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Magnetic resonance spectroscopy standardization and protocol development Brief, Elana Esther 1995

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M A G N E T I C R E S O N A N C E S P E C T R O S C O P Y S T A N D A R D I Z A T I O N A N D P R O T O C O L D E V E L O P M E N T Elana Esther Brief B. Sc. (Physics) York University A THESIS SUBMITTED IN PARTIAL F U L F I L L M E N T OF T H E REQUIREMENTS FOR T H E D E G R E E OF M A S T E R ' S OF SCIENCE in T H E FACULTY OF G R A D U A T E STUDIES D E P A R T M E N T OF PHYSICS We accept this thesis as conforming to the required standard T H E UNIVERSITY OF BRITISH COLUMBIA October 1995 © Elana Esther Brief 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 The University of British Columbia Vancouver, Canada Date Oct i z , iqqS DE-6 (2/88) Abstract Three separate experiments were conducted in order to develop a protocol for collecting mag-netic resonance (MR) data using the MR unit at Vancouver Hospital - UBC Site. These exper-iments examined solutions at millimolar concentrations of N-Acetyl-Aspartate (NAA), Choline (Clio), Creatine (Cr), and myo-Inositol (ml). The 1 H NMR signal from these metabolites varied linearly with their concentration. Various agar gels were made with an NAA solution. The T2 relaxation time of the water signal varied with gel strength. No correlation was seen with the NAA signal T2 time. The scaling factor between the spectroscopy signal and a modified CPMG sequence signal was 2.19 x 105. Theoretical justification is given for choosing TE and TR times for the MRS protocol. The TE and TR times accurately described the water relaxation as was verified by other techniques. The protocol did not fully characterize the metabolites and the quantification method over-estimated their concentrations. ii Table of Contents Ab s t r a c t i i Lis t of Tables v Lis t of Figures v i i Acknowledgements v i i i 1 Introduction 1 1.1 Phantom Work 2 1.1.1 Verification of Known Parameters 3 1.1.2 Robust Analysis 3 1.1.3 T 2 Changes 3 1.1.4 Water Signal Comparisons 4 2 Background Theory 5 2.1 Physics Theory 5 2.1.1 Basic Equations of QM 5 2.1.2 The Zeeman Hamiltonian 7 2.1.3 Dipolar Interactions and Motional Narrowing 7 2.1.4 Relaxation 8 2.1.5 Chemical Shift 9 2.1.6 The Bloch Equations 10 2.2 Quantification 12 2.3 Biochemistry 12 2.3.1 N-Acetyl Aspartate 13 2.3.2 Creatine and Phosphocreatine 14 iii 2.3.3 Choline 15 2.3.4 myo-Inositol 15 3 Mate r i a l s and Methods 17 3.1 Sample Preparation 17 3.2 Spectroscopy Pulse Sequences 18 3.3 Spectroscopy Analysis 20 3.4 32 Echo Relaxation Sequence 20 3.5 Analysis of 32 Echo Relaxation Data 21 3.6 Parameter Choices 22 3.6.1 Signal-to-Noise Ratio 22 3.6.2 Evaluating T i 22 3.6.3 Evaluating T 2 24 3.6.4 Voxel Sizes 25 4 Results and Discussion 26 4.1 Concentrations of NAA, Cr, Cho, and ml 26 4.2 Concentration vs. Signal from NAA 29 4.3 Conversion Factor between Spectroscopy and Relaxation 29 4.4 Relaxation of Agar and Relaxation of NAA 32 4.5 Computer Simulation of the Effect of Relaxation Errors 36 5 Conclusions 37 Bibliography , 39 iv List of Tables 4.1 FWHM Values and Water Flip Angles for Metabolites 26 4.2 Concentrations, Ti , and T2 Relaxations for all Solutions 30 4.3 FWHM Values and Water Flip Angles for NAA 30 4.4 Corrected Concentrations for all Solutions 32 4.5 Water T2 Relaxation Times and Signal Intensity as found by Spectroscopy and Relaxation Techniques 32 4.6 FWHM Values and Water Flip Angles for Agar Gels 32 4.7 Concentrations, Ti , and T2 Relaxation Times for Water and NAA in Agar Gels . 34 4.8 Corrected Concentrations for NAA=14.4mM in % Agar Gels 34 4.9 The Error in the Relaxation Correction Given Errors in Ti and T2 36 v List of Figures 2.1 Spectrum and Chemical Structure of NAA 14 2.2 Spectrum and Chemical Structure of Creatine 15 2.3 Spectrum and Chemical Structure of Choline 16 2.4 Spectrum and Chemical Structure of myo-Inositol 16 3.1 STEAM Pulse Sequence 18 3.2 Third Pulse of CHESS Sequence 19 3.3 The Cumulative Effect of the Baseline in Baseline Corrected and Uncorrected Water Signal Areas 21 3.4 SNR plotted against TR time for Ti=1300ms 23 3.5 The Relaxation Curve for T 1 = 1300ms, Overplot with the Values of TR used Experimentally to Determine Ti 23 3.6 The Relaxation Curve for T2=250ms, Overplot with the Values of TE used Ex-perimentally to Determine T2 24 4.1 Typical NAA fitting (to Large Peak) 27 4.2 Typical Creatine fitting (to Large Peak) 27 4.3 Typical Choline fitting (to Large Peak) 28 4.4 Typical Inositol fitting (to Large Peak) 28 4.5 The Relaxation Curve for T2=1100ms, Overplot with TE Values used Experi-mentally to Determine T 2 29 4.6 Log of Signal Amplitude vs. TE plotted for Inositol, Creatine, and Choline. . . . 30 4.7 Log of Signal Amplitude vs. TE plotted for NAA of Different Concentrations. . . 31 4.8 Calculated Concentrations vs. Actual Concentrations for NAA 31 4.9 Plot of Signals from Spectroscopy and 32 Echo Pulse Sequence where the Differ-ence is the Conversion Factor 33 vi 4.10 Log of Signal Amplitude vs. TE plotted for NAA in Different Percentage Agar Gels 34 4.11 T 2 Relaxation Time of Water vs. Percentage Agar 35 4.12 T 2 Relaxation Time of NAA vs. Percentage Agar 35 vii Acknowledgements im grateful to the Canadian Government for granting me an NSERC PGSA the Faculty and Staff in the UBC Physics Department for their constant supi viii Chapter 1 Introduction In the summer of 1994, Vancouver Hospital Health Sciences Centre - UBC Pavilions (VHHSC-UBC) purchased a magnetic resonance (MR) scanner for clinical magnetic resonance imaging (MRI) diagnoses. This scanner has spectroscopic capabilities. Magnetic Resonance Spectroscopy (MRS) is a relatively new technique available on MR scanners, but echoes the foundations of magnetic resonance: Nuclear Magnetic Resonance (NMR). Using MRS, a spectrum of a volume of interest can be obtained. By interpreting the spectra, information can be determined about NMR signal relaxation times and concentrations of metabolites. An MRS examination is essentially a non-invasive, non-destructive biopsy. The application of this knowledge could range from tracking the progress of a drug treatment to classifying a tumour. MRS is used experimentally to diagnose Temporal Lobe Epilepsy and to observe changes in brain metabolite levels in Hepatic Encephalopathy and Multiple Sclerosis; it cannot yet be used as a clinical tool since it has not been FDA approved [1]. The Radiology Department at VHHSC-UBC has always had a strong commitment to research. Since MRS has been growing as a research tool, the department was interested in incorporating it into the research already being conducted at its facility. To discriminate between spectra from pathological and healthy brains, analysis of the signal must be done. Initially, analysis of spectra consisted of measuring the signal areas of the metabolites in order to compare them relatively. A problem arising from such a method is that an increase in one signal amplitude cannot be distinguished from a decrease in all other signal amplitudes. Quantification resolves this dilemma. The requirements of quantification are a consistent standard against which concentrations are measured and a spectral analysis method which can give reproducible results. Different in vivo quantification results have been reported by various research groups, all of which have 1 Chapter 1. Introduction 2 different protocols and analysis methods. Ernst et al. [2] found that most of the discrepancies between their in vivo results and the in vivo results from other groups had to do with differing baseline corrections, inconsistent concentration units, and differing voxel locations. To avoid the difficulties with concentration units an 'institutional unit' has been used to describe the metabolite signals of the clinical spectra; concentrations are presented in terms of difference between spectra from patients and healthy volunteers. Each site must then examine their own database of healthy volunteers. The only way MRS can be made reproducible between different research groups is by calculating concentrations in absolute units. Before conducting MRS exams in vivo, it is imperative to demonstrate that signals from known samples give the correct concentrations and relaxation times. A protocol must be de-veloped to characterize the various parameters used to calculate concentrations. The work presented in this thesis covers the signal standardization and protocol development at VHHSC-UBC. The protocol is intended for application to in vivo brain studies. This introductory chapter outlines the work in this thesis. A reader who is new to the field of NMR should read this chapter as an overview, with knowledge that the concepts introduced will be developed later in this thesis. 1.1 Phantom Work A phantom is a sample which takes the place of a live subject in the scanner. Discussion of phantom work is uncommon in the literature; only two groups have reported their work with phantoms as an introduction to their in vivo work. Issues dealt with were signal linearity with concentration and voxel size, field homogeneity[3], and attenuation of signal while changing pulse parameters[4]. The phantom work was done in order to verify assumptions which were made when calculating the relaxation times and concentrations of in vivo work. For the research at UBC, there were three aspects to the phantom work: 1. Verification of known parameters with MRS (finding concentration and relaxation times); 2. Verification of robustness of analysis method (measuring the known parameters when changing concentration); Chapter 1. Introduction 3 3. Observation of spectral and parametric changes dependent on metabolite environment (measuring parameters when metabolite is in an agar gel); 4. Correlation of MRS results with other methods (comparing the water signal from MRS with the water signal from a modified CPMG sequence - the 32 echo sequence). 1.1.1 Verification of Known Parameters Solutions were made using four different brain metabolites: N-Acetyl Aspartate (NAA); myo-inositol (ml); Choline (Cho); and Creatine (Cre). These metabolites are studied most frequently because of their prominence in the in vivo spectrum. Ti and T 2 relaxation times, and the concentration were found for each metabolite. The relaxation times were measured in order to compare with the in vivo values. 1.1.2 Robust Analysis The analysis program was challenged by solutions of different concentrations of NAA, in an attempt to show linearity between signal strength and concentration. Pathologically, brain metabolites can vary in concentration from 0 to above 20 mM (metabolite dependent). The analysis method must be able to calculate the correct concentrations throughout this range. 1.1.3 T 2 Changes In order to find concentrations accurately, the relaxation information for the metabolites should be known. The time it takes for a complete MRS study to find the relaxation times is on the order of an hour. This length of study cannot be done clinically. If assumptions could be made about relaxation times, then the entire study could be cut down to 7 minutes. The relaxation mechanisms of these metabolites apparently have not been discussed in the literature. Relaxation rates for biological systems are affected by cell size and cell constituents. A 32 echo pulse sequence collected T 2 relaxation data of water in a voxel [5],[6]. This sequence took 6.5 minutes. It is well established that water in agar gels relax faster than bulk water[7]. Different strength agar gels were made with NAA in order to determine if the T 2 relaxation of NAA Chapter 1. Introduction 4 would be correlated with the relaxation time of water signal. If the metabolites relaxed in a predictable fashion when compared with the water signal relaxation, then an entire spectroscopy exam could take 13 minutes. 1.1.4 Water Signal Comparisons In all MRS studies the water signal was measured and its relaxation times were found. In the agar experiment, as discussed above, the 32 echo pulse sequence was used to collect the water signal in order to verify changes in water relaxation times seen with MRS. To give confidence in MRS values a comparison was made between MRS and the 32 echo sequence. Chapter 2 Background Theory 2.1 Physics Theory The most fundamental explanations of NMR can be found in quantum mechanics (QM). At its most elementary level, NMR 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 motion 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 [8], [9]. The basic equations of quantum mechanics are quickly reviewed to ensure clarity of notation. 2.1.1 Basic Equations of Q M There are four basic ideas which underlie all of QM. These ideas are described in terms of a particle with a certain angular momentum. All particles are defined in terms of their spin 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, 2, where the values of m could range from —/, —7—1,..., 7 — 1 , 7 , where I is an integer or half integer called the angular momentum quantum number, the state can be written as \V >=^2am\m> (2.1) rn where \ty > and \m > are vectors and am are complex amplitudes associated with each \m >. The vectors |m > were chosen to have certain values, m, when measured along the z axis. 5 Chapter 2. Background Theory 6 An eigenvalue equation describes the state of the particle: Iz\m >= m\m > (2.2) where Iz is an 'operator' that, when acting on \m >, gives an eigenvalue, m, which is the value of the angular momentum of the state |m > along the z axis. Iz could operate upon the spin state giving 7*1* >= ^2amIz\m > . (2.3) m The result of any experiment done must give a real quantity. This quantity is calculated by taking the expectation value of the operator, < V\IZ\V >= ]T ama*m, < m'\Tz\m > (2.4) m,m' If the basis states are orthonormal (< m'|m >= Sm^m), then the above equation can be re-written as < ^\IZ\^ >= \am\2™>. (2.5) m This expectation value can be explained in two ways. If |* > is the state of a single particle, then |a, n | 2 is the probability that when operating on the state, one will measure the value m. If I* > describes the state of an ensemble of particles, then ^ m \am\2m is 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 which show that two or more angular momenta cannot be measured simultaneously: [IX, Iy] = TXIy - Iylx = UZ (2.6) The Schrddinger Equation describes what happens to a state when acted on by an energy operator, the Hamiltonian H. *7i—|tf ( t ) > = . f f | # ( i ) > (2.7) Chapter 2. Background Theory 7 where Ti is Planck's constant divided by 2-K. If H is not time dependent, then the solution to equation 2.7 is: \^(t)_>= U(t)\V(0) > . (2.8) where U(t) is the evolution operator, defined as U{t) = e(--iHi/A). (2.9) 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. 2.1.2 The Zeeman Hamiltonian The Zeeman Hamiltonian Hz is given by Hz = -yhB0lz (2.10) where B0 is the magnetic field strength and 7 is the gyromagnetic ratio. For protons, 7 = 2.675 x 108 rad-s^T - 1, and I = \ . The energy separation between levels is JTLB0. Since Hz is not time dependent, an evolution operator can be written as Uz(t) = e(^P) =e(hB0jzt)_ ( 2 1 1 ) A state acted on by the evolution operator precesses at a frequency w0, defined by LO0 = jB0. In a given time, t, the precession would go through an angle jB0t. 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. 2.1.3 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 Chapter 2. Background Theory 8 is a spin ^ nucleus, this perturbation is called the dipolar interaction. Its Hamiltonian is given by ^ = £ E-rafirffr • ii - • • (2-12) i<j In most NMR experiments, #o is quite weak compared to Hz- Since the diagonal terms give energy shifts on the order of / ' ° 7 / ' ' and the off-diagonal terms shift the energy by (*^br)2, to a first order approximation only the diagonal terms influence the energy levels. The Hamiltonian can then be re-written as HDo = £ ^ ( 1 - 3 cos2 etj)[3IizTjz - It • Ij]. (2.13) i<j In the case of molecular tumbling motion (the molecular motion in most liquids), the HD0 is averaged over all possible orientations of the nuclei with respect to B0. Providing that the nuclei sample all possible orientations on the timescale of the dipolar interaction, then < cos2 6 >= |. Quantitatively, this gives a narrowing of the spectrum. If there were only one resonance at a certain frequency, u>0 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. With molecular motion, the HD0 averages to zero, and the spectrum narrows to only resonate at the Larmor frequency. In practice, the NMR spectra have a finite width due to spin relaxation and magnetic field inhomogeneities. 2.1.4 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 [10]; the theory is often referred to as the BPP theory. In the last section, the averaging of cos2 9 led to HD0 = 0. The non-diagonal terms of HD continue to influence the spin states. These energy fluctuations lead to spin relaxation. Chapter 2. Background Theory 9 T i Relaxation T\ 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 Ti , time-dependent perturbation theory is used [11]. Ti is written in terms of the two states of energy and the transition rate between them. In the limit that t 3> ^E ^E y where n and m 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. T 2 Relaxation T2 relaxation times are calculated in the rotating frame where the Zeeman Hamiltonian no longer dominates. One source of T 2 relaxation arises through the interaction of neighbouring nuclei. Density operator formalism is used in order to calculate how the density operator evolves under the Dipolar Hamiltonian. An important consideration is that the time scale 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 time scale faster than the times scale of the interactions between the nuclei, T 2 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. 2.1.5 Chemical Shift Another perturbative effect is that from the surrounding electrons which shield the main mag-netic field. The nuclei experience a slightly shifted magnetic field. The Hamiltonian which describes this is given by Hcs = -o-iV0Iz. (2.14) Hz and HQS lead to a shifted Larmor frequency given by: Ui = 2 7 T 7 / iB 0 ( l - a^, (2.15) Chapter 2. Background Theory 10 The chemical shift, <TJ, 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 is proportional to 5j, 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 UJ0. This leads to a dimensionless unit, quoted in parts per million (ppm) of the magnet field strength [12] where 0 ppm in a proton spectrum is defined by the resonance of tetramethylsilane Si(CH3)4 [13]. 2.1.6 The Bloch Equations A discussion of NMR 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: V = ] M x B (2.16) dt where B = B0z and z is a unit vector along the z direction. In order to flip the magnetization, a magnetic field oscillating with w0 = jB0 in the transverse plane must be applied. The field is given by Bi(i) = B\ cosw0i x — B\ sinu;0£ y (2-17) where x and y are unit vectors along the x and y axes, respectively and B\ is the strength of the applied magnetic field. The equations describing the magnetization vector are = j[MyB0 + MZBX sinu0t] (2.18a) ^ = i[MzBlCosuj0t + MxB0} (2.18b) = j[-MxBis'moj0t - MyBi cos u0t]. (2.18c) Chapter 2. Background Theory 11 Under the initial conditions that M(t) = M 0z, the solution to these equations is Mx = M0 sinwitsinw0t (2.19a) My = M0 sin wit cos w0t (2.19b) Mz = M0 cos wit (2.19c) where co\ = jB\. The magnetization is rotated by an angle wit from the z axis after B\ has been on for a time t. The B\ field perturbs the system from its equilibrium, its introduction to the system is called a 'pulse'. A way to describe Ti relaxation is that it involves an exchange of energy between the spin system and the surrounding thermal reservoir. T 2 relaxation can be described as the individual spins coming to thermal equilibrium with each other. In the rotating frame, with relaxation, the Bloch equations describe evolution of the mag-netization. The phenemonological description of Ti relaxation is dMz _ (Mz - M0) dt ~ Ti ' 1 U j whose solution is Mz(t) = M z (0)e ( - t / T l ) + M0{1 - e(-*/Tl)). (2.21) For transverse relaxation, the phenomenological description is dMx,y _ Mx. (2.22) dt T 2 with the solution Mx,y(t) = Mx,y(0)e^T^. (2.23) Re-writing = 7 M x B with the terms above leads to dMx ,„ w> Mx — = 7 M y ( B 0 - - ) - ^ (2.24a) ^ = jM^-^MAB.-^)-^ (2.24b) dMz „ (Mg-M0) — = —jMyBi - ^— (2.24c) Chapter 2. Background Theory 12 The solution of these equations leads to Lorentzian lineshapes in the frequency domain (as a result of the exponential decays). The phenomenological descriptions of Ti and T 2 relaxation are used in Section 2.2 to correct for relaxation when finding concentrations. 2.2 Quantification The signal which the MR spectrometer produces is a free induction decay (FID) after a pulse. This FID plots signal intensity against time. The data is Fourier Transformed to give signal intensity against frequency. The signal areas are directly proportional to the concentration. The experiments were conducted at different TE (time to echo) times and TR (time to repeat) times during which there was Ti and T 2 relaxation. The signal must be corrected for relaxation before using the signal to find concentrations. More details on TE and TR times is given in Section 3.2. Following from the Bloch equations, the corrections are as follows: M = Moo • (1 - e~TR/Tl) (2.25) where M is the signal at a given TR and is the signal at TR=oo and M = M0 • (e-TE'T*) (2.26) where M is the signal at a given TE and So is the signal at TE=0. The metabolite concentration is found by comparing the metabolite signal to the signal from a standard with a known concentration. The signals are normalized using the number of contributing protons from the standard and the metabolite. Mathematically written: n — n ( \ /Pstandard \ /r, 0 7 \ ui — ^ standard ' VT7 j ' ( ) ^standard Pi where Cstandard a n d C, are the concentrations of the standard and the metabolites, and where Pstandard and pi are the number of contributing protons from the standard and metabolites. 2.3 Biochemistry In vivo X H MRS measures many different chemicals in the brain. The most prominent signals come from N-Acetyl Aspartate (NAA), Creatine and Phosphocreatine (Cr+PCr), Choline con-taining compounds (Cho), and myo-Inositol (ml). These chemicals give rise to well resolved Chapter 2. Background Theory 13 signals which can be fit to Lorentzian lineshapes. Other significant chemicals include N-Acetyl Aspartyl Glutamate (NAAG), Glutamate (Glu), and Glutamine (Gin). The signals from these chemicals are less resolved, thus more difficult to analyse than those listed above. The chemicals are classified in terms of their resonant frequency (shifted from the Larmor frequency of 1 H as a result of B~cs)- As discussed earlier, each chemical environment of a molecule can have a different resonant frequency. The ppm of the chemicals signals seen in the brain have been measured [14]. MRS findings have been compared with results from analytical biochemistry methods. In the case of NAA, post-mortem analysis techniques have determined significantly lower values than MRS [14]. This may be due to the normal depletion of NAA in excised tissue [15]. A philosophical question then arises: does MRS seek to correlate with biochemical values, or is it an analysis technique independent of others? Such a discussion is beyond the scope of this work. The following sections discuss the major chemicals with observable NMR signals. A de-scription of each chemical is given, with a possible function it has in the brain. 2.3.1 N-Acetyl Aspartate NAA was discovered in 1956 by Tallan et al. [16]. They found that the concentration of NAA is higher in grey matter than in white matter. This finding suggested that NAA is confined to neurons, it was confirmed by work done by Roller et al. [17] demonstrating that NAA disappears when the neurotoxin kainic acid is injected into neurons. Choi et al. suggested that NAAG is a storage form for Glu since in high concentrations Glu can be a neurotoxin [18]. NAA can be both the by-product of and the precursor to NAAG. NAA has three distinct proton signals (Figure 2.1.) These signals correspond to the methyl peak (CH3) at 2.02 ppm (the strongest peak) and two others from the CH and the CH2 groups just downfield. Even though it is not obvious from Figure 2.1, the ratio of the peak areas are 2:1:3, in order from left to right. This largest signal (from CH3) is the most easily resolved of all the chemical resonances and was used for the analysis discussed in this work. The concentration has been measured in vivo Chapter 2. Background Theory 14 C - C H , - C H - C , NH c o 4 3 2 ppm 0 C=0 (a) Figure 2.1: Spectrum and Chemical Structure of NAA. ranging from 8.2mM [19] to 11.4mM [3]. The value varies between brain structures. NAA concentrations change in different diseases including ischemic stroke and multiple sclerosis (MS). Arnold et al. were the first to suggest that the metabolite changes in diseases, especially that of NAA, can provide an index of irreversible central nervous system (CNS) disease [20]. 2.3.2 Creatine and Phosphocreatine Creatine is taken in through diet and can also be synthesized in the liver, kidneys, and pancreas. Cr and PCr are present in both muscles and neurons. PCr is considered to be a reserve for high energy phosphates [21]. The chemical structure for Cr is shown along with the spectrum in Figure 2.2. The methyl peak for Creatine is at 3.03 ppm, and the methylene peak is at 3.91 ppm. In this work, only the signal from the methyl group was studied. In 1 H MRS the Cr and PCr signals overlap completely. Whereas in 3 1 P MRS only the PCr signal is seen. For quantification, creatine has been used as an internal standard [14]. Behar et al. have questioned this assumption for diseased brains [22]. The creatine concentration ranges from 5.3mM [19] to 6.8mM [4]. Chapter 2. Background Theory 15 "V J \ i i i ^ C - C H , - N - C - N H , 4 3 2 1 0 o' C ' H I NH ppm (a) (b) Figure 2.2: Spectrum and Chemical Structure of Creatine. 2.3.3 Choline Choline is also absorbed through diet [23] and it provides the precursors for acetylcholine (ACho) and phosphotidylcholine (PhCho), one of the building blocks of cells. Only cholinergic neurons make ACho [24], whereas all cells synthesize PhCho. ACho works as a neurotransmitter and is critical for memory, cognition, and mood. Research with ex vivo choline concentrations has been limited since, after cell death, the choline levels increase unpredictably [21]. It is believed that the choline signal reflects the total brain choline stored [21]. The chemical structure of choline and its corresponding spectrum are shown in Figure 2.3. The choline signal appears at 3.22 ppm. Choline concentrations range between 1.3mM and 2.2mM [19]. The large peak is due to the nine protons contributing to the signal. 2.3.4 myo-Inositol The function of ml is unknown [25]. Dramatic changes are observed in ml levels in diseased brains. Koopmans et al. observe a two-fold ml concentration increase in patients with MS [26], Bruhn et al. also report increases [27]; a reduction is reported in cases of hepatic encephalopa-thy [28]. Using MRS, ml is difficult to measure since some of its signal is obscured by the residual Chapter 2. Background Theory 16 2 ppm CH, HO - C H , - C H , - N - CH, (a) (b) Figure 2.3: Spectrum and Chemical Structure of Choline. J 2 ppm OH OH OH,?—C H /" H \ , \ H O H / , H C C OH OH H (a) (b) Figure 2.4: Spectrum and Chemical Structure of myo-Inositol. water signal. The chemical structure and signal can be seen in Figure 2.4. It is unclear from the structure whether the 3.56 ppm peak has 2 or 4 contributing protons. Toft et al. assumed 2 contributing protons, without citing a reason [29]. This work uses that assumption. The smaller signal at 4.06 ppm is not investigated in this work. Chapter 3 Materials and Methods The ultimate goal of this work is to find a method which gives reliable and reproducible con-centrations for metabolites detected by MRS. Concentrations are calculated using the relaxation times and areas of the metabolites and water signals (Section 2.2). The pulse sequences used to obtain this information are discussed below along with descriptions of the programs used to analyse the data. All work was conducted on a General Electric Signa 1.5 T clinical scanner at 5.x software level. A commercial quadrature birdcage head coil was used for data collection. 3.1 Sample Preparation As mentioned earlier, the four' metabolites used for this work were NAA (Sigma Chemical A8901), Cr (Sigma C0780), Cho (Sigma C9154), and ml (Sigma 15125). Solutions of each metabolite were made at a concentration of 13.4 mM. Additional solutions were made of NAA at 4.5, 8.9, 18.9, and 44.6 mM. All solutions were buffered to 7.2 pH (physiological level) with a lOOmM phosphate buffer. This buffer consisted of NaH2P04-H20 (BDH Chemical 100903/5304) brought to physiological pH with NaOH (BDH 109822/8153). A phosphate buffer was chosen because it did not contribute signal to the spectrum. Each solution was kept in a 125mL Nalgene bottle. Three phosphate buffered NAA solutions of 14.4 mM were mixed with different amounts of agarose to make agar gels. The buffers for these were made using NaH2P04-H20 brought to pH 7.2 with Na 2HP0 4 (BDH 100826/5276). The percentages of agar were 1.0%, 1.5%, and 2.0%. These solutions solidified in 250mL Nalgene bottles. Finally, 500mL of distilled water was doped with 102/dVI of MnCl 2 (BDH 10152). The error in any of these concentrations is below 1%. 17 Chapter 3. Materials and Methods 18 RFj G z Gy Gx 0.0 15.0 30.0 45.0 60.0 time (ms) Figure 3.1: STEAM Pulse Sequence 3.2 Spectroscopy Pulse Sequences STEAM (STimulated Echo Acquisition Mode) employs 3 slice selective 90° radio frequency (rf) pulses (3.6 ms duration) and 3 crusher gradients. A slice selective pulse is a pulse which is combined with a gradient to affect the spins of a chosen region. For the STEAM pulse sequence the pulses are sine functions in the time domain, which Fourier Transform to square functions in the frequency domain. The STEAM sequence is illustrated in Figure 3.1. The purpose of the crusher gradients is to dephase the magnetization outside the voxel. The first 90° pulse tips the magnetization into the transverse plane. Here the signal relaxes with T 2 relaxation. The next 90° pulse brings the magnetization along the longitudinal axis where it relaxes with Ti relaxation. The time between the second and third pulse is called the mixing time (TM). Since Tj relaxation times are long compared to TM there is little relaxation in this time. Narayana et al. show that the signal starts to distort when TM>50ms [4]. For this work TM=13.7ms. The third 90° pulse brings the magnetization back to the transverse plane. Since there is some time while the magnetization is stored along the longitudinal axis, the TE for the sequence is only limited by the time it takes for two slice selective pulses and crusher gradients. Frahm et al. have achieved TE as low as 10ms [30], although in this work TE>30ms. Some parameters used were: slice thickness 20mm; field of view 24cm; image matrix 256x128. The STEAM Chapter 3. Materials and Methods 19 Tipped Dephased After some T1 recovery Figure 3.2: Third Pulse of CHESS Sequence pulses were cycled through eight different phases. The rest of the parameters are discussed individually in Section 3.6. Another important sequence is the CHEmical Shift Selective sequence (CHESS) [31]. The metabolite concentrations in vivo are five orders of magnitude less than the water concentration. It is necessary to reduce the water signal in order to detect the metabolite signal; one frequently used sequence to do this is CHESS. Essentially, CHESS uses three frequency selective 90° pulses (48 ms duration) centered on water with «50Hz bandwidth to select the desired chemical shift. A crusher gradient is then used to eliminate the water signal while it is in the transverse plane. The last pulse has a variable angle. Setting the last pulse to an angle slightly greater than 90° insures that when the crusher gradient takes effect, any Ti relaxation will have caused the signal to be fully in the transverse plane (see Figure 3.2). Typically, 99% of the water signal is suppressed. Chapter 3. Materials and Methods 20 3.3 Spectroscopy Analysis The analysis method incorporates algorithms used by various other spectroscopy groups. Raw free induction decay (FID) traces of water-suppressed and water-unsuppressed spectra are zero-padded to double the number of points and apodized with a decaying exponential whose decay rate was the same as the experimental value for FWHM of water (this value changed with every new phantom). The FIDs are corrected for eddy-currents wherein the water peak is centered by shifting the FID so that the largest magnitude was at t=0, and phase is unwrapped [32]. The residual phase correction is applied to both the water-suppressed and unsuppressed FIDs. The Fast Fourier Transform (FFT) of the FIDs is taken, so that the data are presented in the frequency domain. Baseline corrections are done to-remove the frequency offset caused by the FFT. FFTs assume infinite periodicity. Since the FID did not begin at zero intensity, there is a discontinuity seen by the FFT. The FFT of a discontinuity gives signal at all frequencies in the frequency domain. As a result, there is a shift in the baseline by 0.01% of the maximum peak amplitude. When integrating the area the shift contributes to the signal. The cumulative effect is substantial (see Figure 3.3). The water unsuppressed baseline-corrected spectra are integrated over the entire domain to find the water area. The metabolite signals are fit using a Marquardt-Levenberg algorithm [33] and Lorentzian line-shapes. The peak areas and their corresponding TE and TR times are fit to equation 2.26 and 2.25 to find T 2 and Ti relaxation times, respectively. These values are then used to find the concentrations by equation 2.27. 3.4 32 Echo Relaxation Sequence The 32 Echo Relaxation Sequence was developed by Alex MacKay [5]. The sequence employs a slice-selective 90° pulse (3.2 ms duration), rectangular 180° pulses (400 /J,S duration), and a series of slice-selective crusher gradient pulses of alternating sign and decreasing amplitude on either side of each 180° pulse. The alternating crusher gradient sequence dephased flow effects and eliminated contributions from stimulated echoes and contributions from outside the selected slice. Sequence parameters used were: repetition time TR=3s; echo spacing 10ms; slice Chapter 3. Materials and Methods 21 0.60 0.50 Basel ine Not Corrected 0.10 0.00 E. 0 200 400 600 Point Number 800 1000 Figure 3.3: The Cumulative Effect of the Baseline in Baseline Corrected and Uncorrected Water Signal Areas thickness 20mm; field of view 24cm; image matrix 256x128; and one scan. 3.5 Analysis of 32 Echo Relaxation Data The 32 echo relaxation data were analysed using in-house software which conducted non-linear least squares fits [34]. A region was defined in one of the 32 images and a decay curve was generated by the data. No assumptions were made as to whether the T 2 relaxation was mono- or multi-exponential. Using a non-linear least squares fit, the T 2 relaxation times and amplitudes were evaluated and represented by delta functions. The a priori information used was a grid of T 2 relaxation times at which potential amplitudes could be found, and the assumptions of exponential relaxation and positive amplitudes. The output included the mean T 2 and each recovered T 2 with its corresponding amplitude. Chapter 3. Materials and Methods 22 3.6 Parameter Choices The parameters, TE and TR, were chosen so as to fully characterize the relaxation times of the data. The concentrations of the metabolites simulated what is measured in the human body and the size of the voxels was representative of the size which would include only white or grey matter. A discussion of how these choices affect signal to noise is given. For collecting data the protocol was to conduct localiser (pilot) scans in order to determine voxel placement. In all cases the depth of the voxel was 20mm. The spectroscopy sequence was repeated for all TE and TRs required. In some cases, the 32 echo sequence was conducted on the 20mm slice. 3.6.1 Signal-to-Noise Ratio A qualitative equation describing signal to noise ratio (SNR) in spectroscopy is given by SNR oc p • e-TE'Ti(\ - e - T f i / T l ) ( ^ - ) 2 • (voxel size) (3.1) T i t where p is the proton density and T is the total time of the exam, T = TR • number of averages. (3-2) 3.6.2 Evaluating T a The range for in vivo Ti relaxation times for the metabolites has been found to range between 1100ms [14] and 1500ms [35], (both chemical and region dependent). Assuming a Ti value of 1300ms, the SNR was plotted for TRs ranging from 0 to 3500ms. SNR peaked at TR= 1500ms (see Figure 3.4). To fully characterize the relaxation of Ti the TR values chosen were 1233, 1500, 2500, and 3500ms. Figure 3.5 shows the theoretical relaxation curve for Ti=l 100ms and the placement of the TR values used to characterize the curve. The lowest TR which the scanner would accept was 1233ms. Chapter 3. Materials and Methods 23 0.020 0.015 0.000 Calculated SNR — SNR Magnified by 20 within 1000<TR<2000ms 1000 2000 3000 4000 TR (ms) Figure 3.4: SNR plotted against TR time for Ti=1300ms 1000 2000 TR (ms) 3000 4000 Figure 3.5: The Relaxation Curve for Ti=1300ms, Overplot with the Values of TR used Ex-perimentally to Determine Ti . Chapter 3. Materials and Methods 24 1 c co o o 0 0.0 100.0 200.0 300.0 400.0 500.0 TE (ms) Figure 3.6: The Relaxation Curve for T2=250ms, Overplot with the Values of TE used Exper-imentally to Determine T 2 . 3.6.3 Evaluating T 2 The T 2 times have been found to range between 150ms [14] and 350ms [19], they are also chemical and region dependent. The values for TE (30, 60, 100, 150, 200ms) were chosen in order to characterize both fast and slow relaxing metabolites. A plot of the T 2 relaxation for T2=250ms is overplot with the TE values (see Figure 3.6). Values below 30ms were not used since the pulse sequence changed slightly to accommodate these lower times. Two control variables, squeeze and sharp, which determine the duration and the intensity of the pulses, respectively, were 1 and 0 for TE 30ms and over, but 0 and 1 under TE 30ms. Data were taken from the doped water in order to compare results with the 32 echo sequence. The TE times used were 30, 60, 90, 120, 150, 180, 210, 240, 270, 300, and 320 ms, insuring that data would be taken over the full range of the 32 Echo Sequence. Chapter 3. Materials and Methods 25 3.6.4 Voxel Sizes The voxel size simulated in vivo sizes. The dimensions used were 18.8mmx 18.8mmx20.0mm, giving a volume of 7.07mL. To increase the SNR, 64 averages were taken. This led to a scan time of under 2 minutes for each TR 1500ms scan. The voxels were 23.3mmx23.3mmx20.0mm for the agar gel, giving a voxel of ~ 10.9 mL. The number of averages was dropped to 32 because the voxel was large. Since the doped water was being used for calibration purposes, the parameters had to be the same as for the 32 Echo Sequence. The voxel size was chosen to be 30mm x30mm x20mm, giving 18 mL. All scans for the water phantom had 128 averages and used TR=3000ms. Chapter 4 Results and Discussion 4.1 Concentrations of N A A , Cr , Cho, and m l Table 4.1 lists the full width at half maximum (FWHM) values in Hz and the angles of the last CHESS pulse. The water suppression was 99%. The data were analysed as described in Section 3.3 and the results are given in Table 4.2. Figures 4.1, 4.2, 4.3, and 4.4 are examples of the fits to metabolite signals. The downfield peaks are due to residual water. In Table 4.2, the calculated concentrations were significantly higher (with the exception of Cr) than the actual concentrations. The Ti and T 2 relaxation times of water remained consistent for all of the solutions, those for NAA did not. There seemed to be a trend of decreasing Ti or T 2 relaxation with increasing concentration of NAA. T i relaxation times were in the in vivo range. The T 2 relaxation times of the metabolites were five times longer than those quoted from in vivo work. The TE times chosen, therefore, did not characterize the T 2 relaxation well (see Figure 4.5). The decreased length of T 2 relaxation times in vivo suggested that biological systems may effect relaxation times. Plots of the signal areas against TE times for each of the phantoms are shown in Figures 4.6 and 4.7 with the corresponding exponential fit plotted over the graph. The only metabolites with T 2 fits corresponding to their decays were creatine (Figure 4.6(b)) and the 18.9mM NAA Metabolite FWHM (Hz) Flip Angle (°) NAA 3 116 Cr . 2 117 Cho 2 115 ml 2 113 Table 4.1: FWHM Values and Water Flip Angles for Metabolites. 26 Chapter 4. Results and Discussion 27 0.8 j < ' I 4 3 2 1 0 ppm Figure 4.1: Typical NAA fitting (to Large Peak) ppm Figure 4.2: Typical Creatine fitting (to Large Peak) Chapter 4. Results and Discussion 2 8 Figure 4.4: Typical Inositol fitting (to Large Peak) Chapter 4. Results and Discussion 29 1 (0 c in o cn o 0 0.0 100.0 200.0 300.0 400.0 500.0 TE (ms) Figure 4.5: The Relaxation Curve for T 2 =l 100ms, Overplot with TE Values used Experimen-tally to Determine T 2 . (Figure 4.7(d)). The better of the two fits is for creatine. The calculated concentration for creatine matches its actual concentration this is likely due to the quality of the T 2 fit. 4.2 Concentration vs. Signal from N A A Table 4.3 lists the FWHM and flip angles for various concentrations of NAA. The calculated concentration increased with the actual concentration (see Table 4.2); it is plotted in Figure 4.8. The actual and calculated concentrations varied linearly, where the slope was 0.75 units and the y-intercept was -0.85 units. Using these values as a correction factor, corrected values for the calculated concentrations were found and are listed in Table 4.4. 4.3 Conversion Factor between Spectroscopy and Relaxation The MnCl 2 doped water signal from MRS and the 32 echo pulse sequence were analysed using the spectroscopy program and the non-linear least squares fit. FWHM was 2 Hz. The results Chapter 4. Results and Discussion Metabolite Actual Calculated Ti met T 2 met Ti water T 2 water (mM) (mM) (s) 00 (<0 (s) Cho 13.4 19.1 1.85 1.63 2.36 1.31 ml 13.4 18.6 0.749 0.263 2.39 1.63 Cr 13.4 13.8 1.37 1.16 2.42 1.96 NAA 4.5 9.23 1.83 2.93 2.31 1.82 NAA 8.9 14.7 0.997 1.64 2.38 2.37 NAA 13.4 21.9 1.40 0.591 2.34 1.49 NAA 18.9 31.2 1.31 1.05 2.42 1.95 NAA 44.6 62.4 1.15 1.03 2.41 1.77 Table 4.2: Concentrations, T i , and T 2 Relaxations for all Solutions. " » ISO 200 250 0 50 1 00 1 50 200 250 0 50 100 150 200 250 T E <m&) TE (mi) TE (ms) (a) Inositol (b) Creatine (c) Choline Figure 4.6: Log of Signal Amplitude vs. TE plotted for Inositol, Creatine, and Choline. Concentration (mM) FWHM (Hz) Flip Angle (°) 4.5 3 117 8.9 2 117 18.9 2 115 44.6 3 114 Table 4.3: FWHM Values and Water Flip Angles for NAA. Chapter 4. Results and Discussion 31 50 200 250 (a) 4 .5mM (b) 8.9mM (c) 13.4mM (d) 18.9mM (e) 44.6mM Figure 4.7: Log of Signal Amplitude vs. TE plotted for NAA of Different Concentrations. 50 40 •S 30 < < § 20 o < 10 slope = 0.75 y-intercept = -2.85 20 40 60 Calculated [NAA] (mM) 80 Figure 4.8: Calculated Concentrations vs. Actual Concentrations for NAA Chapter 4. Results and Discussion 32 Metabolite Actual (mM) Calculated (mM) Corrected (mM) Cho 13.4 . 19.1 11.5 ml 13.4 18.6 11.1 Cr 13.4 13.8 7.5 NAA 4.5 9.23 4.1 NAA 8.9 14.7 8.2 NAA 13.4 21.9 13.6 NAA 18.9 •31.2 20.5 NAA 44.6 62.4 44.0 Table 4.4: Corrected Concentrations for all Solutions. Technique T 2 (s) Signal Intensity (arb. units) Spectroscopy Relaxation 0.1205 0.1252 6.2158x10s 2833.0 Table 4.5: Water T 2 Relaxation Times and Signal Intensity as found by Spectroscopy and Relaxation Techniques. are given in Table 4.5, and are plotted in Figure 4.9. Only one component for the relaxation was found. Also in Figure 4.9 there is a plot of the difference between the results of the spectroscopy fit and non-linear least squares fit. This difference fitted to 2.19 x 105 • e-*/32iom S_ 4.4 Relaxation of Agar and Relaxation of N A A Table 4.6 gives the FWHM of the water and the CHESS flip angle for these phantoms. The reason for the large FWHM was because FWHM is proportional to jr. The T 2 re-laxation for water in the agar gel decreased dramatically, and thus caused an increase in the % Agarose FWHM (Hz) Flip Angle (°) 0.0 2 114 1.0 5 120 1.5 5 119 2.0 6 122 Table 4.6: FWHM Values and Water Flip Angles for Agar Gels. Chapter 4. Results and Discussion 33 10 6 o O CO "5 4 Spectroscopy Water T2 - - 32 Echo Water T2 — Difference of Signals 2 0 0 100 200 300 time (ms) Figure 4.9: Plot of Signals from Spectroscopy and 32 Echo Pulse Sequence where the Difference is the Conversion Factor The concentrations found for NAA, and the Ti and T 2 relaxation times for NAA and water are given in Table 4.7 for each percentage agarose. Separate plots are shown for T 2 relaxation vs. percentage agarose for water (Figure 4.11) and NAA (Figure 4.12). The T 2 relaxation of water decreased with percentage agar, as expected. No correlation ex-isted for NAA in changing percentage agar, neither in the T 2 , nor the Tj relaxations. However, there was a trend for the T 2 relaxation times to decrease in NAA with increased percentage agar. Plots of the signal area against TE times are shown for the metabolite signal for each of the agar gels (Figure 4.10.) Compared to the metabolite T 2 fits, the fits for the agar gels are reasonably good. Table 4.8 confirmed that the NAA concentrations were close to the actual concentrations after the correction was applied (as discussed in Section 4.2.) line-width. Chapter 4. Results and Discussion 34 W (0 (0 E "E c (a) 1.0% (b) 1.5% (c) 2.0% Figure 4.10: Log of Signal Amplitude vs. TE plotted for NAA in Different Percentage Agar Gels % Agar Calc. (mM) Ti NAA (s) T 2 NAA (s) Ti water 00 T 2 water 00 T 2 water 00 (32 Echo) 1.0 20.0 0.916 1.59 1.52 0.134 0.134 1.5 20.7 0.882 0.619 1.70 0.0794 0.0808 2.0 21.4 1.16 0.860 1.94 0.0576 0.0596 Table 4.7: Concentrations, Ti , and T 2 Relaxation Times for Water and NAA in Agar Gels % Agar Calculated (mM) Corrected (mM) 1.0 20.0 14.7 1.5 20.7 14.7 2.0 21.4 15.2 Table 4.8: Corrected Concentrations for NAA=14.4mM in % Agar Gels. Chapter 4. Results and Discussion 35 140 Figure 4.11: T 2 Relaxation Time of Water vs. Percentage Agar 160 140 E 120 < < 100 1.5 % Agarose Figure 4.12: T 2 Relaxation Time of NAA vs. Percentage Agar Chapter 4. Results and Discussion 36 T 2 (ms) crT2 (ms) T i (ms) o T l (ms) •Snoise 0~S noise Sno noise 300 40 1300 200 0.761 0.0775 0.757 300 80 1300 200 0.767 0.1067 0.757 300 40 1300 300 0.764 0.1055 0.757 1100 100 1400 100 0.681 0.0283 0.676 1100 200 1400 200 0.689 0.0567 0.676 1100 300 1400 300 0.689 0.0878 0.676 Table 4.9: The Error in the Relaxation Correction Given Errors in Ti and T 2 . 4.5 Computer Simulation of the Effect of Relaxation Errors Computer simulations calculated the error in the relaxation correction given noise in the Tj and T 2 relaxation values. This was done by calculating the relaxation correction factors (equa-tions 2.25 and 2.26) using noisy Ti and T 2 values. The uncertainty in the corrected signal was determined and the error in concentrations could be estimated. Table 4.9 lists the relaxation times, the errors in the relaxation times, the calculated relaxation correction with noise and without noise, and the standard deviation of the relaxation time with noise. The TE and TR times were assumed to be 30ms and 1500ms, respectively. The first three rows in Table 4.9 list in vivo relaxation times and the resulting uncertainties with their associated errors. Increasing the errors in either the T i or T 2 time increases the correction uncertainty. The last three rows list average relaxation times found for the phantoms in this work. The resulting uncertainties range between 4 and 13%. Chapter 5 Conclusions A protocol has been developed in order to measure Ti and T 2 relaxation times and metabolite concentrations. Based on SNR, justification was given for choosing TR=1500ms while mea-suring the T 2 relaxation curve. The TE times to characterize a signal relaxing with T 2 on the order of hundreds of milliseconds were: 30; 60; 100; 150; and 200ms. The TR times of 1233, 1500, 2500, and 3500ms characterize signals with Tj relaxation between 1000 and 1500ms. The choice of TE and TR times have'been verified experimentally for the water signal using the spectroscopy sequence and the 32 echo sequence. The scaling factor between the spectroscopy signal and the 32 echo signal was found to be 2.19 x 105. Since the results vary between these two methods by only a scaling factor, spectroscopy and 32 echo results could be compared. The water signal from the agar gave similar T 2 relaxation information for the 32 echo and the spectroscopy sequence. The T 2 relaxation of water in the three agar gels decreased with percentage agar. The T 2 of the NAA signal decreased slightly when in agar, but not as signifi-cantly as the water signal. The variation of T 2 relaxation for NAA at different concentrations was not consistent, a trend for NAA may exist in varying agar strengths, but it was obscured by the uncertainty in the T 2 relaxation value. The calculated concentrations for the NAA in agar gave the actual concentrations after the correction factor was applied. The calculated concentrations of metabolites increased linearly with the actual concentra-tions. When a correction factor was applied, the calculated concentrations ranged around the actual concentration values. The inaccuracy of the calculated concentrations could be due to a number of possible factors: 1. Perhaps most significantly are the consistently poor fits found for T 2 relaxation, as seen in Figures 4.6 and 4.7. As a result of poor fitting, a T 2 correction cannot be adequately determined. 37 Chapter 5. Conclusions 38 2. The TE times used did not characterize the Ti and T 2 relaxation times, as seen in Figure 4.5 for T 2 . This could lead to the errors discussed above and in Section 4.5; 3. Integration underestimated the water peak. 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