification of Organic Compounds. John Wiley & Sons (1991).  Appendix A  Physics of M R  A.l  T h e P h y s i c s of M a g n e t i c R e s o n a n c e  The most fundamental explanations of Nuclear Magnetic Resonance ( N M R ) can be found in quantum mechanics (QM). At its most elementary level, N M R is a phenomenon which describes .the interaction of a nucleus with a magnetic field. Within this description, one can explain why a certain frequency of rf excitation is needed to 'flip' a spin, how motions of the nuclei narrow the linewidth, and why, from a fluid, lineshapes are Lorentzian (in the limit of rapid motion.) In this chapter both the quantum mechanical description and the semi-classical description are presented.  The explanations for the phenomena listed above are described in terms of  quantum mechanics, but are not derived. There are many good reference books which derive this material. For an introductory mathematical treatment please read [138, 139] and for greater detail consult [87, 140, 141]. The basic equations of quantum mechanics are quickly reviewed to ensure clarity of notation.  A.1.1  Basic Equations of Q M  There are four basic ideas which underlie all of Q M . These ideas are described in terms of a particle with a certain angular momentum. A l l particles are defined in terms of their s p i n state. A spin state is a vector which is a linear combination of all of the discrete states it could take on. For a particle with an angular momentum, m, measured along an axis, z, where the values of m could range from —I, —7—1,..., 7 — 1,1, where I is an integer or half integer called the angular momentum quantum number,  108  109  Appendix A. Physics of MR  the state can be written as  |*> = $ > | m >  (A-l)  m  m  where |*J/) and \m) are vectors and  CLfji  ELT6  complex amplitudes associated with each |m).  The vectors \m) were chosen to have certain values, m , when measured along the z axis. A n eigenvalue equation describes the state of the particle:  (A-2)  I \m) = m\m) z  where I is an 'operator' that, when acting on |m), gives an eigenvalue, m , which is the value z  of the angular momentum of the state \m) along the z axis. I could operate upon the spin z  state giving I | * ) = Y, rnh\m).  (A-3)  a  2  m  The result of any experiment done must give a real quantity. This quantity is calculated by taking the expectation value of the operator, (*\Iz\*) = J2 ama* (m'\I \m) ml  (A-4)  z  m,m'  If the basis states are orthonormal ((m'|m) = < 5 ' ) , then the above equation can be re-written m  ]m  as (WzW  = Y \ m?m.  (A-5)  a  J  m  This expectation value can be explained in two ways. If  is the state of a single particle,  then | a | is the probability that when operating on the state, one will measure the value m . 2  m  If |^) describes the state of an ensemble of particles, then J2 l m | a  m  2 r n  i  s  the mean eigenvalue  which would be measured, weighted by each value's probability. Since the eigenvectors are defined in relation to the operator along the z axis, it is impossible to find eigenvalues of the eigenvectors when acting with the angular momentum operators along the x or y axes. This is due to the Heisenberg Uncertainty Principle, which describes the limit of knowledge one can have of any state. The principle comes through in commutation relations  Appendix A. Physics of MR  110  which show that two or more angular momenta cannot be measured simultaneously: [ 4 , Ij,] = I Iy ~ lyl X  (A-6)  = HZ  X  The S c h r o d i n g e r E q u a t i o n describes what happens to a state when acted on by an energy operator, the Hamiltonian H.  ih^mt))  (A-7)  = #!*(*)>  where Tt is Planck's constant divided by 2TT. If H is not time dependent, then the solution to equation A-7 is: |tf(t)) =  tf(*)|tf(0)).  (A-8)  where U(t) is the evolution operator, defined as U(t) = e ^  i H t  l \  (A-9)  h  In order to understand the phenomena listed in the introduction, various Hamiltonians need to be introduced. The following sections will discuss these operators and their affect on the states.  A . 1.2  T h e Zeeman Hamiltonian  The Zeeman Hamiltonian Hz is given by H  z  = -jhB l  (A-10)  0 z  where B is the magnetic field strength and 7 is the gyromagnetic ratio. For protons, 7 = 0  2.675 x 10 r a d - s T , and I = \. The energy separation between levels is jhB 8  _ 1  _ 1  c  and the  proton precesses about the B field with a frequency 0  co = 5 . 7  (A-ll)  0  Since Hz is not time dependent, an evolution operator can be written as U (t) = z  = e^ " ^. 8  1  (A-12)  Appendix A. Physics of MR  111  A state acted on by the evolution operator precesses at a frequency w , defined by u 0  a given time, t, the precession would go through an angle jB t. 0  a  = ^B . 0  In  Thus, the Zeeman Hamiltonian  explains precession of a nucleus in a magnetic field and how the magnetic field influences the energy state of a nuclear spin. It should be noted that when one speaks of the interactions of the nuclei in the x-y plane, for ease of discussion, all equations are transformed into a frame rotating at the Larmor frequency.  A.1.3  Dipolar Interactions and Motional Narrowing  The systems discussed in this thesis are in solution, hence the nuclei are oriented randomly. Each nucleus perturbs the field felt by surrounding nuclei. Since the nucleus being investigated is a spin ^ nucleus, this perturbation is called the dipolar interaction. Its Hamiltonian is given by £ ^ 7 ^  = ^  D  H  3  [ T . • I, - 3(1, • )(Ii  (A-13)  • )].  Tij  rij  In most N M R experiments, Ho is quite weak compared to Hz- Since the diagonal terms give energy shifts on the order of ^ f f i and the off-diagonal terms shift the energy by ( ^ f / ) , to a 1  3  2  ij  l  first order approximation only the diagonal terms influence the energy levels. The Hamiltonian can then be re-written as ffr  Jo  =  ^^^4-i( 1  3 c o s 2 e  y)[3/«/j -Ii-Ij].  (A-14)  2  In the case of molecular tumbling motion (the molecular motion in most liquids), the H  Do  is  averaged over all possible orientations of the nuclei with respect to B . Providing that the nuclei 0  sample all possible orientations on the timescale of the dipolar interaction, then < cos 6> >= | . 2  Quantitatively, this gives a. narrowing of the spectrum. If there were only one resonance at a certain frequency, u  a  then, in the absence of molecular motion, as a result of the Dipolar  Hamiltonian perturbing the Zeeman energy state, there would be a range of frequencies at which the nuclei would resonate. W i t h molecular motion, the Ho  0  averages to zero, and the  spectrum narrows to only resonate at the Larmor frequency. In practice, the N M R spectra have  Appendix A. Physics of MR  112  a finite width due to spin relaxation and magnetic field inhomogeneities. A.1.4  Relaxation  A complete discussion of spin relaxation is beyond the scope of this thesis. A more qualitative explanation will be given in this section, referring to the ideas of quantum mechanics developed above. The original description of relaxation in the limit of rapid molecular motion was given by Bloembergen, Purcell, and Pound [142]; the theory is often referred to as the B P P theory. In the last section, the averaging of cos 9 led to HD = 0. The non-diagonal terms of Ho continue 2  0  to influence the spin states. These field fluctuations lead to spin relaxation. Spectral Density and Correlation Times It is useful here to introduce the concept of the spectral density function. The random field fluctuations discussed above can described by an autocorrelation function G(t) which is a measure of how rapidly the local field changes in magnitude and direction. The autocorrelation function for random tumbling is given as the scalar product G(i) oc h(t) • h(0) oc e~  t/Tc  (A-15)  where h(t) and h(0) are the local field measured at time t and time t = 0. This means that the probability of finding a correlation between the local field at time t and at t = 0 decreases as g-i/Vc  s o  that  T c j  the correlation time for the motion, is the mean time elapsed until there is no  correlation between field fluctuations. The spectral density, J(w) is the frequency spectrum corresponding to the autocorrelation function G(i) J(w) = / G{t)e- dt J oo ibjt  (A-16)  Conceptually, if two spins are moving randomly with respect to each other there will be an energy of interaction distributed randomly in frequency and time. The frequency dependence of the power is the spectral density and the time dependence is the autocorrelation function.  Appendix A.  Physics of MR  113  A typical term of the spectral density function has the form T / ( 1 + OJ T ). In a particular 2  c  2  C  system and for a given r , the spectral density is a constant at small ui and falls off as 1/OJ at 2  c  large UJ. There are no components at frequencies significantly higher than l / r . c  To link the concepts of spectral density and relaxation, we can consider two spins a distance R apart from each other and rotating randomly. The spectral densities of the motion due to the dipole-dipole interaction are (stated without proof) [141] J(°)(w) = (24/15i? )[r /(l + UJ T )} 6  2  2  c  J  ( 1 )  (A-17)  H = (l/6)jW(w)  (A-18)  (2/3)J<°V)  (A-19)  3^(UJ) =  The three different expressions correspond to cases in which there is no net spin flip, one spin flip and two flips, respectively. The relaxation rates for two spins on a rotating molecule are given by [141]: 1 / T i = (3/2)-f h I(I+l)[J^(uj) 4  1/T = j h 1(1 4  2  2  2  + J^(2uj)]  + 1) [(3/8) J(°V) + (15/4) J ^ M + (3/8)J^(2UJ)}  (A-20) (A-21)  The meaning of these relationships are discused in the following sections.  T i Relaxation T i is a time constant which describes the change in magnetization along the z axis. The Zeeman Hamiltonian dominates along the z axis.  The off-diagonal terms in Hp  are perturbative; thus to find the expression for T i , time-dependent perturbation theory is used [143]. T i is written in terms of the two states of energy and the transition rate between them. In the limit that t 3> (g, _E ); where n and rn are the higher and lower energy state respectively the transition rate depends on the intensity of fluctuations in the field at the Larmor frequency and double the Larmor frequency as seen in equation A-20. T i does not have a  (OJ) component because this component acts only in the x — y plane and is collinear  with the z axis.  Appendix A. Physics of MR  T  2  114  Relaxation  T2 relaxation times are calculated in the rotating frame where the Zeeman Hamiltonian no longer dominates. One source of T relaxation arises through the interaction of neighbouring 2  nuclei.  Density operator formalism is used in order to calculate how the density operator  evolves under the Dipolar Hamiltonian. A n important consideration is that the timescale of the interactions is the 'precession period in the dipolar field', or the inverse of the dipolar linewidth in the absence of motion. The key result of this analysis is that, when the fluctuations in the Hp are on a timescale faster than the timescale of the interactions between the nuclei, T2 relaxation is governed by exponential decays along the time axis. The Fourier Transform of an exponential decay is a Lorentzian lineshape. Thus a signal from a liquid sample leads to a narrow Lorentzian lineshape in the frequency domain. As stated above, the expression for T2 contains a  term (equation A-21). This makes  T2 behave differently from T i . As the temperature becomes lower so that T becomes larger, c  the significance of the j(°'(u;) becomes greater since the other terms contribute less. Thus, at certain temperatures it is expected that T2< T i . Weak and Strong Collision Regimes When T is determined by a thermally activated process obeying an Arrhenius relation, r oc c  e  _ E / / k T  c  , a plot of the relaxation times against temperature can give information on the magnitude  of T . A plot of the natural log of T i against 1/T forms a parabola-like curve which dips in the c  middle. The minimum point occus where  LOT  C  ~ 1.  The assumption for the B P P formulation of T i and T2 is that the dipolar interactions are weak compared with the Zeeman interactions and could be described with time-dependent perturbation theory. Metabolites randomly tumbling in the weak regime describe a negative slope in the Arrhenius plot where  UT 0  C  <?C 1.  For completeness, the strong collision regime is that in which the dipolar interactions are as strong as the Zeeman interactions. This is likely to happen in solids and is not relevent for  Appendix A. Physics of MR  115  this thesis.  A . 1.5  C h e m i c a l Shift  Another perturbative effect is that from the surrounding electrons which shield the main magnetic field. The nuclei experience a slightly shifted magnetic field. The Hamiltonian which describes this is given by (A-22)  Hcs = —o-iU I . 0  z  Hz and Hcs lead to a shifted Larmor frequency given by: Mi = 2irjhB (l 0  -  a)  (A-23)  The chemical shift, <jj, varies depending on the electronic environment of the nucleus which is dictated by the position of the nucleus on the molecule. Protons on a methyl group give a different chemical shift than the protons from a methylene group on the same molecule. Similarly the protons on a methyl group on one molecule may have a different chemical shift than those from another type of molecule. This is the basis of spectroscopy, since molecules can be identified by their shift, and different environments on the same molecule can be discriminated. Since u>i is proportional to B j , referring to chemical shift by its frequency would cause confusion when quoting results from magnets of different field strength. To standardize results, the shifted frequency is divided by the Larmor frequency OJ . 0  This leads to a dimensionless unit,  quoted in parts per million (ppm) of the magnet field strength [144] where 0 ppm in a proton spectrum is defined by the resonance of tetramethylsilane Si(CHs)4 [145].  A . 1.6  The Bloch Equations  A discussion of N M R would not be complete without introducing its semi-classical description. The ensemble of magnetic dipoles is described as a spin magnetization vector, M . In a magnetic field B it experiences a torque: (A-24)  Appendix A. Physics of MR  116  where B = B z and z is a unit vector along the z direction. In order to flip the magnetization, 0  a magnetic field oscillating with ui = jB 0  in the transverse plane must be applied. The field  0  is given by B i ( i ) = B\ cosu t x — B\ s\nu) t y 0  (A-25)  0  where x and y are unit vectors along the x and y axes, respectively and B i is the strength of the applied magnetic field. The equations describing the magnetization vector are  ^  =  <y[M B + M B smu t]  =  j[M B osto t  y  z  0  z  lC  7  (A.26a)  0  + M B]  0  — [-M Bi  1  X  (A.26b)  0  sin uj t - My Bi cos u t}.  x  0  0  (A.26c)  M ( t ) = M z , the solution to these equations is 0  M  =  M sin wit sin u t  (A.27a)  My  =  M s i n a ; i i c o s Lo t  (A.27b)  M  =  M cos u\t  (A.27c)  x  z  Q  0  0  0  0  where OJ\ = ^B\. The magnetization is rotated by an angle u\t from the z axis after B i has been on for a time t. The B i field perturbs the system from its equilibrium, its introduction to the system is called a 'pulse'. In this thesis, pulse angles of 90° and 180° are used to tip the magnetization. A way to describe T i relaxation is that it involves an exchange of energy between the spin system and the surrounding thermal reservoir. T relaxation can be described as the individual 2  spins coming to thermal equilibrium with each other. In the rotating frame, with relaxation, the Bloch equations describe evolution of the magnetization. The phenemonological description of T i relaxation is dM _ ~dT -  (M  z  z  -M) 0  T[  '  ( A  -  2 8 )  whose solution is MS)  = M (l-e- / t  0  T l  ).  (A.29)  Appendix A. Physics of MR  117  For transverse relaxation, the phenomenological description is dM  _  X:V  M,  x y  dt  T  2  (A.30)  '  with the solution M , {t)  = M  x y  Re-writing  ,(0)e- / 2. t  X i J  (A.31)  T  = 7 M x B with the terms above leads to dM -df  =  ^  =  M-r  UJ  ,  x  y W . - - ) - ^ 7  M  Z  5  1  -  7  M  X  (A.32a)  ( ^ - ^ ) - ^  (A.32b)  =•  (A.32c)  The solution of these equations leads to Lorentzian lineshapes in the frequency domain (as a result of the exponential decays). The phenomenological descriptions of T i and T relaxation 2  are used in to correct for relaxation when finding concentrations.  Appendix B  Accuracy and Precision  Figures 4.6 and 5.5 both demonstrated that at high noise levels the data was biased towards higher T i and T times. Because the N N L S estimation of relaxation time is a non-linear process, 2  the error in estimation is also non-linear. To demonstrate the effect of noise on a non-linear process, we will analytically calculate the expected error dy in y the function y = 1/x if there is some error, dx. To better understand the relaxation bias seen in the simulations in chapters 4 and 5 we will look at the estimations of relaxation times due to noise in individual datum.  B.l  P r o p a g a t i o n of N o i s e i n N o n - L i n e a r F u n c t i o n s  First, let us assume that we have a function y = f(x) where f(x) = x. For some average value of (x) there will be a corresponding average (y) — f((x)).  If there is some error dx in x, then  the corresponding error in y would be v  d  = =  ^-\x={x)-  ( )  f'((x))-dx.  (B.lb)  d  dx  Bla  Therefore, for any change in dx there is a corresponding linear change in dy. In fact, if f(x) = x, then f'(x) = 1 and there is an identical change between dx and dy. In fact, the expression B . l b yields the error for any function (linear or not) that has a derivative at the point x, provided that the changes are small in dx and dy. The expression (y) — f(( )) x  means that the precision of x does not affect the accuracy of y, since only the  mean value of x determines the value of y. The above expressions are no longer valid if y = f(x) and y are not small. 118  is non-linear and the changes in x  Appendix B. Accuracy and Precision  119  For a non-linear function like f(x)  = 1/x, one can see that for small x the function f(x)  becomes very large. If the value of x was between (0,a) then the corresponding value in y would be (oo,l/a). It is obvious that the propagation of error in a non-linear function such as 1/x is not linear. Furthermore, if you calculate (y) for x between (0,a) with (y) =  l/(x),  (y) = l/(a/2) = 2/a. But, (y) over (oo,l/a) is oo. Thus an error in the precision of x could lead to a bias in the accuracy of y.  B.2  Noise Plots  For the simulations in chapters 4 and 5 every point in the recovery or decay curve had Gaussian noise added to it. A bias .was observed, but its origin was unknown. Here recovery and decay curves were generated with only one point varying and the rest of the points remaining their true signal area.  One point was multiplied by numbers in the range of 0.6 to 1.4 and the  T i of the entire curve was measured with N N L S (section 2.3.3). Plots of T i and T  2  against  the multiplication factor have two interesting characteristics: the total difference between the simulated and true relaxation time determines the bias, and the standard deviation of the simulated relaxation time shows how greatly the relaxation time is affected by noise at any given point. For T true= 200ms and 400ms, figures B . l and B.2 plot the fitted T against the multiplicative 2  2  factor for each point in a 5 T E decay curve ( T E = 20, 35, 50, 75 and 100ms). The bias and the standard deviation are tabulated in table B . l .  Comparing T true= 200ms and T 2  2 t r u e  =  400ms, it can be seen in figures B . l and figure B.2 and table B . l that both the bias and the standard deviation of the estimated T times are lower in the T 2  the maximum T = 8 s in this application of the T 2  2  2 t r u e  = 200ms case. Note that  fit.  In contrast, for both the T true= 200ms and when T 2  2 t r u e  = 400ms cases the 8 T E data ( T E  = 30, 60, 100, 150, 200, 400, 600, 800ms) has similar bias and standard deviations (table B . l ) . There are four ideas illustrated in this error analysis which contribute to understanding the bias in the simulations at high noise (chapters 4 and 5):  Appendix B. Accuracy and Precision  120  1. There exists a bias in possible relaxation time values when noise is added to single recovery or decay points. 2. For smaller ranges in the multiplicative factor (figure B . l ) , the deviation from the true relaxation time is smaller. Thus, at smaller noise levels there is less bias. 3. Some curves may have a similar bias, but different standard deviations. If the variation in one point leads to a large standard deviation (as the first points in the decay curve do) then it is particularly important to measure that point precisely and accurately. 4. In this idealized simulation in which only one point has noise, the other points remaining true minimizes the bias. This is why the 8 T E data has less bias than the. 5 T E data, for instance. Simulations with the recovery curves were also conducted and confirmed the findings of bias in chapter 4.  Appendix B. Accuracy and Precision  121  Point #1 2.72237  0.4  Point #2 0.305994  0.2 0.0 I 0.6  0.8 1.0 1.2 Multiplier of True Signal Point #3 -0.00722218  0.4  0.8 1.0 1.2 Multiplier of True Signol Point #4 0.279427  0.2  0.8 1.0 1.2 Multiplier of True Signal  1.4  0.0 L _ 0.6  0.8 1.0 1.2 Multiplier of True Signol  Point #5 1.22679  0.8 1.0 1.2 Multiplier of True Signal  1.4  Figure B . l : Simulated T against noise for each point in a 5 T E decay curve, T2true=200ms. 2  Appendix B. Accuracy and Precision  122  Point #1 37.5720  Point #2 5.35399  0.8 1.0 1.2 Multiplier of True Signal  0.8 1.0 1.2 Multiplier of True Signal  Point #3 0.0681 181  Point #4 3.04122  0.8 1.0 1.2 Multiplier of True Signal  0.8 1.0 1.2 Multiplier of True Signal  1.4  1.4  Point #5 37.6922  0.8 1.0 1.2 Multiplier of True Signol  Figure B.2: Simulated T against noise for each point in a 5 T E decay curve, T2tme=400ms. 2  Appendix B. Accuracy and Precision  point number 1 of 5 2 of 5 . 3 of 5 4 of 5 5 of 5  true T 200ms 200ms 200ms 200ms 200ms  bias (no unit) 2.7 0.3 -0.007 0.28 1.2  standard deviation 0.3 0.05 0.005 0.07 0.16  1 2 3 4 5  of 5 of 5 of 5 of 5 of 5  400ms 400ms 400ms 400ms 400ms  37.6 5.3 0.07 3.0 37.8  3.2 0.7 0.02 0.4 3.2  1 2 3 4 5 6 7 8  of 8 of 8 of 8 of 8 of 8 of 8 of 8 of 8  200ms 200ms 200ms 200ms 200ms 200ms 200ms 200ms  0.07 0.03 -0.02 -0.02 0.003 0.006 0.001 0.000  0.04 0.01 0.01 0.02 0.02 0.007 0.002 0.000  1 of 8 2 of 8 3 of 8 4 of 8 5 of 8 6 of 8 7 of 8 8 of 8  400ms 400ms 400ms 400ms 400ms 400ms 400ms 400ms  0.07 0.06 0.01 -0.02 -0.03 0.01 0.02 0.01  0.07 0.04 0.009 0.02 0.03 0.03 0.02 0.01  2  Table B . l : Point number, bias and standard deviation for simulated T  2  

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