Technical Developments of in vivo Proton Magnetic Resonance Spectroscopy

Transcription

1 Technical Developments of in vivo Proton Magnetic Resonance Spectroscopy by Karl Landheer A thesis submitted in conformity with the requirements for the degree of Doctor of Philosophy Graduate Department of Medical Biophysics University of Toronto Copyright 2017 by Karl Landheer

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3 Abstract Technical Developments of in vivo Proton Magnetic Resonance Spectroscopy Karl Landheer Doctor of Philosophy Graduate Department of Medical Biophysics University of Toronto 2017 Proton magnetic resonance spectroscopy (MRS) is a powerful non-invasive technique to probe the biochemistry of the brain and body. Because MRS signals are collected from metabolites in concentrations on the order of a few mm in biological tissues, (rather than from water at approximately 40 M concentration, as in magnetic resonance imaging) low signal-to-noise ratio (SNR) poses a major challenge. In the face of this challenge, there is an ongoing need for improved techniques to enhance the clinical applicability of MRS. One area of interest, for example, involves using MRS data as a biomarker for the assessment of early response in radiation therapy. This thesis focuses on the development of three MRS techniques, with the ultimate goal of this work being used in early radiation detection response protocols. First, a technique is developed to extend single voxel MRS to MRS of a small number of voxels (eg. two) without the need for spatial frequency encoding, using customized selective radiofrequency (RF) excitation iii

4 and the localized sensitivity of multichannel receiver coils. The SNR efficiency of this technique is demonstrated in phantoms, healthy adult volunteers and patients with brain cancer. Second, a novel inversion and saturation recovery sequence is developed in conjunction with a spectral editing module to estimate the longitudinal relaxation time (T 1 ) of lactate in vivo at 3 T. Lactate is of significant interest due to its role in cellular metabolism, and particularly its elevation in tumors. The resulting T 1 estimate enables further optimization of MRS protocols and assists in estimating the absolute concentration of lactate from MRS data. Third, a diffusion-weighted two-dimensional spectroscopy sequence is developed, subsequently referred to as DW-JPRESS. This sequence, as well as an optimized processing pipeline, is demonstrated to provide estimates of the apparent diffusion coefficient (ADC) of brain metabolites beyond those typically accessible at 3 T, namely glutamate, myo-inositol and scyllo-inositol. The DW-JPRESS data provide unique information concerning the local diffusion environment of each measured metabolite, with the potential to characterize microstructural changes from different brain pathologies including cancer. Collectively, the technical development undertaken in this thesis promises to enhance future clinical applications of MRS, such as its use in distinguishing between neoplastic and nonneoplastic lesions, or for assessing tumor recurrence. iv

5 Acknowledgments First of all I would like to thank my supervisor, Dr. Simon Graham, for this thesis would not be possible without his constant guidance, support, and commitment. I would also like to thank my supervisory committee members, Dr. Charles Cunningham and Dr. Kullervo Hynynen, for their encouragement and enthusiasm throughout my project, as well as Chuck s happiness to discuss anything related to RF pulses. I would like to thank Jeff Stainsby and Dr. Albert Chen for their help navigating the tricky world of EPIC. I thank Dr. Arjun Sahgal for being the most enthusiastic clinical collaborator I could hope for, as well as his record-breaking response times. Thanks to Fred Tam for his technical assistance and Rafal Janik for always being willing to explain why what I m doing is the wrong way of doing things. Thanks to Justin Lau for his help in understanding the quantum side of this research. Thanks to all the volunteers, in particular James Mester, Lech Skórski and Philip Chen who spent several hundred hours lying still inside the magnet without any complaints. Thanks to Dr. Diana Sima for her help with AQSES, and Dr. Martin Wilson for his unending and insightful support on the TARQUIN help forums. Thanks to Rolf Schulte and Ben Geraghty for their help in implementing ProFit. Thanks to all my friends for their much needed comic relief and Sarah for her love and support. Additionally I acknowledge the pivotal roles my brother, Alex, and my grandparents, Ann, Percy David, and Cath have played in my life without them I would not be where I am today. Finally I am deeply grateful for the support of my parents Karen and Dolf, who always nurtured my curiosity and pushed me to do my best. v

6 Table of Contents Contents List of Tables... ix List of Figures... x List of Acronyms... xii Chapter Introduction Basic Physics of Nuclear Magnetic Resonance Spectroscopy Quantum Mechanics of a Spin ½ Particle in a Magnetic Field Product Operator Formalism Relaxation Spectral Editing Two-dimensional Spectroscopy Relationship of the Semi-Classical Formalism to the Quantum Mechanical Formalism In vivo MRS of the brain In vivo MRS acquisition Biochemistry of the Brain Gliomas Other brain lesions Spatial Localization of in vivo MRS Parallel Imaging Absolute Quantitative MRS Diffusion-weighted MRS vi

7 1.7 Hypotheses and Thesis Outline Chapter Introduction Materials and Methods Results Discussion Conclusions Chapter Introduction Theory Methods Results Discussion Conclusions Chapter Introduction Methods Results Discussion Conclusions Chapter Summary Future Directions for CSSMRS Future Directions for DW-JPRESS Early Radiation Treatment Response vii

8 5.5 Final Remarks Bibliography viii

9 List of Tables Table 2.1: Summary of brain tumor patients for Chapter Table 2.2: Quantified NAA values from PRESS and CSSMRS Table 2.3: Quantified Cho values from PRESS and CSSMRS Table 2.4: Quantified Cr values from PRESS and CSSMRS Table 2.5: Quantified Lac values from PRESS and CSSMRS Table 3.1: Summary of radiofrequency (RF) pulses in the prototype pulse sequence Table 3.2: The TI, TR and total scan time values for all experiments in Chapter Table 3.3: T 1 values measured within the white matter in two healthy volunteers Table 3.4: Estimated T 1 values from six patients with high grade glioma Table 3.5: Estimated absolute concentration of metabolites from six high grade glioma patients Table 4.1: ADC estimates obtained from the BRAINO phantom Table 4.2: ADCs estimated from 6 subjects for 2D and 1D pipelines ix

10 List of Figures Figure 1.1: Graphical representation of the effect of an RF pulse on spin states... 6 Figure 1.2: The conversion of to with an RF pulse... 8 Figure 1.3: Effects of chemical shift and J-coupling on the measured absorption spectrum for lactate Figure 1.4: 2D JPRESS signal as a function of time (horizontal axis) obtained with maximum-echo sampling Figure 1.5: Logarithmically-compressed contour plot of the JPRESS absorption spectrum from the Braino MRS phantom Figure 1.6: Spectrum obtained from parietal brain tissue of a healthy volunteer using PRESS with TE = 30 ms echo time at 3 T Figure 1.7: Pulse sequence diagram for PRESS Figure 1.8: Spatial localization obtained from PRESS Figure 1.9: The effect of the order of summing and phasing the individual excitations in DW- MRS Figure 2.1: a) Pulse diagram for CSSMRS. b) An anatomical T 1 -weighted image of a patient with nominal voxel locations overlaid Figure 2.2: Spectra from both a healthy volunteer (a and b) and a brain cancer patient (c and d) measured with both CSSMRS and PRESS Figure 2.3: Spectra from a healthy volunteer at 30-milisecond echo time, obtained by using both CSSMRS and PRESS Figure 2.4: The unapodized spectrum obtained from CSSMRS from a patient 1along with the fit x

11 Figure 2.5: Measured and simulated differences between the CSSMRS and PRESS measurement for six different voxel separations Figure 2.6: Simulated metabolite quantification values for seven different voxel separations.. 56 Figure 3.1: Spectroscopic pulse sequence for measuring T 1 relaxation Figure 3.2: T 1 weighted anatomical image with voxel placement Figure 3.3: Inversion recovery results for Braino phantom for the four major metabolites observed at TE = 144 ms (creatine, lactate, NAA, choline) Figure 3.4: Singlet and doublet spectra for two different inversion times from high grade glioma patient Figure 4.1: DW-JPRESS pulse sequence for the a) initial echo time and b) intermediate k th echo time Figure 4.2: Flow chart of the processing steps used to estimate ADCs from the raw DW-JPRESS data Figure 4.3: a) Axial prescription and b) coronal prescription of the DW-JPRESS voxel Figure 4.4: Water-suppressed JPRESS spectra obtained from healthy volunteer for two different b-values, along with fit and residual obtained from ProFit Figure 4.5: Plot of ADCs estimated from the 2D pipeline versus those estimated from the 1D pipeline Figure 5.1: Four voxel profile overlaid on an anatomical axial MR image xi

12 List of Acronyms Acronym ADC Ala Definition Apparent Diffusion Coefficient Alanine Asc Ascorbic acid (Vitamin C) Asp AQSES BASING CHESS Cho Cr CSSMRS DW-JPRESS DW-MRS FGRE FOV Aspartate An automated quantitation of short echo time MRS spectra Band Selective Inversion With Gradient Dephasing Chemical Shift Selective Choline Creatine Constrained Source Space Magnetic Resonance Spectroscopy Diffusion-Weighted J-Resolved Spectroscopy Diffusion-weighted Magnetic Resonance Spectroscopy Fast Gradient Echo Field of View xii

13 FSPGR GABA Gd-DTPA g-factor GRAPPA Gln Glu Gly Glx GPC GSH HVSD IR JPRESS Lac MFIR MRI MRS Fast Spoiled Gradient Echo -amintobutyric acid Gadopentetic acid Geometry factor Generalized Autocalibrating Partially Parallel Acquisitions Glutamine Glutamate Glycine Glutamine + Glutamate Glycerophosphorylcholine Glutathione Hankel Singular Value Decomposition Inversion Recovery J-Resolved Spectroscopy Lactate Modified Fast Inversion-Recovery Magnetic Resonance Imaging Magnetic Resonance Spectroscopy xiii

14 NAA NAAG NMR PCh PE PRESS ProFit RF Scy SENSE SLR SNR STEAM TARQUIN TE TI tnaa TR Tau N-Acetylaspartic acid N-acetylaspartylglutamate Nuclear Magnetic Resonance Phosphorylcholine Phosphorylethanolamine Point-Resolved Spectroscopy Two-dimensional Prior-Knowledge Fitting Radiofrequency pulse Scyllo-inositol Sensitivity Encoding Shinnar-Le Roux Signal-to-Noise Ratio Stimulated Echo Acquisition Mode Totally Automatic Robust Quantitation in NMR Echo Time Inversion Time N-acetylaspartate + N-acetylaspartylglutamate Repetition Time Taurine xiv

15 1.1 Introduction Chapter 1 This thesis develops several technical advances in the field of in vivo magnetic resonance spectroscopy (MRS), focusing on applications to the brain. The following introduction provides an overview of the necessary physics required to motivate the research, and to understand the research methodology and analysis described in subsequent chapters. The specific introductory topics of interest are the basic physics of nuclear magnetic resonance spectroscopy, spectral editing, two-dimensional spectroscopy, in vivo MRS, magnetic resonance parallel imaging, absolute quantitative spectroscopy and the measurement of the diffusion of brain metabolites. 1.2 Basic Physics of Nuclear Magnetic Resonance Spectroscopy The basic physics underlying MRS is the logical starting point to understand the work described in this thesis. This foundation is provided by physics underlying nuclear magnetic resonance (NMR) for spin ½ particles, which fully applies to all the chemical species of specific interest within the thesis context. Although the common semi-classical formalism used in magnetic resonance imaging (MRI) is sufficient to describe the spin dynamics of uncoupled spin systems, many of the chemical species of interest exhibit coupling phenomena. Thus, the full quantum formalism must be summarized. A section of the introduction is also devoted to translating between the semi-classical and quantum formalism, as the semi-classical formalism is used for simplicity within this work when the effects of coupling can be neglected Quantum Mechanics of a Spin ½ Particle in a Magnetic Field Elementary particles contain an intrinsic angular momentum referred to as spin. It is taken here as an empirical fact that protons have an intrinsic angular momentum of ½ħ, where ħ is Planck s reduced constant ( x m 2 kg/s). The factor ħ is frequently omitted due to convenience and is implicitly assumed, thus a proton is hereafter referred to as a spin ½ particle, or in MR jargon as a spin. 1

16 2 Every NMR experiment measures how a group of spins evolve with time. A spin ½ particle in the presence of an applied magnetic field (by convention chosen to be along the z direction, also referred to as the longitudinal direction) can occupy one of two stationary Zeeman eigenstates of energy: one aligned with the field, referred to as the spin up state, and one anti-aligned with the magnetic field, referred to as spin down state. These two eigenstates are conveniently expressed using either the bra-ket notation or the vector notation: ( ) (1.1) ( ) (1.2) where is aligned with the field and is anti-aligned. These two spin states are referred to as the Zeeman eigenbasis because any spin state can be expressed as a linear combination of these two. The second value in the bra-ket notation indicates the projection of the spin angular momentum onto the z-axis, as chosen by convention. eigenbasis are The matrix representations of the three angular momentum operators in the Zeeman ħ ( ) (1.3) ħ ( ) (1.4) ħ ( ) (1.5) It can easily be shown that the application of the z angular momentum operator to the spin state or yields the eigenvalues ħ/2 and -ħ/2, respectively. By the Heisenberg uncertainty principle, a spin cannot be in simultaneous eigenstates of all three operators, since the operators do not commute. This is evident as the states or are not eigenvectors

17 3 of or, which provide the components of angular momentum in the transverse plane orthogonal to the longitudinal direction. The Hamiltonian for a single spin in the presence of an applied magnetic field is given by 1 ħ ( ) (1.6) where is the gyromagnetic ratio (267.5 x 10 6 rad/s/t for protons) and is the magnitude of the applied magnetic field. Application of this Hamiltonian to the two eigenstates yields the two energy eigenvalues: ħ (1.7) ħ (1.8) Thus, the spin-down state is at the higher energy state and the spin-up state is at the lower energy state. The difference between the two energy levels is ħ ħ and spins can undergo transitions between the two states when this amount of energy is applied in the form of a radiofrequency (RF) pulse, as explained further below. Although there are only two eigenstates for a spin ½ particle, a very small number of spins in a typical NMR experiment are actually in either of the eigenstates due to various timedependent processes, such as molecular motion. The vast majority of spins are in a superposition of spin-up and spin-down states, which can be written using the superposition principle as (1.9) where and are complex numbers called position coefficients. These coefficients must be normalized such that: (1.10)

18 4 The spin state obeys the time-dependent Schrödinger equation 1 : ( ) ( ) (1.11) where is the spin Hamiltonian operator, the operator representation of the total energy of the system. Schrödinger s time-dependent equation is a first-order ordinary differential equation with the solution, ( ) ( ) ( ) (1.12) Equation 1.12 indicates that the spin state at a later time ( ) is completely determined by knowledge of the initial spin state at time and the Hamiltonian of the system. Typically the dynamics of spins are expressed in the rotating reference frame which simplifies the solution of the Schrödinger equation in the presence of an applied RF pulse. This is done by viewing the experiment from a frame that rotates about the -z axis at a chosen reference angular frequency,. It can then be shown 1 that the solution to the Schrödinger equation in the rotating frame is given by ( ) ( ) ( ) (1.13) where is the Hamiltonian in the rotating frame and is the state of the spin in the rotating frame, given by ( ) (1.14) and is the rotation matrix about the z axis in the rotating frame. The Hamiltonian in the rotating frame,, can be related to the Hamiltonian in the laboratory frame by 1 ( ) ( ) (1.15) The convenience of the rotating frame is not immediately clear from Equations However, if a circularly-polarized RF pulse is applied at the chosen reference angular frequency, using an electromagnetic coil of appropriate geometry such that magnet field

19 5 components of the pulse rotate in the transverse plane, then the Hamiltonian in the laboratory frame is given by 1 { ( ) ( )} (1.16) where is the amplitude of the applied RF pulse (given in units of Tesla), and is a chosen phase factor that controls the orientation of the effect of the RF pulse. It can be shown by applying Equation 1.16 to Equation 1.15 that the effect of the Hamiltonian of the RF pulse can be written in the rotating frame as ( ) ( ){ ( ) ( )} (1.17) where is the amplitude of the magnetic field of the applied RF pulse. It can then be shown by applying Equation 1.17 to Equation 1.13 that the state after application of the RF pulse is related to the state before application of the RF pulse by ( ) ( ) ( ) (1.18) where ( ) is the rotation operator with matrix representation ( ) ( ( ) ( ) ( ) ) (1.19) ( ) ( ) ( ) Equation 1.19 shows that the effect of an RF pulse is the rotation of the state of the particle in the rotating frame by the flip angle. For all work presented here the phase factor is arbitrarily set to be zero, thus the effects of the RF pulses are to rotate the spin state around the x axis. If the phase factor was changed to then the effect of RF pulses would be to rotate the spin state about the y axis instead. Modern NMR instrumentation provides full control over the phase of the applied RF pulses, but for all the pulse sequences presented here there is no such need, thus it is neglected for simplicity. For an amplitude-modulated pulse ( ) is given by

20 6 ( ) (1.20) where is the RF pulse duration. A graphical representation of the effects of Equation 1.19 is shown in Figure 1.1, depicting how common RF pulses act on spins initially in state. A rotation about the x axis by radians places spins in the state, which is an eigenstate of the angular momentum operator. A further /2 rotation places spins in the state. Figure 1.1: Graphical representation of the effect of Equation 1.19 (an RF pulse causes rotation of spin states, represented by dark arrows, about the x axis in the rotating frame when the phase equals zero). The initial, spin-up state is ; is an eigenstate of the momentum operator ; is the spin-down state. x is the rotation operator about the x axis with brackets indicating the flip angle rotated, according to Equation by which the angular momentum operator is

21 7 Alternatively, spins in the state can be placed into state by a rotation about the x axis Product Operator Formalism In a typical in vivo MRS experiment the chemical species are present in concentrations of a few millimoles, which means the signal from roughly spins is measured. Two tricks have been developed to circumvent the need to develop an eigenstate that spans all particles. These two tricks are referred to as the density matrix and product operator formalism 2. The density matrix formalism is complete and is able to describe the result of any general NMR experiment. The product operator formalism is only applicable in the weak-coupling regime, where the Hamiltonian is dominated by the Zeeman term. In this scenario, all terms within the Hamiltonian commute. This approximation is sufficient for this thesis as most biological molecules are weakly-coupled. The benefit of the product operator formalism is that an implicit expectation value is taken over many spins. This gives a clear physical meaning to the angular momentum operators and much of the subsequent quantum mechanics can be ignored, including the density matrix. In the following, the terms and refer to the longitudinal, x and y magnetization components of spin k, respectively. Strictly, spin k is not a single spin but the average over all magnetically equivalent spins. For example, spin k could represent all the hydrogens in water or the methyl protons in lactate. The measured signal from spin k in an MRS experiment is given by (i.e., only magnetization in the transverse plane is measured). The relevant Hamiltonians can be summarized by a few simple rules explained below. This formalism offers the ability to predict the outcome of complicated multi-pulse experiments for weakly-coupled spins with the successive application of simple rules. The effect of RF pulses on the magnetization terms is identical for the individual spin states, as all individual spin states experience the same rotation, as shown in Figure 1.2.

22 8 Figure 1.2: The conversion of to produced by an RF pulse. The net magnetization in these directions is represented by the grey arrows. Notice that the effect of the RF pulses, ( ) and ( ) is identical for each different spin. The product operator analog of Equation 1.13 is given by ( ) ( ) ( ) ( ) (1.21) After application of an RF pulse, the spins are said to be in free precession. For a typical in vivo proton MRS experiment involving N magnetically different types of spins in an isotropic liquid, this condition is governed by two relevant terms in the Hamiltonian: (1.22) where is the spin angular momentum vector for the k th spin; is the scalar J-coupling value between two different spins, a measured (field-independent) constant; and is the relative Larmor frequency given by (1.23) where and, which is dependent on the magnetic field experienced by the particular spin is a reference frequency which is under experimental control, typically tuned to water

23 9 due to its high signal. The first term in Equation 1.22 is referred to as the chemical shift term, resulting from shielding of the applied magnetic field by the electron cloud surrounding the proton nucleus. This value is by convention measured in reference to the molecule tetramethylsilane (TMS) and is usually stated in parts per million (ppm). The conversion between the angular frequency, measured in rad/s, and the chemical shift measured in ppm is given by (1.24) where is the precessional frequency of the protons in TMS. Measuring chemical shift in ppm is convenient because the magnetic field dependence of the frequency of spins is removed. The second term in Equation 1.22 characterizes the J-coupling interaction that arises between neighboring nuclear spins from an indirect coupling that is mediated by the surrounding electron cloud. Briefly, each spin has its own associated magnetic field which slightly alters the electromagnetic characteristics of the surrounding electron cloud. This altered electron cloud then affects the local magnetic field of the coupled spin, slightly changing its precessional frequency. This mediation through the electron cloud is why J-coupling is also referred to as indirect coupling. (As an aside, each spin can affect the local magnetic field of a neighboring spin and is referred to as direct dipole-dipole coupling, or simply dipole-dipole coupling. In an isotropic liquid it can be shown that the dipole-dipole effect averages to zero and therefore does not affect the observed spectrum beyond influencing the rate of relaxation processes 1. More will be said about relaxation processes below.) Using the product operator formalism by applying the Hamiltonian given in Equation 1.22 to Equation 1.21 the freely precessing magnetization of one spin weakly-coupled to another (in the absence of relaxation), referred to as an AX system, is given by 1

24 10 ( ( )( ( ) ( ) )) (1.25) ( ( )( ( ) ( ) )) ( ( )( ( ) ( ) )) (1.26) ( ( )( ( ) ( ) )) (1.27) with similar transformations for and. Equations 1.25 and 1.26 are generated from several other assumptions beyond weak spin coupling. The RF pulse duration is considered to be short in comparison to both longitudinal and transverse relaxation processes. This is a good approximation for the RF pulses used in this thesis, which have duration of 3-30 ms. For substantially longer RF pulses, the effects of relaxation must be included for quantitative measurements. Furthermore, for simplicity when applying the rules of the product operator formalism, relaxation is often suppressed at the outset then added post-hoc by following the appropriate echo pathway 3 which generated the acquired signal. As can be seen from the timeevolution of the transverse operators and (Equations 1.25 and 1.26), the terms ( ) and ( ) are to the chemical shift evolution, and terms ( ) and ( ) are due to J-coupling evolution. The chemical shift evolution is simply an accrual of phase (interconversion of and ), whereas J-coupling results in an inter-conversion from in-phase magnetization ( ) to anti-phase magnetization (, ). The term does not evolve under chemical shift or J-coupling. It should also be mentioned that the process of spin echo formation discussed above must be qualified slightly when J-coupled species are considered. By allowing magnetization to evolve in the transverse plane for time and then applying a pulse, the resulting magnetization after another evolution time is still modulated by J-coupling effects whereas chemical shift effects are completely refocused. This is what allows for J-resolved spectroscopy, as discussed in further detail in Section

25 11 The most common in vivo MRS experiments use either point resolved spectroscopy (PRESS) 4 or stimulated echo acquisition mode (STEAM) 5 sequences. Both sequences use identical spatial localization techniques to obtain MRS data from a single coarse volume element (voxel), but PRESS involves spin echo formation (a pulse followed by two pulses) whereas STEAM uses a stimulated echo involving three pulses. The PRESS sequence offers a factor of two improvement in the amplitude of the signal, but STEAM uses shorter RF pulses (since, for a given max B 1 amplitude, a pulse will be of shorter duration as evident from Equation 1.20) and thus the echo time can be reduced, making STEAM better suited for chemical species whose signal decays rapidly. Additionally pulses deposit a quarter of the energy when compared to pulses and have more flexibility in the choice of bandwidth and slice profile. Due to their inherent similarities STEAM, with suitable modifications, could be used interchangeably for all the work presented here. After the MRS signal is acquired in the time domain by PRESS or STEAM sequences, the spectral information is usually interpreted in the frequency domain after Fourier transformation of the signal. In the frequency domain, different chemical species are present at their characteristic chemical shifts in the form of Lorentzian functions. The Lorentzian nature is due to the monoexponential decay of the transverse magnetization, and deviation from this monoexponential decay will result in other lineshapes. By taking the Fourier transform of a measured time-dependent MRS signal with a relative frequency value T 2, the following spectral lineshape is obtained: and transverse relaxation { ( ) ( )} ( ) ( ) ( ) ( ) ( ) (1.28) The real portion of Equation 1.28 is a Lorentzian lineshape, and is referred to as the absorption portion of the spectrum, whereas the imaginary portion is referred to as the dispersion portion. Of the two portions, the absorption lineshape has much narrower linewidth and is conventionally displayed as a consequence. All spectra in this thesis consist of absorption lineshapes. The measured signal is multiplied by an arbitrary phase factor to display

26 12 Figure 1.3: Effects of chemical shift and J-coupling on the measured absorption spectrum for lactate. A molecule of lactate has two chemical groups which give measurable proton MRS signal: a methine [CH] and a methyl [CH 3 ] group. The methine proton gives rise to a quartet (left side of the bottom spectrum) because it is coupled to three protons, whereas the methyl group is a doublet (right side of the bottom spectrum) because it is coupled to a single proton. The area under the doublet is three times as large as that under the quartet, due to the factor of three times as many protons from the methyl group than the methane group. The chemical shift and J-coupling value are not shown to scale, for display purposes. The hydroxyl group does not contribute to measurable signal at room temperature due to its very fast T 2 relaxation.

27 13 the real portion as the Lorentzian lineshape, which is referred to as zero-order phasing the spectrum. Considering now the MRS data from multiple weakly-coupled species, the resulting absorption spectrum will consist of a set of Lorentzians separated by the relative chemical shift,, of each species, with the Lorentzians split further by the J-coupling effects that occur between each species. A peak which has no J-coupling is referred to as a singlet, and a peak which is split into two peaks (due to its coupling with a single neighboring spin) is referred to as a doublet. A peak which is split into three peaks (due to coupling with two neighboring spins from the same nuclei) is referred to as a triplet, etc. The relative amplitudes of the split lines are given by the binomial distribution. Splitting is additive: for example, if a spin is coupled to two different nuclei each with a single spin, the resulting splitting would produce a doublet of doublets (a quartet) with four spectral lines of identical amplitude. As another example, Figure 1.3 shows the effects of chemical shift and J-coupling on the spectrum from lactate Relaxation Both spin-lattice (T 1 ) and spin-spin (T 2 ) relaxation are caused by fluctuations in the magnetic field experienced by the spins due to thermal molecular motion. The T 1 relaxation effect characterizes the restoration (or recovery ) of magnetization toward the equilibrium state of alignment with the applied main magnetic field. This longitudinal relaxation occurs because the spin state aligned with the field minimizes potential energy and after each thermal collision, a small amount of energy is lost such that the magnetization will very slightly preferentially align with the field. After very many collisions, the original thermal equilibrium magnetization is restored. In practice, T 1 is an empirically measured parameter on the order of 1000 ms for most of the biologically relevant molecules considered in this thesis. The other relaxation parameter, T 2 characterizes how each molecular collision affects the phase of the individual spins. Initially after RF excitation, a net polarization exists indicating that the spins are freely precessing in phase in the transverse plane. After a molecular collision between spins, however, the phase of the spins is altered. After many collisions, the phase across all spins approaches a uniform distribution and the transverse magnetization decays (relaxes) to zero. For the biological chemicals described here, T 2 is typically on the order of 100 ms, although the value varies

28 14 significantly across chemical species. The T 1 and T 2 values for a group of spins are affected by numerous physical factors such as the temperature, magnetic field strength, and the surrounding molecular environment. Some chemical agents, such as the commonly used contrast agent gadolinium, can drastically shorten the T 1 of surrounding molecules due to its unpaired electrons which cause magnetic field variations that induce relaxation. The two most common NMR methods to measure longitudinal relaxation are the Inversion Recovery 6 and Saturation Recovery 7 sequences of RF pulses. The Inversion Recovery sequence initiates with an RF pulse of flip angle, referred to as an inversion pulse for its ability to make the equilibrium magnetization point in the opposite direction. The time between the inversion pulse and a subsequent RF excitation pulse, used to measure or read out the NMR signal, is referred to as the inversion time (TI). The signal is measured at a variety of TI values and then fit to a mono-exponential model to estimate the T 1 value. In a typical Inversion Recovery experiment, the magnetization is allowed to relax very nearly to equilibrium between successive measurements at different TI values. Thus, the repetition time (TR) is usually set to a value much greater than the T 1 value of interest. In a Saturation Recovery experiment, the signal is measured at a variety of different TR values, where the signal is not allowed to relax to equilibrium in between successive RF excitations, and fit to a monoexponential model to estimate T 2. The T 2 relaxation is typically measured via a spin-echo pulse sequence 7. In this experiment, the magnetization is excited by a RF excitation pulse and then allowed to relax (de-phase) in the transverse plane for a duration. A pulse, referred to as a refocusing pulse is then applied to flip the orientation of spins in the transverse plane. As the spins retain the same precession characteristics after refocusing as they had before (see below for further clarification), the magnetization re-phases at a time afterwards when a spin-echo is said to have formed. To estimate T 2 values, this spin echo sequence can be repeated for many different values and the measured spin signal amplitudes can then be fit to a monoexponential model as a function of TE. Alternatively, it is also possible to sample the T 2 decay curve by creating multiple spin echoes with a single RF excitation pulse followed by an appropriately-spaced train of refocusing pulses. These methods are in no way exhaustive,

29 15 as virtually any pulse sequence which causes magnetization to evolve in the transverse plane and longitudinal plane will be sensitive to both T 1 and T 2, and in principle can be used to perform relaxation measurements. However, the pulse sequences described have the merit that they enable measurements of a single type of relaxation in a relatively straightforward manner Spectral Editing One challenge of in vivo MRS is that many of the chemical species of interest have very similar chemical shift values. Thus, the overlap of spectral lines causes difficulties in accurately separating the signals and quantifying relative concentrations. One method to overcome this pitfall is referred to as spectral editing, which has been applied to a wide array of different chemical species. Spectral editing falls into two categories: J-difference editing and multiple quantum coherence editing. The former is used within this thesis and is subsequently discussed below, whereas the latter is rarely used for in vivo MRS due to time constraints as well as hardware limitations. The J-difference editing category exploits the differences in the J-coupling between metabolites with comparable chemical shift. Initially, this spectral editing technique used different echo times to produce different evolutions through J-coupling 8. For example, it can be shown that for an AX system (two individual weakly coupled spins) a spin-echo experiment can be represented by ( ) (1.29) If the pulse sequence is repeated with twice the evolution time, then ( ) (1.30) The subtraction of the measured signal from these two experiments yields the magnetization ( ). For spins that are uncoupled, the resulting measured magnetization is ( ) for both evolution times, thus subtraction eliminates the signal component from uncoupled spins. This neglects transverse relaxation effects, however, as the measurement

30 16 with the longer echo time will have reduced signal. To circumvent this problem, improved spectral editing techniques have been developed which use frequency-selective RF pulses to refocus J-coupling effects 9. These spectral editing techniques selectively edit one spin thereby modifying the measured magnetization of the associated coupled spin. Typically two cycles are repeated, one with the editing pulses off, and one with the editing pulses on. The measurements are then subtracted to yield the J-coupled spin of interest. The results from these selective-editing sequences are similar to the original spectral editing method, but are insensitive to T 2 relaxation effects because both cycles have equal echo time. This spectral editing technique is used in Chapter 3 for the separation of the lactate methyl group and contaminating lipid signals Two-dimensional Spectroscopy An alternative to spectral editing pulses is two-dimensional (2D) MRS. Similar to spectral editing techniques, 2D spectroscopy techniques exploit J-coupling to distinguish between overlapping metabolites 10. Used widely in the field of in vitro NMR, 2D MRS offers significantly more information over 1D spectroscopy, such as molecular connectivities through correlation spectroscopy (COSY 11 ) and molecular distances through Nuclear Overhauser Effect spectroscopy (NOESY 12 ). Due to hardware constraints and scanning time, however, only the most basic of 2D spectroscopy techniques have been applied in vivo 13. The 2D spectroscopic technique referred to as J-resolved spectroscopy (JPRESS) is used within this work due to its comparatively shorter 2D spectroscopic acquisition time compared to other alternatives 13 together with 2D spectral fitting software referred to as ProFit 14,15. The JPRESS experiment can be understood by considering how the magnetization of J- coupled species evolves with time. From Equation 1.25 and Equation 1.26, J-coupling results in an interconversion of in-phase and anti-phase magnetization. The resultant magnetization for a spin-echo experiment with echo time frequency of the spin is given by with a reference frequency tuned to the Larmor ( ) ( ) (1.31)

31 17 Thus, the measured signal is modulated by the cosine term ( ) due to J-coupling. The second term in Equation 1.31, the anti-phase magnetization, is not directly measured but can be detected by converting it to in-phase magnetization through RF pulses or timeevolution. By measuring the signal with sequentially increasing echo time,, metabolites that overlap in chemical shift can be discerned by their J-coupling value. In principle, in vivo JPRESS uses two pulses for spatial localization as necessitated by PRESS 4 but the result of Equation 1.31 still holds. Typically, in vivo JPRESS spectra are acquired with a maximum echo sampling scheme (data collection begins immediately after the last crusher gradient, instead of the usual 1D approach of acquiring beginning at the peak of the echo) to increase available SNR as well as to improve sensitivity by shifting the tails of the absorption lineshapes off the horizontal axis 16. Figure 1.5 displays an example 2D JPRESS signal obtained over time from a phantom test object. The corresponding spectral data after Fourier Transformation are shown in Figure 1.5. The directly measured frequency dimension is referred to as (chemical shift) and the indirectly measured frequency dimension (from the sequential increase in echo time) is referred to as (J-modulation). The benefits of acquiring with a maximum echo sampling scheme can be readily observed from Figure 1.4 and Figure 1.5, as the ripples in the time-domain data ensure that the tails of the lineshapes are now oriented at 45 o. If data sampling commenced at the spin echo maximum, then the tails would lie on the F 1 = 0 axis, contaminating the measurement of smaller resonances along this line. The tails are inherently lengthy due to the Lorentzian nature of the absorption spectrum, caused by taking the Fourier transform of the exponential envelope of the time-dependent signal recorded during JPRESS Relationship of the Semi-Classical Formalism to the Quantum Mechanical Formalism In the classical formalism, the magnetization is governed by the classical equivalent of the Schrödinger equation, the Bloch equations: ( ) ( ( ) ( )) ( ) (1.32)

32 18 ( ) ( ( ) ( )) ( ) (1.33) ( ) ( ( ) ( )) ( ) (1.34) where is the equilibrium magnetization value, and the magnetic field ( ) ( ) ( ). The terms ( ) and ( ) represent the magnetic field of the RF pulse, and the terms, and are the longitudinal magnetic field gradients in the Figure 1.4: 2D JPRESS signal as a function of time (horizontal axis) obtained with maximumecho sampling. The data were acquired with a total of 100 different echo times ( echo steps, vertical axis), each with an acquisition time of ms. The Fourier transform of these data is shown in Figure 1.5.

33 19 Figure 1.5: Logarithmically-compressed contour plot of the JPRESS absorption spectrum from the Braino MRS phantom. The x axis is the chemical shift frequency dimension (measured in ppm), and the y axis is the J-modulation frequency (measured in Hz because it is fieldindependent). three orthogonal directions. These gradient terms are critical for in vivo MRS, as they are used to together with RF pulses to select regions of interest and to de-phase the signal from other regions 4,5, as explained in more detail in Section The classical formalism involves simpler equations than the quantum mechanical formalism and thus is preferential when small effects such as J-coupling can be neglected. For proton magnetic resonance imaging (MRI) which measures signal almost entirely from the uncoupled protons of water and fat, or when the applied RF pulse dominates the Hamiltonian (and thus J-coupling effects can be neglected) the classical formalism is the obvious method of choice. Solving the Bloch equations reveals that the magnetization behaves identically to the quantum mechanical formalism in the absence of coupling, namely RF pulses rotate the magnetization, transverse magnetization (the measured portion of the magnetization) accrues phase with time and relaxation of the magnetization vector components is identical to relaxation of the angular momentum operator analogs. It is evident from solving Equations

34 that the transverse magnetization decays exponentially whereas the longitudinal magnetization recovers exponentially. equation In the semi-classical formalism the detected signal from a coil, ( ), is given by the ( ) ( ( ) ( ( ) ( ) ) (1.35) where ( ) is the vector field produced by a unit current of one of the fields at the position,. This is a statement of Faraday s law combined with the principal of reciprocity. In particular it is the free-precession behavior (accrual of phase with time) of the magnetization that induces the signal. For the quantum mechanical picture a similar expression can be developed using the angular momentum operators instead. In a modern clinical scanner it is typical to receive the signal using an array of 8 to 64 different channels. Data from these channels are then combined to give a single measured signal from the sample. 1.3 In vivo MRS of the brain In vivo MRS acquisition The previous section described the physics required for in vivo MRS. In this section, applications of MRS will be investigated focusing on the brain and brain tumors, due to the relevance with the rest of the thesis. Because of its biological abundance and strong NMR signal, the proton, also referred to as 1-Hydrogen ( 1 H), is the nucleus of choice for MRS although 31 P, and 13 C are also used in research settings 17. To reiterate, the chemical environment slightly alters the magnetic field experienced by the nucleus 18 in the form of chemical shift and J-coupling effects, as shown by the Hamiltonian in Equation The measured signal in space and time is then a superposition of precessing magnetization at several different frequencies for each chemical species, also referred to as compounds or metabolites. Spectroscopy can be used to assess non-invasively the in vivo relative concentrations of these different compounds, providing additional biological information beyond anatomical MRI. Because these metabolites are found at concentrations much smaller than water (on the order of a few mm) it is important to

35 21 remove the water signal so that dynamic range issues do not occur. The most common method of water removal for in vivo MRS involves a chemical shift selective (CHESS) module 19, which selectively excites water and then dephases it with a large gradient. The typical processing steps in almost every in vivo MRS experiment are: Phasing of the data acquired from each coil element prior to summation by the inverse of the coil sensitivity phase. The coil sensitivity is typically estimated from a waterunsuppressed measurement, and the lack of this step can drastically reduce SNR if there is a significant variation in phase across coils. Water removal via Hankel singular value decomposition. Despite the use of a water suppression module, there typically remains some residual water signal which can be several times larger than any of the metabolites. The long tail of the residual water lineshape can contaminate MRS results, and thus requires this additional processing step. Remove eddy currents (as explained below), either using a water-unsuppressed acquisition 20 or analytical methods 21. Zero filling, typically by a factor of two (appending zeros to the end of the measured signal). This increases the spectral resolution by a factor of two after the measured signals are Fourier transformed. Fourier transformation of the signal to obtain the spectrum. Zero order phasing (applying a single phase factor to the entire spectrum) to separate the absorption (real) and dispersion (imaginary) line shapes. First order phasing (applying a linear phase variation across the spectrum) to correct for how the digital sampling comb used to measure the signal does not coincide precisely with the spin echo maximum.

36 22 Reduction of spectral noise by mathematical convolution (optional). Convolution is typically performed with a Gaussian kernel of 1 or 2 Hz full-width at half-maximum at the cost of broader linewidths. There are a variety of commonly encountered artefacts which can cause erroneous quantification in both 1D and 2D in vivo MRS. Below is a summary of some of the most relevant artefacts typically encountered, however a more comprehensive examination of all encountered artefacts is available in the literature 22. Motion artefacts arise due to the movement of the subject either in-between or during scans. Some degree of motion is unavoidable in in vivo experiments but attempts should be taken to minimize excessive motion as it results in increased linewidths, improper voxel localization and decreased water suppression efficacy as well as a reduction in the peak area due to phase cancellation 23. Some degree of motion can be corrected by aligning peaks prior to averaging the spectra, however motion which happens during a single acquisition cannot be fully corrected in this manner, as it will lead to signal cancellation due to gradient dephasing, as explained further in Section 1.6. Unbalanced crusher gradients can be caused by an improperly tuned final crusher gradient or due to eddy currents. Unbalanced gradients manifest as a shift of the peak of the echo, resulting in an alteration of the Lorentzian lineshape of the spectrum. This can be corrected for post-acquisition by first order phasing, however the underlying cause may also result in other artefacts. Chemical shift artefact is caused by the frequency-selective RF localization pulses exciting slightly different locations for different metabolite peaks. For singlets, this results only in a positional shift of the voxel, however for coupled metabolites such as lactate, it results in a positional shift as well as changes in phase and amplitude at the edges of the voxel (referred to as anomalous J-modulation 24 ). This can be corrected by using larger bandwidth pulses or by inner volume saturation 25, where voxel boundaries are defined by the edges of saturation pulses instead of through the intersection of three frequency-selective RF pulses.

37 23 Spurious echoes are the result of the refocusing of water or fat signals from outside the voxel. When shimming to minimize the magnetic field homogeneity across a small voxel a large set of linear shim gradients may be applied, which can shift the water resonance of regions outside the voxel so that they are no longer captured within the water suppression band. Because the water concentration is approximately 10,000 times greater than the metabolites, even if a small fraction of the water signal is unspoiled it can be comparable to the metabolite amplitudes. Spurious echoes can be effectively eliminated by customizing the spoiling power and directions for the particular scan 26. Eddy currents are small electrical currents in the sample which are induced by changing magnetic fields (such as the switching of gradients), inducing their own local magnetic field fluctuations. As mentioned above, they can cause unbalanced gradient crushers and they can also induce large phase distortions over the acquisition of the signal. Phase distortions induced by eddy currents can be corrected, most commonly by using a water-unsuppressed signal to estimate the phase distortion and deconvolving this component from the spectra Biochemistry of the Brain The exact roles of all the metabolites measurable by MRS are unknown. However, MRS has played a critical role in improving understanding of the physiology of many brain metabolites. This has been achieved due to the high specificity, non-invasiveness and minimal attributable risk of MRS, permitting measurement of healthy volunteers as well as patients. A summary of the most commonly measured metabolites is given below, although this is non-exhaustive as virtually any molecular compound with hydrogen groups with sufficiently long T 2 present in concentrations of ~1mM or greater can in principle be measured by MRS. A more comprehensive list of 35 metabolites that can be detected with 1H MRS, as well as the chemical shifts, J-coupling patterns of each metabolite and full in vitro spectra can be obtained from Govindaraju et al. 27 The five brain metabolites most commonly measured by MRS are: N-Acetylaspartic acid (NAA), myo-inositol (mi), choline (Cho), creatine (Cr) and lactate (Lac). Of these metabolites,

38 24 NAA exhibits the highest spectral amplitude in a healthy adult brain. This compound is produced in the mitochondria of neurons and transported into the neural cytoplasm. The NAA molecule is the second most abundant amino acid in the brain 27 (the first being glutamic acid) and is characterized in MRS by strong resonance at 2.0 ppm. Although its exact function is not fully understood, NAA is believed to act as an osmolyte as well as a precursor to N- acetylaspartylglutamate (NAAG), which is believed to be involved in glutamatergic neurotransmission 28. The NAA signal is treated as a biomarker of neuronal density, with a reduction from normal levels reflecting either neuronal loss or dysfunction 27. Myo-inositol has several prominent resonances at ~3.5 ppm, and is primarily found within glial cells, 29 which are support cells within the brain. Myo-inositol is the most abundant isomer of inositol and is an osmolyte and precursor to membrane phospho-inositides, phospholipids and myelin sheet structures 30, and plays a key role in signal transduction 31. The exact roles of mi are unknown, although it appears to be a storage form of glucose 32. Myoinositol has been found to be increased in amyotrophic lateral sclerosis (ALS), with the ratio of NAA/mI being decreased by 22% (P = 0.001) compared to healthy tissue 33. Creatine has two prominent singlets at 3.0 and 3.9 ppm, and is associated with energy metabolism through its role in phosphocreatine phosphorylating adenodiphosphate into adenotriphosphate in times of high energy demand 27. Creatine is often used as a control for the changes in other metabolites measured in MRS, as it does not vary significantly with age 34 and a variety of diseases. However, some diseases can affect Cr levels, such as brain tumors 35, which can confound ratios 36. Choline (Cho) has a strong peak at 3.2 ppm and is the precursor of the active form phosphorylcholine 37 (PCh), which plays a role in cell membrane turnover, and in the production of acetyl-choline 38, an excitatory neurotransmitter that plays a role in memory and learning 39. Typically, glycerophosphorylcholine (GPC) and PCh cannot be distinguished by in vivo MRS, and the total spectral content is simply referred to as Cho. Choline has been found to have a significant increase (P < 0.01) in both low and high grade brain tumors as compared to healthy controls 35.

39 25 Lactate is the end product of anaerobic glycolysis and is increased when normal metabolism is disrupted 40. The most prominent resonance of lactate is from the methyl group (CH 3 ) J-coupled to the methine group (CH). This J-coupling causes a splitting of the three protons into a doublet located at 1.3 ppm. The CH group produces a quartet at 4.1 ppm which is not typically quantified, due to its proximity to the very large resonance from water in comparison. The CH 2 chain of lipids also resonates at approximately 1.3 ppm, thus lactate is typically measured at an echo time of 1/2J (144 ms) when the doublet is in phase but with distinctive negative amplitude in relation to lipids. To quantify lactate accurately in the presence of lipids, spectral editing techniques or 2D spectroscopy must be used. Due to the very small concentration of lactate in the healthy brain, coupled with the overlap of lipids, this metabolite is detected at elevated levels only under numerous pathological conditions such as stroke 41, bipolar disorder 42, cancer 35, among others. All five of these metabolites are disrupted by a variety of disorders such as brain tumors 43, stroke, 41 Alzheimer s disease 44 and Schizophrenia 45. Indeed, most brain pathologies that influence brain biochemistry are likely to result in measurable MRS changes, and the implications of these changes are an aspect of ongoing research. The MRS focus on these five metabolites is not due to their greater biological importance than other chemical species within the brain but due to relative ease of measurement. Figure 1.6 displays the MRS result obtained from a voxel within parietal white matter of a healthy volunteer. The four main metabolites are labelled, as well as glutamine/glutamate (Glx). Lactate is not present due to its very small concentration in a healthy brain.

40 26 Figure 1.6: Spectrum obtained from parietal brain tissue of a healthy volunteer using PRESS with TE = 30 ms echo time at 3 T. Metabolites Cr, glutamate/glutamine (Glx), mi, Cr, Cho, NAA and lipids are labelled. Beyond these five metabolites (NAA, Cr, Cho, Lac, mi) the remaining metabolites are more reliably measured at 3 T by employing special spectral techniques, such as editing (Section 1.2.4) or 2D MRS (Section 1.2.5), due to their relatively low metabolite concentration and strong spectral overlap with other resonances. Some of these lesser metabolites are studied in Chapter 4, and are briefly summarized below. Glutamate (Glu) and gamma- Aminobutyric acid (GABA) are of particular interest due to their roles as the main excitatory and inhibitory neurotransmitters, respectively 46, as well as a variety of other functions 32. Glutamate and GABA typically reside in the synaptic vesicles 29,46 within neurons but are released into the synaptic cleft where they bind to postsynaptic receptors. Alanine (Ala) is a non-essential amino acid used in protein synthesis and in the transfer of ammonia from astrocytes to neurons in the glutamate/glutamine cycle 47. Ascorbic acid (Asc), more commonly known as Vitamin C, is found in measurable quantities within the brain and is a vital antioxidant. It also plays a role in catecholamine synthesis, collagen production and regulation of the protein HIF-1α 48. Aspartate (Asp) is a neurotransmitter that plays a role in the termination of the signals from

41 27 neurotransmitters at the excitatory synapse 49. Glutamine is a precursor of several amino acids such as glutamate, aspartate and GABA. Glutamine also plays a role in the synthesis of the messenger molecule nitric oxide (NO) by controlling the supply of the precursor of NO, arginine 50. Glycine (Gly) plays a significant role as one of the other major inhibitory neurotransmitters 51. Glutathione (GSH) is a tripeptide that plays a critical role in disposal of peroxides by brain cells and in the protection from reactive oxygen species due to the high rate of oxidative metabolism within the brain 52. Glutathione is also an anti-oxidant that is essential in maintaining healthy red blood cell structure 27. Phosphorylethanolamine (PE) is the main precursor of ethanolamine, which is an essential structural component of cell membranes and is involved in regulatory roles such as cell division, activation, cell signaling, autophagy and phagocytosis 53. Scyllo-inositol is the second most abundant naturally occurring isomer of inositol and acts as a main precursor to mi 31. Taurine (Tau) is one of the most abundant amino acids in the brain and has been shown to activate glycine receptors as well as an activator of extrasynaptic GABA A receptors Gliomas Gliomas are characterized by uncontrolled growth of a variety of different cell types within the brain. There are many different types of glioma neoplasms, each with their own respective biology. The incidence rate within the United States for primary brain tumors is 18.1 per 100,000 person-years, with a 2-, 5-, 10- and 20-year observed survival rates of 62%, 54%, 45% and 30%, respectively 55. Despite their underlying biological differences the clinical presentation, diagnostic approach and initial treatment plan are similar across different glioma types 56. Initial symptoms are categorized into two different types: generalized or focal. Generalized symptoms are usually the results of increased intracranial pressure (due to tumor growth) and include headaches as well as nausea, vomiting and sixth-nerve palsy in severe cases. The location of the tumor impacts the presentation focal symptoms which can include hemiparesis (partial paralysis on one side of the body) or aphasia (speech deficit). Seizures also occur in 15 to 95 percent of patients and may be either focal or generalized 56. Neural stem cells, progenitor cells or de-differentiated mature neural cells can all mutate into gliomas 57. Depending on the

42 28 cellularity, cytonuclear atypia, tumor differentiation, mitotic activity, microvascular proliferation and degree of necrosis, gliomas can be further subdivided into four grades established by the World Health Organization (WHO). Grades 1 and 2 are diffuse infiltrating low-grade gliomas, Grade 3 are anaplastic gliomas and Grade 4 are glioblastomas, with increasing grade indicating increasing aggressiveness 57. Grades 1-3 are considered low-grade, whereas Grade 4 is considered high grade. Over time Grade 2 and Grade 3 will progress to highgrade gliomas, which are referred to as secondary glioblastomas. Glioblastomas are the most deadly and common form of glioma. Magnetic Resonance Imaging is the most common diagnostic test for patients presenting with symptoms of brain cancer 56. A typical MRI protocol for this application, depending on the healthcare centre and time permitting, consists of a localizer (T 2 -weighted fast spin echo), T 2 fluid-attenuated inversion recovery sequence followed by a pre- and postcontrast (gadolinium) T 1 -weighted spin echo sequence 57, such as the clinical portion of the protocol used in Chapter 3. Furthermore other magnetic resonance techniques may provide complimentary information and may also be applied, such as tumor-cell density from diffusion imaging or proliferation rate of tumor cells as well as necrosis (from the presence of lactate and lipids) from MRS 57. Additionally other medical imaging such as positron emission tomography (PET) is also sometimes supplemented, especially in patients with presumed low-grade gliomas 56, which are characterized by glucose hypometabolism 58. Although relatively independent of glioma type, as mentioned above, the exact treatment plan depends on the grade of the glioma. Treatment of direct symptoms involves steroids to relieve edema, anticonvulsants in patients with seizures and antianxiety or antidepressants for help with the psychological effects. For gliomas treatment includes surgical resection of the tumor, as well as radiotherapy (60 Gy to the tumor) with or without the use of chemotherapy agents such as temozolomide 57. For grade 3 gliomas typical treatment includes maximal possible surgery and radiotherapy (60 Gy). Low grade gliomas account for only about 25 % of diffuse gliomas and present as a non-contrast enhancing lesion on MRI. Typically disease progression involves slow growth followed by a malignant transformation to a glioblastoma that is the cause of death around 5 15 years after onset 57. Retrospective studies

43 29 have shown that patients with an early and greater extent of resection have postponed transformation to a secondary glioblastoma and improved survival 59. Radiation is also a standard treatment (50 54 Gy), but the optimal timing and delivery is an open topic of research 57, as the tumors are relatively benign for a long period of time. It is well known that the rate of anaerobic glycolysis is markedly elevated in neoplastic cells even in the presence of sufficient oxygen, and this phenomenon is referred to as the Warburg effect 60. Because of this, MRS has been used to differentiate between neoplastic and nonneoplastic lesions due to the differences in metabolism 43, and to differentiate between low and high grade gliomas 61. Extensive literature has investigated these prospects with MRS metaanalysis 62 showing the use of MRS to supplement anatomical MRI in the diagnosing of brain tumors, exhibit sensitivity and specificity of 80 % and 78 %, respectively. Another meta-analysis observed no observed statistical significance in the accuracy of assessing tumor recurrence between MRS and PET 63. This is an important result as PET is recognized to be sensitive to radiolabeled compounds at much lower concentrations (~nm) than MRS, which detects metabolites at ~mm concentration at 3 T. Compared to healthy tissue, neoplastic lesions have decreased NAA concentration due to neuronal breakdown, increased Cho due to increased cellular turnover, increased levels of mi due to increased number of glial cells, a large increase in lactate due to anaerobic glycolysis, and increased lipids due to necrosis and membrane breakdown 43. In addition, MRS provides a measurement of 2-hydroxyglutarate 64 which is only present in glioblastomas that have the genetic mutations IDH1 or IDH2 65.Thus, MRS potentially provides useful information as a diagnostic and prognostic biomarker in this context, as IDH1 and IDH2 confer improved prognosis when compared to wild-type IDH 65. At present, it is very difficult to evaluate the efficacy of radiation therapy as outcomes depend on the underlying pathology. Typical treatment responses are observable by solid tumor changes on anatomical MR images after 6 to 8 weeks 66. There are also short term and long term side effects of radiation therapy. Short term side effects are generally mild and include vomiting, tinnitus (ringing of the ears), alopecia (loss of hair) and skin changes, resolving

44 30 after the cessation of treatment. Long term side effects are more detrimental and include brain necrosis, demyelination, calcifications, hearing loss and, due to the large radiation dose involved, the potential for new tumors 67. It is desirable to monitor response to treatment as early as possible; in order to change treatment course and, if necessary, in non-responding cases, avoid unnecessary harmful and expensive treatments. There are numerous techniques which aim to detect treatment response before anatomical MRI changes. Three of the most promising are diffusion-weighted MRI 66, which measures microstructural changes, and chemical exchange saturation transfer imaging 68 and MRS 69, which both measure changes in metabolism. The application of MRS to early radiation response is currently limited by inherently low SNR per unit time of the available methods. The aim of this thesis was to develop techniques which can combat the issue of low SNR, improving clinical MRS, as well as develop new techniques which could be used for early radiation treatment response. Within Section 5.4 a new study is proposed which aims to utilize the techniques developed here to provide earlier detection of treatment response, thereby potentially saving patients from harmful and unnecessary radiation exposure Other brain lesions Differentiating between tumor recurrence and radiation-induced necrosis is an ongoing issue in neuro-oncology. Their appearance from diagnostic imaging and clinical symptoms are typically similar, but their treatment course and outcome is different. Even specialized sequences are not sufficient in some cases, as typically radiation necrosis is marked by elevated ADC on diffusion-weighted imaging and low choline from MRS as compared to tumor recurrence but both techniques yield results with substantial overlap, yielding in some cases false positive or negatives 70. The development of novel non-invasive diagnostic techniques to differentiate between these two types of lesions is an active field of ongoing research which could have large ramifications for those undergoing radiation treatment. Although MRS has been shown to be useful in differentiating neoplastic and nonneoplastic lesions another ongoing challenge is the differentiation of primary gliomas with brain metastases, which may require different courses of treatment. Both typically exhibit decreased NAA/Cr, increased Cho/Cr and a notable increase in lactate and lipids in the 1.3 ppm

45 31 region 71 or an increase in ADC in diffusion-weighted images, as well as similarities in both T1 and T2-weighted anatomical MRI scans. Despite their similarities on currently available diagnostic tests the prognosis and treatment is often quite dissimilar, thus it is clear that improved diagnostic techniques could have large ramifications on the treatment of both patients with metastases and gliomas Spatial Localization of in vivo MRS There are two different categories of MRS: single voxel spectroscopy (SVS), which measures only one coarse voxel; and magnetic resonance spectroscopic imaging (MRSI), which measures many spectra simultaneously over a coarse Cartesian grid of voxels. The SVS category will be explained more thoroughly as it is used preferentially in the thesis. To localize a coarse voxel, SVS applies three orthogonal gradients during three frequency-selective RF pulses. The effect of applying a gradient during an RF pulse is most easily understood from the small tip angle approximation of the Bloch equations. Under this approximation 72 and ignoring relaxation (especially the change in longitudinal magnetization from RF pulses) it can be shown that the resulting transverse magnetization profile is 73 ( ) ( ) ( ) ( ) (1.36) This equation shows that the transverse magnetization as a function of z can be expressed as the Fourier transform of the applied RF pulse waveform when in the presence of a gradient applied along the z axis. To excite a slice of magnetization, mathematically expressed as a rect function, the appropriate RF pulse waveform is a sinc function. This type of excitation is desirable in many MRI applications as it simplifies spatial encoding of magnetization, defining the through-plane resolution and requiring subsequent encoding in the remaining two spatial dimensions within-plane. Equation 1.36 is used in Chapter 2, where two bands of magnetization (instead of one) are excited by amplitude-modulating the excitation pulse by a cosine function. More generally, the relationship between the magnetization profile and the applied RF pulse is obtainable by solving the Bloch equations using the Shinnar-Le Roux (SLR) transform method,

46 32 which is applicable in the small-tip as well as large-tip regimes 74,75. Other specialized solutions are possible, such as adiabatic pulses 76,77, as used in Chapter 4, and RF pulse design continues to be an important area of research. Irrespective of the precise nature of the RF pulse, spatial localization is achieved in MRS through the subsequent application of RF pulses played out in the presence of three orthogonal gradients, followed by large gradients referred to as crushers which de-phase magnetization and eliminate any echo pathway outside the voxel 78. The area under the crusher gradients is carefully balanced to ensure that the echo pathway of magnetization within the voxel, which experiences all three RF pulses, remains unaffected. Figure 1.7 is the pulse sequence diagram for a typical PRESS experiment. In general, this pulse sequence is repeated many times and the acquired signal from each repetition is averaged to improve SNR. Figure 1.8 is a diagram depicting how spatial localization is achieved in most in vivo SVS experiments. A magnetic field gradient, or gradient, is depicted as a function of time and is a linear spatially-varying field term added to the main magnetic field ( ) ( ) (1.37) where ( ) ( ) is the gradient vector, which is typically depicted by three separate lines in a pulse sequence diagram, such as in Figure 1.8. The most commonly used MRSI technique maps out spatial frequency using phaseencoding gradients (referred to as k-space ) to obtain spectroscopic data throughout the field of view (FOV) 79,80. Ignoring relaxation, the measured signal for a single coil can be expressed as ( ) ( ( ) ( )) ( ) (1.38) where is the k-space vector, ( ) mapped out by the magnetic field gradient function, i.e. ( ) ( ) (1.39)

47 33 ( ) ( ) (1.40) ( ) ( ) (1.41) Figure 1.7: Pulse sequence diagram for PRESS. Three orthogonal slices of magnetization are excited by pulses, and. The crusher scheme dephases all magnetization outside of the intersection of the three orthogonal slices, allowing the acquisition of a spin echo signal from a single localized region, as shown in Figure 1.8. The data acquisition (DAQ) begins at the spin echo maximum. The echo time is when the spin echo is fully rephased, and is equal to twice the spacing between the two refocusing pulses. In principle the excitation pulse does not

48 34 need to be 90, nor the refocusing pulses need not be 180, however for a single shot this produces the maximum signal. Figure 1.8: Spatial localization obtained from the pulse sequence shown in Figure 1.7. Three orthogonal bands of magnetization are excited and crushers are used to de-phase excited magnetization outside the voxel. Spatial localization is identical for the STEAM pulse sequence, except the RF pulses are each appropriate echo pathway. and a different set of crushers is used to select the This four-dimensional space can then be mapped out by applying a different combination of gradients in the three orthogonal directions for each successive excitation (referred to as phase-encoding ). The result of taking the 4D Fourier transform of this data is a 4D space where three of the dimensions are the position in each of the three orthogonal directions (as prescribed by the phase-encoding gradients) and the fourth dimension is the associated spectrum at each location. Due to time constraints typically only a two dimensional image is encoded with k-space and the third spatial direction (usually the axial direction) is localized using a slice-select RF pulse. Both MRSI and SVS are widely applied in humans to measure

49 35 metabolic changes, aid in diagnosis of various cancers and to monitor therapeutic response. Typical MRSI scan times are long, however, and spatial resolution suffers from an inherently broad sinc point spread function. The SVS method has improved SNR per unit time compared to MRSI and when a single localized region is of interest, SVS is usually the preferable option. For this reason, SVS is used exclusively throughout the thesis. 1.4 Parallel Imaging Multi-channel receiver coils are an important feature of modern MR systems. Each individual coil has its own spatial sensitivity for measuring magnetization at a particular position in space. Each coil can be used to produce its own separate image and the individual images can then be combined to produce a single image 84, with an increase in overall SNR when compared to imaging with a single large coil. The SNR increase is achieved because each individual coil is designed with spatial sensitivity for a small fraction of the intended imaging volume, and thus is only sensitive to noise sources arising from this fraction. In contrast, single channel coils are designed for sensitivity to the entire imaging volume and all the associated noise sources. The SNR benefits provided by multi-channel coils can also be used to speed up MRI. A technique referred to as parallel imaging uses the signals from each coil creatively so that the sampling distance between k-space lines can be increased when traversing k-space. This decreases the acquisition time (fewer k-space lines are required), but also decreases the FOV because the Nyquist sampling criterion is no longer satisfied over the entire imaging volume (ie. high spatial frequency information will now masquerade as low frequency spatial information). Aliased images with a characteristic overlapping artifact are formed if an inverse 2D Fourier transform is used on undersampled raw k-space data. Several techniques have been developed to disentangle the aliased images based on multi-channel coil information; the two most common are generalized autocalibrating partially parallel acquisitions (GRAPPA) 85 computed in k-space, and sensitivity encoding (SENSE) 86 computed in image space. These techniques use the inherent spatially limited sensitivity of the receiver coils to estimate the data for the absent k- space lines to reconstruct the unaliased image.

50 36 This thesis adopts SENSE reconstruction, as summarized below. The most common SENSE image reconstruction is the weak reconstruction with SNR optimization. The unfolding matrix,, used to disentangle the aliased images, is expressed as ( ) (1.42) where the superscript indicates Hermitian conjugate, is the coil sensitivity matrix (coil sensitivity for each voxel), and is the receiver noise covariance matrix (the covariance between the noise from each of the coils). The disentangled signals,, are then obtained by (1.43) where is the measured signal. The SENSE reconstruction results in increased noise because the coils are not perfectly uncoupled (the coils exhibit correlations between both MR signals and noise) and because less k-space data are used for spatial encoding, such that (1.44) where is the SNR of an image reconstructed using SENSE, is the SNR of an image from fully sampled k-space, g is the geometry factor or g-factor of the multi-channel coils, and is the reduction factor by which k-space measurement is reduced. Using the definition of the g-factor, the noise amplification due to the condition of the coil sensitivity matrix 86 is ( ) ( ) ( ) (1.45) where n is the index for the n th reconstructed voxel. The parallel imaging formalism described above was initially developed for imaging, however it has since been used to speed up MRSI 87,88. Previously, a novel technique for functional MR imaging (fmri) of brain activity was also developed, which used SENSE to select a few coarse voxels 89,90, instead of the more traditional method of acquiring an entire brain image. The

51 37 technique used cosine modulation of the RF excitation pulses (thus exciting two slabs of magnetization instead of one), and coil sensitivity to reconstruct the signal from the simultaneously excited voxels. This technique, however, could alternatively be used to speed up MRS acquisitions instead of fmri acquisitions. This idea is pursued in Chapter 2 of the thesis. 1.5 Absolute Quantitative MRS Beyond qualitative analyses of MR spectra, quantitative MRS seeks to extract metabolite values that are proportional to concentration by fitting the acquired spectra to a basis set containing the quantum-mechanically simulated signal from all the different metabolites within the spectrum. Several such packages exist such as LCModel 91, jmrui 92, AQSES 93, TARQUIN 94 and ProFit 14,15. Often the estimated concentration values are expressed as ratios to Cr, as it is considered the most stable metabolite. It has been previously shown, however, that implicitly assuming Cr to be stable can confound the quantitative analysis based on ratios 36, as Cr levels can also be strongly affected by disease. Furthermore, the ratios depend on the concentration, T 1 and T 2 of both the metabolite of interest and creatine. Thus, changes in the ratio could be due to a variety of factors, and in some cases the ratio may not change when the underlying values do. For this reason, it is desirable to estimate the physical concentration of these metabolites (not just ratios), which is referred to as quantitative MRS. It can be shown that for a particular chemical species, the magnetization measured with PRESS is given by ( ) [ ( ) ( ) ( )] (1.46) where is the equilibrium magnetization for the particular chemical species and TR is the repetition time. Thus to obtain estimates of, which is proportional to physical concentration, the measured signal must be multiplied by a correction factor:

52 38 ( ) [ ( ) ( ) ( )] (1.47) In quantitative MRS the values obtained from the fitting software are corrected for relaxation and then scaled to represent actual physical concentrations. The two most common ways to scale to absolute concentration are using an internal 35,64 or external 95,96 reference. When an internal reference is used, the measured signal from a certain chemical species (typically water) is set to be a concentration that is previously known from the scientific literature. When an external reference is used, the known concentration is typically taken from a phantom that is measured using MRS before or after in vivo MRS measurements are made. In both cases, the measured reference signal must also be corrected by Equation 1.47 using the appropriate relaxation values prior to scaling and obtaining quantitative MRS data. 1.6 Diffusion-weighted MRS By applying a series of refocused gradients, it is possible to make proton MR signals attenuate in a manner that is sensitive to diffusion 7,97,98. The attenuation is a result of spins diffusing inbetween successive gradients, resulting in a slight phase accrual upon refocusing. This phase accrual integrated over many spins results in a reduction in the measured signal dependent on the amplitude of the amplitude ( ) and duration of the applied gradients ( ), the time between refocusing gradients ( ) as well as the rate of diffusion of the spins. The diffusion characteristics of spins are highly sensitive to tissue geometry and morphometry 99. Water is the molecule of interest in diffusion-weighted MRI (DW-MRI). The basis of diffusion-weighted MRS (DW-MRS) is identical to DW-MRI, except that the molecules of interest are now metabolites (typically NAA, Cr and Cho), and not water. The SNR is thus substantially decreased for DW-MRS in comparison to DW-MRI, and this has meant that SVS approaches have been adopted. However, DW-MRS has recently been extended to multiple voxels using the MRSI technique 100 (as explained in Section 1.3.5). The most basic of DW-MRS experiments involves measuring the spectra twice: once using large applied diffusion-sensitizing gradients (DSGs) and once using the identical pulse sequence with negligible DSG amplitude.

53 39 The apparent diffusion coefficient, ADC, of the metabolite can then be estimated through the equation 98 ( ) ( ) (1.48) where is the value estimated for a particular metabolite by fitting the measured signal obtained with negligible DSGs, and is the corresponding value with the DSG amplitude set to. The spin accrues a phase, in the presence of gradients according to ( ) ( ) (1.49) where is the position vector of the spin as a function of time. By Taylor series expanding the position vector and ignoring the terms above linear motion it can be shown that the phase accrued due to a bipolar gradient is ( ) (1.50) where is the angle between the applied gradient direction and the motion and v is the average velocity of the spin. Using Equation 1.50 and typical values for diffusion-sensitizing gradients (as given in Chapter 4) a velocity of approximately 1 mm/s in the same direction as the applied gradient results in a full phase accrual, which is approximately the macroscopic motion of the head during in vivo experiments. It is therefore paramount to re-phase the individual excitations prior to averaging due to the interaction with motion and the large DSGs resulting in large phase variations from one TR to the next 101. Figure 1.9 is a diagrammatic explanation of the need for re-phasing MRS data prior to summing over successive excitations in a healthy volunteer.

54 40 Figure 1.9: The effect of the order of summing and phasing the individual excitations in DW- MRS from in vivo healthy volunteer data with 64 individual excitations. The vertical scales for each row are constant. The measured amplitude of the metabolites is drastically reduced when the excitations are summed prior to phasing. In the presence of non-linear motion, Equation 1.50 is no longer valid and DW-MRS signals suffer further attenuation artifact. Because of this, cardiac gating is usually necessary in DW-MRS to limit the effects of non-linear motion from cardiac pulsatility 101 in the brain. Failure to correct for motion by re-phasing and cardiac gating will result in substantially reduced values when measuring MRS signals at high-b values, producing ADC estimates that are artificially high. Diffusion-weighted MRS offers unique intracellular information as the metabolites exhibit much more restricted diffusion than water, with correspondingly lower ADC values The DW-MRS experiment is usually limited to investigating NAA, Cr and Cho, largely due to the relatively high SNR and ease of measuring these metabolites in relation to the others that have weaker single strength. Thus, there is a need to improve on the current capabilities of DW- MRS, so that signals from other metabolites can be measured reliably.

55 Hypotheses and Thesis Outline This thesis focuses on the technical development and application of three novel in vivo MRS pulse sequences. Ultimately these sequences may be applied in a variety of different applications, although their motivation was ultimately towards using MRS as a predictor for early treatment response to radiation therapy, as discussed further in Section 5.4. Chapter 2 tests the hypothesis that by using tailored RF excitation and SENSE parallel imaging methods, it is possible to obtain high quality MRS data from two voxels simultaneously without the need for a full k-space encoding procedure, as is typically done in MRSI. This new approach should offer all the benefits of SVS over MRSI, such as shorter scan times and lack of point spread function effects on spatial resolution, while allowing the simultaneous measurement of both voxels. The method is demonstrated in phantoms, healthy controls and patients with brain cancer. For this chapter I implemented the developed pulse sequence, performed all experiments on phantoms, healthy volunteers and patients, and analyzed all data using a combination of custom scripts and a quantitative MRS software package. Chapter 3 develops a novel inversion recovery sequence which is then combined with spectral editing to measure the longitudinal relaxation time of lactate in a cohort of glioma patients. This technique enables T 1 to be estimated with improved precision compared to the use of standard inversion recovery for a fixed experiment time. This novel sequence is then used to test the hypothesis that lactate has a significantly different T 1 relaxation value than the contaminating lipids in patients with brain cancer. The lactate T 1 value is then used to obtain estimates of absolute metabolite concentration and to optimize the TR value in MRS experiments involving this metabolite. For this chapter I developed the concept for the pulse sequence as well as identified the gap in the literature, in addition to writing the pulse sequence, performing all experiments and analyzing all data using a combination of custom scripts and a quantitative MRS software package. Chapter 4 develops a novel technique that combines DW-MRS and JPRESS. This sequence is then used to investigate what metabolites beyond NAA, Cr and Cho can have their diffusion coefficients reliably estimated at 3 Tesla in healthy volunteers. For this chapter I

56 42 developed the concept for the pulse sequence, in addition to writing the pulse sequence, performing all experiments and analyzing all data using a combination of custom scripts and a quantitative MRS software package, with the help of Rofl Schulte and Ben Geraghty to implement the software package. Lastly, Chapter 5 provides the overall conclusions of the thesis and discusses work that could be done in the future to extend the research, including technical improvements and potential applications of the sequences developed here.

57 43 Chapter 2 Constrained Source Space MR Spectroscopy: Multiple Voxels, No Gradient Readout A paper published in American Journal of Neuroradiology, 2015, pp 1-8 by Karl Landheer, Arjun Sahgal, Sunit Das and Simon J. Graham. 2.1 Introduction There are two major categories of magnetic resonance spectroscopy (MRS) pulse sequences on current clinical MRI systems: single voxel spectroscopy (SVS), which measures one voxel; and magnetic resonance spectroscopic imaging (MRSI), which measures many spectra simultaneously over a Cartesian grid of voxels. Both SVS and MRSI are widely applied in humans to detect certain molecular constituents of normal and abnormal tissues, especially those associated with cellular metabolism, and to monitor therapeutic response Each MRS category has its application niche, as SVS and MRSI exploit different spatial and temporal resolution trade-offs. SVS is attractive when anatomical MRI provides precise indication of where spectral information should be collected. When pathology is more diffuse, widely distributed, or not detectable on anatomical MRI, MRSI is the technique of choice to generate spectra from many voxels using multiple repetitions for k-space encoding 79,80. To reduce spectroscopic scan times various "parallel imaging" approaches have been applied to reduce the amount of k-space data acquired. These techniques exploit the spatial sensitivity of individual elements in multi-channel receiver coils 87,88,110,111 and can substantially reducing scan times. The spatial limitations of SVS are well recognized; it is usually the case that SVS spectra are required at more than one location, either to compare spectra from diseased and normal

58 44 tissue, or in the case of multi-focal disease. This naturally leads to execution of SVS pulse sequences successively for each voxel location. There have been some attempts to modify spectroscopy acquisition to extend the volume of coverage of SVS, such as line scan echo planar spectroscopic imaging 112 which provides spectra from a column of voxels. However, for clinical applications, standard SVS methods, notably point resolved spectroscopy (PRESS) 4 and stimulated echo acquisition mode(steam) 113 remain entrenched. Previously, a technique was developed that uses RF localization and sensitivity encoding (SENSE) 86 for fast functional magnetic resonance imaging 90. It is reasonable that this approach, appropriately modified for MRS applications, should be investigated more to determine whether it usefully augments existing SVS capabilities. In the present work, referred to as constrained source space magnetic resonance spectroscopy (CSSMRS), a prototype pulse sequence is developed and analyzed for its ability to acquire and separate spectra from two voxels simultaneously with no k-space encoding. The efficacy of spectral separation is investigated for a variety of distances between the two voxels in a healthy volunteer. Additionally, numerical simulations are preformed to assess the validity of certain assumptions made in the reconstruction and to predict CSSMRS performance in cases where lengthy experimentation is impractical. Lastly, two-voxel CSSMRS data are reported in relation to conventional SVS data acquired successively at each voxel location for patients with a variety of different brain cancers ranging from low grade to high grade. 2.2 Materials and Methods All experimental data were collected using a GE 750MR 3.0T MRI system (General Electric Healthcare, Waukesha WI) with a standard 8-channel head coil receiver. To achieve CSSMRS for proof-of-principle demonstrations, a standard PRESS sequence was modified to excite two voxels arbitrarily in space, instead of one (Figure 2.1a). Illustrative voxel locations are shown overlaid on the anatomical image of a patient with brain cancer in Figure 2.1b (see Patient 6 in Table 2.1 below). The two user inputs were the voxel size, chosen throughout as (20 mm) 3 ; and the x, y, z coordinates of each voxel location. In this approach, two arbitrarily positioned voxels were excited via cosine modulation of the first RF pulse, which resulted in the excitation of two

59 45 parallel slices, followed by the standard spin echo formation process thereafter. Arbitrarily localization is obtained by modifying the offset frequencies of the RF pulses and changing the rotation array between logical and physical gradients. The three RF pulses were Shinnar-Le Roux pulses 75 with durations of 3600, 5200 and 5200 ms and bandwidths of , and Hz for the first, second and third pulse, respectively. The additional pulse sequence parameters for this initial work included a repetition time (TR) and echo time (TE) of 1500 ms and 288 ms (unless otherwise stated), respectively; a flip angle of 63 (approximately the Ernst angle); a readout bandwidth of 2500 Hz; and 1024 points data acquisition (total acquisition time of ms). The value TE = 288 ms was chosen because it has been shown to have high MRS reproducibility 114, an important clinical factor compared to the other common TE values of 30 and 144 ms, despite the associated reduction in signal-tonoise ratio (SNR). Water suppression was implemented using chemical shift selective saturation 19. Prior to all data acquisitions, 1 st and 2 nd order shimming was applied encompassing most of the brain to decrease spectral linewidths. The typical linewidth of the water peak was about 8 Hz. The total number of excitations was 128, with a total scan time of 3.2 minutes. The reconstruction of CSSMRS requires a calibration scan to measure the coil sensitivity, which is explained below. Regarding spatial reconstruction of CSSMRS data to separate spectra from the two voxels, the governing equation can be expressed in matrix form as 86,90 ( ) ( ) ( ) (2.1) where the sensitivity matrix relates how the magnetization signals ( ) from each voxel result in the acquired signals ( ) from each element in the receiver coil, and ( ) represents coil element-dependent noise. The sensitivity matrix is generated by assuming that the spatial sensitivity of each coil element varies slowly over the extent of each voxel. For each of the coils and slices,

60 46 ( ) (2.2) where is the number of pixels within the specified region inside the voxel, and are the respective minimum and maximum row pixel limits on the voxel and and are the respective minimum and maximum column pixel limits on the voxel. Equation 2.1 can be solved by the SENSE formalism using weak reconstruction with SNR optimization 86 : a) b) Figure 2.1: a) Pulse diagram for CSSMRS. The first RF pulse has a flip angle of α (where α < 90 ) and is cosine-modulated, such that the subsequent spin echo after the third RF pulse excites two coarse voxels. Shaded gradients are crusher gradients. The slice-select rephasing lobe for the y gradient is added directly to the first crusher. The gradient echo readout in the dotted box is optional for voxel localization verification. See text for further details. b) An anatomical T 1 - weighted image of patient 6 with the nominal voxel locations overlaid, and a brain tumor evident in the left middle temporal gyrus. The two spectra for this patient are displayed in the bottom row of Figure 2.2.

61 47 ( ) ( ) ( ) (2.3) where is the estimated magnetization signal for each voxel, denotes the pth repetition and represents the noise covariance matrix between the coils. For example, ( ( ) )( ( ) ) (2.4) where the complex noise samples can be taken from the last datum of each acquisition, and the covariance is calculated over the total number of excitations, The matrices can be estimated by various approaches although previous CSS work has shown that a simple procedure is sufficient for proof-of-concept implementation 90. Two sets of fast gradient echo (FGRE) images were acquired with the same pulse sequence parameters (TE/TR = 1.3/34 ms, flip angle = 5, field of view = 30 cm, 64 by 64 acquisition matrix, 5 mm slice thickness): one set with the body coil, and one set with the multi-channel head coil receiver. These images were then spectrally interpolated to produce 256 by 256 images with an isotropic in-plane resolution of 1.17 mm. For each of the coils and slices, the coil sensitivity map at each in-plane coordinate, ( ), was estimated by dividing each of the individual head coil images by the analogous body coil image, and then thresholding using an object indicator to set the coil sensitivity to zero in regions where noise dominates object signal. The CSSMRS reconstruction was performed using specially-written scripts in MATLAB (the Mathworks, Inc., Natick, MA). The two separated signals were first zero-filled by a factor of two, then transformed to the spectral domain by fast Fourier transformation. The spectra were then phase-corrected including zero and first order correction terms using an automated algorithm based on minimizing entropy. 118 The spectra were then shifted in frequency to place the peak for N-Acetylaspartate (NAA) at 2.04 ppm; normalized by their L2-norm; and subjected to Hankel Lanczos singular value decomposition 93 for removal of residual spectral content arising from water. Spectral components were then quantified automatically using the

62 48 Figure 2.2: Spectra from both a healthy volunteer (a and b) and a brain cancer patient (c and d) measured with both CSSMRS and PRESS. Spectra from Patient 6 (See Table 2.1 for list of all patients) are shown because this patient exhibited the median g-factor, typifying CSSMRS reconstruction quality. Errors represent the standard deviation over 128 excitations. a.u. = arbitrary units. freeware SPID which utilizes a separable nonlinear least-squares fitting algorithm known as automated quantitation of short echo time MRS spectra (AQSES). 93 The AQSES algorithm provides Cramer-Rao lower bound estimates of the standard deviation of each quantified spectral component. The basis set used was simulated using Java Magnetic Resonance User Interface (jmrui) and the input scan parameters. The values obtained from the quantification algorithm for NAA, Cho and Cr were then scaled by attenuation factors to account for transverse and longitudinal relaxation effects using relaxation constants obtained in a normal brain 119. The values for lactate were not adjusted for attenuation according to common practice. Bloch equation simulations confirmed that cosine modulation had negligible effect on the integrity of the spatial profile. A water/fat phantom was used to measure the bleed

63 49 between voxels. One voxel was placed inside a stationary fat container and another voxel was placed inside the surrounding water bath. Typical scan parameters were used except an echo time of 40 ms (for increased SNR) and a total number of excitations of 32. This scan was repeated for centre-to-centre distances of 40.2 to 70.2 mm. The bleed was defined to be the amplitude of the contaminating absorption spectrum divided by the amplitude of the main absorption spectrum in the other voxel multiplied by 100%. Two validation experiments were subsequently conducted on healthy volunteers and patients with brain cancer, to assess CSSMRS capabilities in practical scenarios. All volunteers participated with free and informed consent and with the approval of the hospital research ethics board. Experiment One was performed to investigate how CSSMRS results are affected by voxel placement in relation to coil sensitivity profiles. Because CSSMRS involves SENSE reconstruction, overall performance depends on the condition number of the reconstruction matrix, as quantified by the "g-factor" 86 : ( ) ( ) ( ) (2.5) where the integer is used to denote the different voxels that are reconstructed (ie. [ ] in this case). To assess CSSMRS results for various g-factors, one voxel was placed in a fixed central location in the brain, and the other was placed to achieve centre-to-centre separations between voxels varying from 20 mm (ie. adjacent voxels) to 70 mm in the radial direction toward the head coil. SVS PRESS data were acquired in each successive location for comparison. These CSSMRS and PRESS data were collected for one healthy young male adult (23 years old). Equation 2.2 was then used to calculate the sensitivity matrix from the measured coil sensitivities at each individual voxel location, which, along with the noise covariance matrix (Equation 2.4) can be used to calculate the g-factor using Equation 2.5. Experiment Two was performed to investigate how well CSSMRS distinguishes spectra from cancerous and normal tissue over a representative range of clinical presentations. Six patients with brain cancer were recruited from the Sunnybrook Odette Cancer Centre during the course of their treatment (see Table 2.1 for tumor characteristics). Patients were included if

64 50 they presented with a tumor volume approximately the same size or larger than the prescribed voxel. Tumor location was verified using a high resolution fast spoiled gradient echo with an anatomical inversion recovery preparation (FSPGR IR prep, acquisition parameters given below). For all patients, one voxel was placed at the centre of the tumor and the other was placed on the contralateral side in the analogous neuroanatomical region within normalappearing brain tissue. PRESS data were also acquired successively in these two locations for comparison purposes. In both experiments, PRESS was performed with the identical acquisition parameters used in CSSMRS and with the same spectral analysis pipeline. The total examination time for comparing CSSMRS and PRESS data from two voxels was approximately 20 minutes, which included scout images, anatomical MRI (FSPGR IR, 256 by 256 pixels, pixel size = 0.86 mm by 0.86 mm, TR/TE = 8.2/3.2 ms, flip angle = 8 ), two FGRE scans (for measuring coil sensitivity as described above), higher order shim, CSSMRS and PRESS acquisitions. Table 2.1: Summary of brain tumor patients studied in Experiment Two. Patient Age (years) Sex Disease Radiation Treatment Status 1 36 F grade II oligodendroglioma 2 84 M grade IV glioblastoma 3 79 M grade IV glioblastoma 4 61 F brain metastases from breast cancer 5 79 M brain metastases from colon cancer 6 61 M grade IV glioblastoma none currently undergoing focused radiation currently undergoing focused radiation 60 days since completion of focused radiation 70 days since completion of focused radiation currently undergoing focused radiation Tumor Location right cingulate gyrus left middle temporal gyrus left superior temporal gyrus left middle temporal gyrus right superior temporal gyrus left middle temporal gyrus Tumor Size (vs Voxel Size) Larger Compara ble Larger Smaller Smaller Larger

65 51 A simple numerical simulation was also written in MATLAB for additional insight into the results of Experiments One and Two. The simulation assessed the impact on spatial reconstruction of the important assumption underlying Equation 2.1, namely that coil sensitivity could be reasonably approximated as a constant over each voxel. Given good agreement between experimental results and simulations for Experiment One (see Results) the simulation also was used to predict CSSMRS performance under conditions that were not possible to measure experimentally during Experiment Two, due the inherent time restrictions for collecting MRS data in patients. The simulation used measured coil sensitivity data and PRESS data from two voxels as initial inputs. In the context of the simulation, the PRESS data (obtained according to experimental parameters given above, averaged over 128 excitations) were considered to represent a situation in which signal components were uniformly concentrated over each voxel volume. Simulated signals were then generated for each coil element while accounting for nonuniform coil sensitivity, by performing the appropriate spatial integral. Complex Gaussian noise was added to each simulated signal to approximate the levels observed experimentally for each coil. These simulated coil signals were then used for spatial reconstruction of two voxel signals according to the Equations above, for subsequent comparison with the PRESS data that were originally input. Spatial reconstruction, spectral processing and analysis were conducted identically to the procedures outlined above for experimental data. 2.3 Results For centre-to-centre spacings of 40.2, 50.2, 60.2, 70.2 mm the observed bleed of water into the fat voxel was 2.0%, 1.4%, 1.5%, 1.7% and 1.3%, respectively, and the observed bleed of fat into the water voxel was 3.7%, 4.7%, 4.0%, 3.0%, 0.7%, respectively. For visual comparison, Figure 2.2 displays four representative spectra obtained by CSSMRS (solid black line) and PRESS (dashed grey line), respectively. As commonly performed for display purposes, all spectra were apodized by a Gaussian filter with 2 Hz full-width-at-halfmaximum. The spectra shown in Figure 2.2a and Figure 2.2b are qualitatively similar and were obtained from a healthy volunteer with both voxels placed inside the prefrontal cortex. The

66 52 spectra shown in Figure 2.2c and Figure 2.2d were obtained from Patient 6 (see Table 2.1) and are substantially different for the two voxels, with the spectra in Figure 2.2c obtained from tumor tissue inside the left middle temporal gyrus and those in Figure 2.2d obtained from contralateral homologous tissue, as shown in Figure 2.1b. Spectra from Patient 6 were chosen for display in Figure 2.2 because CSSMRS results were obtained in this case with the median g- factor observed over the patient cohort. Figure 2.3 displays spectra obtained from both CSSMRS and PRESS for the minimum achievable echo time of this pulse sequence (30 ms). Figure 2.4 shows the tumor spectrum obtained from CSSMRS for patient 1 and the fit obtained from AQSES. The results of Experiment One and related numerical simulations are shown in Figure 2.5, which plots the difference between quantified spectral components measured by CSSMRS and PRESS for six different voxel separations (one voxel held fixed, one moved radially) and the three main metabolites observed in Figure 2.2a and Figure 2.2b: NAA, creatine (Cr) and choline (Cho). The difference values (CSSMRS minus PRESS) reported are specifically for the voxel that was maintained in a fixed position. For both the experimental and simulated results, the difference between CSSMRS and PRESS remained constant within error over all voxel separations. Furthermore, the difference values for experimental and simulation results also agreed within error, with the only exception being a slight bias in NAA quantification when voxels were placed adjacent to one another (20 mm separation distance). Given the good level of agreement between experiment and simulation observed in Figure 2.5, numerical simulations were then extended to assess CSSMRS reconstruction quality as a function of voxel separation with spectra that were substantially different in the two voxels. Figure 2.6 plots the difference between quantified spectral components measured by CSSMRS and PRESS in a manner analogous to that shown in Figure 2.5, however in this case the inputs to the simulation were provided from Patient 6 with the difference values relating to quantification of the tumor spectral components: NAA, Cho, Cr, and lactate (Lac). For additional context, the difference values obtained experimentally for Patient 6 are also indicated as single data points in Figure 2.6. Similar to Figure 2.5, Figure 2.6 shows difference values of zero within error for all voxel separations and metabolites except choline for the first

67 53 Figure 2.3: Spectra from a healthy volunteer at 30-milisecond echo time, obtained by using both CSSMRS and PRESS. The labeled metabolites are myo-inositol (mi), Cho, Cr, Glx, and NAA. Figure 2.4: The unapodized spectrum obtained from CSSMRS from patient 1 (highest g-factor) along with the automated quantitation of short echo time MR spectroscopy spectra (AQSES) fit.

68 54 two separations and NAA for adjacent voxels, indicating that good CSSMRS reconstruction quality is maintained even when the two voxels are located in close proximity to one another. Additionally the reconstruction tends to improve as the distance between the voxels increases for all metabolites. The simulation results and experimental results also agree within error for the single experimental data point. Figure 2.5: Measured and simulated differences between the CSSMRS and PRESS measurement for six different voxel separations for the three main metabolites within a healthy adult brain: N-acetylaspartic acid (NAA), choline (Cho) and creatine (Cr). The signal from the CSSMRS coarse voxel that was kept in fixed position was reconstructed and compared to the PRESS measurement obtained from the same location. The black line and gray lines are the measured and simulated values, respectively. The g-factors are also displayed for reference at the top x- axis, although there is a non-linear relationship between g-factor and voxel displacement. Error bars denote Cramer-Rao bounds. a.u. = arbitrary units. Summarizing the results of Experiment Two, CSSMRS and PRESS results are quantified in Tables for Patients 1-6 across tumor and normal tissue voxels for NAA, Cr, Cho, and Lac,

69 55 including the differences in spectral quantification. The CSSMRS g-factors for Patients 1-6 were 1.67, 1.01, 1.21, 1.23, 1.13 and 1.18, respectively; this indicates that there should be a SNR per square root of unit time benefit for CSSMRS over PRESS in all cases except for Patient 1. Overall, large decreases in NAA and increases in Lac and Cho were observed for tumor voxels in relation to normal tissue voxels for CSSMRS and PRESS for most patients, consistent with previous papers 43. Tables also show a large variability in the tumor spectra across patients. A Mann-Whitney U test on the pooled values from all metabolites obtained from CSSMRS versus PRESS yielded a p-value of 0.90, indicating no significant difference. It should be mentioned that the bleed values estimated in a water-fat phantom may not be representative of those obtained in vivo, due to the differences in linewidths in a phantom versus a human, in addition to the bleed being estimated from water and fat and not from metabolites. There is no evidence of significant voxel bleed in the in-vivo experiments, as no systematic increase in Lac was observed in normal tissue CSSMRS voxels (Table 2.5), except that a large Lac value was obtained from CSSMRS and PRESS spectra in healthy tissue for Patient 4. Voxel placement was close to the scalp in this particular patient, which produced contaminating lipid signals that were subsequently misinterpreted as Lac by the AQSES software. Thus, this specific result should be discounted. In addition there is a significant increase observed for this patient in both NAA and Cr in the tumor voxel from CSS. This is likely due to motion which exacerbated bleed effects, as this particular patient had difficulty remaining still.

70 56 Figure 2.6: Simulated metabolite quantification values for seven different voxel separations for the four main metabolites within the tumor spectra for Patient 6: NAA, Cho, Cr, and lactate (Lac). The quantified values were from the stationary voxel placed within the tumor, and are plotted in gray. The black data points located at 78 cm in each plot are the experimental results for this patient, corresponding to the first difference column values listed in Tables for Patient 6. The estimated g-factors are also displayed at the top x-axis for reference, although there is a non-linear relationship between g-factor and voxel displacement. a.u. = arbitrary units.

71 57 Table 2.2: Quantified NAA values from PRESS and CSSMRS for both voxels in arbitrary units (a.u.). The standard deviations are Cramer-Rao bounds. Patient 1 CSSMRS tumor voxel PRESS tumor voxel Difference CSSMRS healthy voxel PRESS healthy voxel Difference Table 2.3: Quantified Cho values from PRESS and CSSMRS for both voxels in arbitrary units (a.u.). The standard deviations are Cramer-Rao bounds. Patient 1 CSSMRS tumor voxel PRESS tumor voxel Difference CSSMRS healthy voxel PRESS healthy voxel Difference

72 58 Table 2.4: Quantified Cr values from PRESS and CSSMRS for both voxels in arbitrary units (a.u.). The standard deviations are Cramer-Rao bounds. Patient 1 CSSMRS tumor voxel PRESS tumor voxel Difference CSSMRS healthy voxel PRESS healthy voxel Difference Table 2.5: Quantified Lac values from PRESS and CSSMRS for both voxels in arbitrary units (a.u.). The standard deviations are Cramer-Rao bounds. Patient 1 CSSMRS tumor voxel PRESS Tumor voxel Difference CSSMRS healthy voxel PRESS healthy voxel Difference * Lipid contamination from scalp mislabelled as Lac in healthy voxel.

73 Discussion This work has introduced a prototype pulse sequence for CSSMRS, a novel spectroscopy technique that measures spectra from multiple voxels simultaneously without the need for k- space encoding. Instead, spatial encoding is achieved by multi-voxel RF selective excitation, signal readouts from a multi-channel receiver coil, and SENSE 14 reconstruction to separate the signals from each voxel. The CSSMRS method is important from the perspective of SNR per square root of acquisition time, potentially providing efficiency in comparison to the standard clinical practice of performing successive SVS acquisitions at different voxel locations. Careful experiments and simulations were undertaken to investigate the capabilities of CSSMRS for simultaneous measurement of two voxels. In particular, considerable attention was paid to whether CSSMRS provides adequate spatial localization in relation to the standard SVS PRESS method. In a water/fat experiment it was shown that the bleed was on the order of 2-5%, which is acceptable for spectroscopic applications. Experiments One and Two, conducted in healthy volunteers and a diverse group of six brain tumor patients with four different types of cancer, showed overall that CSSMRS and successive PRESS spectra agreed within experimental error. Furthermore, CSSMRS spatial reconstruction was shown to be robust over a range of voxel prescriptions (with one voxel held fixed and the voxel separation varied), by both experiment and numerical simulation. Experiment and simulation were in agreement for a healthy volunteer, indicating excellent reconstruction even when the two voxels were placed adjacent to one another. The only additional feature of note in this regard was a slight, systematic discrepancy between the simulated and measured NAA values observed in Figure 2.5 for all voxel separations. This feature is likely due to the relatively simplistic nature of the simulations, which did not account for various experimental factors. However, given that the overall level of agreement between experiment and simulation was very good, these factors evidently have a small influence. The simulation therefore helps to support the assumption made in CSSMRS reconstruction that coil sensitivity variations can be neglected within the voxels.

74 60 The agreement between these experiments and the simulation provided rationale for using the simulation further to predict CSSMRS capabilities in a brain cancer patient. As expected, slightly larger variations were observed as a function of voxel separation in this case, likely due to the larger spectral differences between the two voxels. However, with the exception of choline quantification for very closely spaced voxels (20 and 30 mm centre-tocentre) and NAA with adjacent voxels, all CSSMRS results were predicted to be consistent with PRESS results within error. Given that CCSMRS has been demonstrated to provide robust, high-quality results, discussion can turn productively to the potential efficiency of this pulse sequence in terms of SNR per square root of acquisition time. In the two-voxel implementation investigated in the present work, spectra were obtained in half the time compared to successive application of PRESS. The quality of CSSMRS results is potentially affected by noise amplification in the SENSE reconstruction, however, as parameterized by the g-factor. Therefore, the appropriate context for using CSSMRS advantageously over PRESS is when the g-factor is less than. This corresponds to a minimum centre-to-centre separation in voxels of about 55 mm near the centre of the 8-channel head receiver coil used in this work. All but Patient 1 (who had a tumor approaching the midline) had a g-factor below this threshold. It is also interesting to note that CSSMRS is compatible with another approach that avoids using k-space for spatially encoding spectral information. In principal, if the flip angles assigned to each voxel can be modulated appropriately, then simple algebraic combinations of the successive spectroscopic readouts can be used to localize each voxel without SENSE reconstruction, as achieved in Hadamard Spectroscopic Imaging (HSI) 24. The HSI approach is independent of g-factor and also provides improvements in SNR per square root of time, but has traditionally required excellent RF fidelity and is sensitive to how spatial RF nonuniformity and patient motion influence algebraic combination and the subsequent leakage of signals between voxels. In addition, the algebraic combination of multiple recordings reduces the minimum temporal resolution that is achievable with HSI, whereas CSSMRS provides spectral separation in as little as a single TR value. CSSMRS and HSI are not mutually exclusive,

75 61 however, and it is possible that a robust, hybrid technique can be developed in the future for further scan time reductions. Irrespective of developing such a hybrid technique, the present method has potential applications in any in vivo spectroscopy experiment in which there are two regions are of interest and the lengthy acquisition times of MRSI are impractical. CSSMRS could also be beneficial in a research setting where sophisticated 2-dimensional MRS experiments have inherently long acquisition times, such as JPRESS 120. Another promising application of CSSMRS is in functional spectroscopy where real-time changes in metabolic information could be measured from multiple points within the brain simultaneously with high temporal resolution. Further development and applications of CSSMRS will be explored in the future. 2.5 Conclusions CSSMRS has been developed to extract signals from two localized regions simultaneously and reliably. Utility was demonstrated in a clinical setting, although the technique has promising applications in the research setting as well.

76 62 Chapter 3 A Rapid Inversion Technique for Measurement of Longitudinal Relaxation Times of Brain Metabolites: Application to Lactate in High Grade Gliomas at 3 T A paper published in NMR in Biomedicine, 2016, vol. 29, pp by Karl Landheer, Arjun Sahgal, Sten Myrehaug, Albert P. Chen, Charles H. Cunningham and Simon J. Graham. 3.1 Introduction Proton magnetic resonance spectroscopy (MRS) is a powerful non-invasive technique used to measure biomarker activity within the brain and body. This technique has been used extensively to investigate the biochemical profiles of brain tumors 121. Typically, gliomas exhibit a decrease in N-acetylaspartic acid (NAA) due to the degradation of neurons, and an increase in choline (Cho) due to elevated cell density and membrane turnover in neoplasms. Especially when necrosis is present, there is also often an accompanying increase in lipids. Lastly, a significant increase in lactate is common, widely attributed to the increase in anaerobic glycolysis 40. Lactate is of particular interest due to its role in metabolism and its negative correlation with survival time 43. For MRS results to be interpreted in detail, the magnetic resonance properties of each spectral component must be well understood. One important property is the relaxation time, which describes the timescale for longitudinal recovery of magnetization after resonant excitation. The value depends on the static magnetic field strength and indirectly reflects molecular dynamics within tissue microstructure. From an experimental standpoint, the value is important for determining the optimal repetition time (TR) between spectral acquisitions so that signal-to-noise ratio (SNR) is maximized (eg. according to the efficiency

77 63 metric ). Together with knowledge of the relaxation time, the value also enables correction of spectral components to estimate absolute concentrations. The values for the major spectral components of brain tumors have been well studied at 3 T 122, the preferable field strength for clinical MRS in terms of SNR and spectral resolution. Lactate is the notable exception, however. Despite the importance of lactate as a biomarker of tumor aggression, measurements of lactate are challenging because of three inter-related factors. First, lactate is not typically detectable by MRS in normal brain, necessitating that dedicated efforts must be made to measure values in patients prior to or during their cancer treatment. Second, the most common methods for measurements are time-consuming (see below). Third, the measurements of the lactate methyl [CH 3 ] doublet (coupled to a methine [CH] proton) are confounded by spectral overlap from lipids. To our knowledge, the only pertinent human MRS data were acquired at 1.5 T without accounting for the overlap 123. The present work was conceived to address these challenges and fill the gap in the existing literature through dedicated study of brain cancer patients. Regarding the method for measurement, the two most common choices are progressive saturation recovery 124 and inversion recovery (IR) 125. When naively applied, both are inherently slow and suboptimal for measuring low concentrations of in vivo brain metabolites in a time efficient manner in patients, because they conventionally require use of a TR value that is multiples of the T 1 value of interest. More rapid methods such as the Look-Locker approach 126 are difficult to combine with the required spatial localization and spectral editing schemes. Alternatively, the modified fast inversion-recovery (MFIR) method enables T 1 measurements without full longitudinal recovery 127. This approach has been modified, characterized and validated appropriately for the present spectroscopic application, allowing flexible choice of TR and a simple fitting approach to estimate T 1 values. In addition, the lactate and lipid signals are separated using the radiofrequency (RF) band selective inversion with gradient dephasing (BASING) 128 lactateediting sequence. The BASING sequence also provides lactate refocusing 129, offsetting the anomalous J-modulation 24 and substantial signal reductions at odd multiples of 1/J that are commonly observed using point resolved spectroscopy (PRESS) 4. The anomalous J-modulation

78 64 of lactate is the result of the excited magnetization of the quartet and the doublet being slightly shifted in space relative to each other. This shift results in voxel boundaries where both coupled groups are not affected by both the refocusing pulses, resulting in a change in the phase of the measured doublet signal. This results in some signal cancellation at the voxel boundaries, thereby reducing the overall amplitude of the doublet signal. This approach also elevates the available signal-to-noise ratio (SNR) by enabling robust lactate data collection at an echo time of 144 ms (the most common clinical choice of long echo time) rather than 288 ms. In summary, the present work addresses two aims. The first aim is to develop and validate a novel MRS pulse sequence for measuring T 1 values of metabolites in a time efficient manner, suitable for use in patient populations and when J-coupled metabolites are present in low concentration. The second aim is to use the developed pulse sequence to report the T 1 value of lactate at 3 T in patients with brain cancer. In particular we measure the of the lactate doublet averaged over all microenvironments, as it is typically what is of interest in clinical MRS. These values, taken together with values from the literature as appropriate, are then used to provide a quantitative estimate of the brain lactate concentration in vivo. 3.2 Theory A diagram of the prototype pulse sequence for spectroscopic T 1 measurement is shown in Figure 3.1. The main elements consist of an inversion pulse followed some time later (as selected by the inversion time, ) by point resolved spectroscopy 4 (PRESS) localization with spectroscopic readout. However, rather than performing acquisitions for multiple values in sequence, as in IR experiments, paired acquisitions are performed at each value. One acquisition includes the inversion pulse, producing the signal ( ). The other acquisition is performed without the inversion pulse, producing the signal ( ). When the paired signals are subtracted to yield a difference signal, it can be shown by solving the Bloch equations that if TR is chosen to track with (i.e.,, where C is a constant) then can be modeled by a simple two-parameter, monoexponential decay function involving the T 1 relaxation time constant. The optimal choice of TI and TR values (given practical constraints, such as the total time allowed for MRS measurement) can then be determined using

79 65 computational methods to estimate the T 1 value and minimize the uncertainty of the estimate. This overall approach allows measurements with comparatively small TR values without the need for a third parameter in the monoexponential model. The approach also provides time efficiency by removing the need for all measurements to be made with large TR values for full longitudinal recovery of magnetization, as adopted in conventional IR, and removes the need for a fourth TI point as in MFIR 130. A similar pulse sequence approach for T 1 measurement has been used recently, although without thoroughly validating optimal TI and TR selection as well as time efficiency in relation to other measurement methods 131. These issues are addressed as part of the experimental methods outlined below. 3.3 Methods Spectroscopic data were collected using a GE 750MR 3.0T MRI system (General Electric Healthcare, Waukesha WI) with a standard 8-channel head coil receiver. Considering the prototype pulse sequence (Figure 3.1) in more detail, the standard PRESS sequence was modified to include four additional elements: 1) a frequency-selective (not spatially selective) hyperbolic secant inversion pulse was added prior to the chemical shift selective saturation 19 water suppression; 2) BASING RF pulses 132 were added after the first and second refocusing pulses, using linear-phase Shinnar-Le Roux 75 (SLR) design with minimal transition width, to reduce unwanted coherences and reduce co-editing of metabolites other than lactate; 3) custom SLR 180 refocusing pulses were used to increase SNR and further reduce unwanted coherences; and 4) the crusher gradient scheme was modified to include bipolar gradients which selected the proper echo pathway for BASING. BASING is a two-cycle technique which refocuses the lactate doublet (by inverting the lactate quartet) on the first cycle, and leaves the lactate doublet unaffected on the second cycle. Subtraction of these two cycles results in the addition of the lactate doublet, whereas the overlapping lipid signals are theoretically unaffected by the cycling scheme and thus cancelled. Table 3.1 provides the details of all the RF pulses within the sequence. The pulse sequence uses a four cycle scheme: two for the separation of coupled and uncoupled resonances via BASING, and two for the interleaving of the inversion pulse. For the first and second cycle, the inversion pulse is on, and for the third and fourth cycle the inversion pulse amplitude is set to zero. For the first and third cycle, the

80 66 Figure 3.1: Spectroscopic pulse sequence for measuring T 1 relaxation. is the inversion pulse and TI is inversion time. A subsequent PRESS module is characterized by the time between the isoflip time of the excitation pulse ( ) and the middle of the first refocusing pulse ( ); the time between the middle of and the second refocusing pulse ( ); and, the time between the middle of and the start of the acquisition time. is equal to the echo time (TE), 144 ms. The time between the first BASING pulse ( ) and the second BASING pulse ( ) is TE/2 (72 ms) for this editing scheme. BASING pulses ( and in Figure 3.1) are centred at water and invert the lactate quartet at 4.1 ppm. For the second and fourth cycles, the BASING pulses are shifted downfield by 198 Hz to not invert the metabolites. Thus the uncoupled singlet signal,, is obtained from ( ) (3.1) where the subscript on denotes the cycle number of the measured signal. The coupled doublet signal,, is obtained from

81 67 ( ) (3.2) This four cycle scheme is then repeated as necessary for signal averaging. For the work presented here, 128 excitations were performed for each was averaged over 32 trials in each case. value. Thus, the four cycle scheme The signal processing was performed using specially-written scripts in MATLAB (the Mathworks, Inc., Natick, MA). Prior to reconstruction, the first point in the raw FID of the unsuppressed water acquisition was used to estimate the coil sensitivity, which was then used to rephase and scale the signals from each of the individual coils. By scaling and phasing prior to summation over the eight coils, SNR is substantially improved compared to direct summation. The net signals were then combined over the four-cycle scheme according to Equation 3.1 for singlets and Equation 3.2 for lactate, averaged over all repetitions as appropriate, and input to the freeware known as Totally Automatic Robust quantitation in NMR (TARQUIN 94 ). Algorithms within TARQUIN enabled fitting of the data to the four metabolites of interest: NAA, lactate, creatine and choline. Because the BASING pulses have some effect on some downfield smaller peaks, a more physically realistic basis set was used by taking the default basis set in TARQUIN and removing the smaller resonances. The concentration values obtained from TARQUIN were then used to estimate values. For computational simplicity, the monoexponential equation for was linearized by taking the natural logarithm and weighting the noise contribution at potential TI values appropriately. This enabled use of linear least squares fitting to estimate T 1, and optimization of TI and TR values using a closed-form expression to minimize the uncertainty of the estimate. White Gaussian noise was assumed and standard error propagation was used to derive the expression for estimating the standard deviation of,. To estimate reliably while accounting for imperfect model fitting or spurious artefacts in the experimental data which were not well represented by the standard deviation of the spectral components, the calculation was performed using both the Cramer-Rao lower bounds from TARQUIN, and from the standard deviation of the residuals of the least squares fit. The larger of the two estimates was reported.

82 68 The unsuppressed water acquisition was then used to provide an absolute reference, setting the concentration of water at 42.3 M, as is common when attempting to quantify metabolite Table 3.1: Summary of radiofrequency (RF) pulses in the prototype pulse sequence (Figure 3.1). Pulses and are centred on water for the first and second cycles of the four-cycle scheme (and invert the lactate quartet) and for the third and fourth cycles they are shifted downfield from water to leave the metabolites unaffected. Pulse inverts all the metabolites for cycles 1 and 2 but is set to zero for cycles 3 and 4. Shinnar Le-Roux 75 (SLR) pulses are used for all but the inversion pulse, and BASING 128 pulses are the minimum-phase SLR pulses used for the lactate-editing sequence. B1 is the amplitude of the applied RF pulses. Name Pulse type Pulse duration (ms) Bandwidth (Hz) Offset frequency (Hz) Max B1 ( ) Custom adiabatic hyperbolic secant Stock excitation SLR Custom spin-echo SLR Custom minimumphase BASING SLR Custom spin-echo SLR Custom minimumphase BASING SLR / / / concentrations from MRS data 64. All concentrations were obtained using water as an internal reference, as implemented in TARQUIN, similar to the procedure by Madan et al. 35 The water unsuppressed signal had its concentration set to be 42.3 M, with a water attenuation factor of exp(-te/t 2water ), where the T 2 of water was 56 ms for healthy white matter or 156 ms for glioma tissue 35. For each metabolite the straight line intercept of the concentration vs TI plot was used to correct for inversion effects. This value was then corrected for non-equilibrium steady-state

83 69 T 1 effects and T 2 relaxation using T 2 values obtained from the literature for lactate 35 and the other metabolites 122. Statistical comparison between the T 1 of lactate and the other three metabolites was subsequently performed using a Wilcoxon signed-rank test, with the threshold for statistical significance set according to a Type 1 error of. The additional pulse sequence parameters for this initial work included an echo time (TE) of 144 ms (the TE value providing the maximum SNR achievable with this editing scheme 128 ) and a voxel size of 20 mm 20 mm 20 mm. Water suppression was implemented using the standard CHESS 19 method immediately preceding the excitation pulse for all inversion times. The uncertainty on T 1 derived from the least squares fit was numerically minimized to yield the optimal sets of TIs and TRs. The optimization was subject to three physical constraints: (the minimum allowable inversion time to perform CHESS prior to the excitation pulse); TR exceeds the time from pulse sequence onset to the end of readout; (necessary for the monoexponential model to hold); and a fixed total experiment time (chosen for in vivo work to be 30 minutes, ignoring calibration time). The number of individual measurements (i.e., TI points within the 30 minute measurement time) was allowed to vary from 3 to 8. Numerical minimization of the expected uncertainty on T 1 was achieved using the iterative sequential quadratic programming algorithm in MATLAB that required a priori knowledge of the value of interest. The only inputs required to optimize the choice of TI and TR values were the estimated T 1 and the total experiment time. The algorithm commenced with a starting value of, the reported of rat glioma measured at 4.7 T 60, to approximate the expected human analogue. Briefly summarizing the subsequent experiments, tests were first undertaken in phantoms to confirm that the prototype pulse sequence produced results in agreement with a standard interleaved inversion recovery sequence with equilibrium achieved in-between successive excitations. Next, validation experiments were undertaken with two healthy volunteers (23 year old male and 36 year old female for volunteer 1 and 2, respectively) to ensure that the sequence provided physically realistic measurements of relaxation in vivo.

84 70 Finally, the sequence was used to estimate lactate in a group of patients with brain cancer. All volunteers participated with free and informed consent and with the approval of the research ethics board at Sunnybrook Health Sciences Centre. The values of lactate, NAA, creatine and choline were initially estimated from the Braino phantom (GE Healthcare). As a proof of principle the measurement was done using four linearly spaced values of 160, 260, 360, 460 ms using both the prototype pulse sequence, and for comparison an inversion recovery (IR) PRESS sequence with an interleaved adiabatic hyperbolic secant inversion pulse 76,77 added prior to water suppression with a TR of 4 seconds. The TI, TR as well as the total experiment time for all experiments are shown in Table 3.2. For these initial measurements, identical values were used in both sequences to control for possible systematic variation in the precision on associated with the sampling of longitudinal relaxation. The TR values for the prototype pulse sequence were 1.5, 1.6, 1.7 and 1.8 s, respectively, with a total experiment time of 14 minutes. For the standard IR PRESS sequence, an appropriate TR of 4 s was chosen to allow close to full recovery between each successive inversion for the metabolites of interest, with a total experiment time of 34 minutes. For practical application of the prototype pulse sequence, the optimal values were determined for a given total acquisition time according to the optimization procedure described above. Notable exceptions were that a) the optimization algorithm was run with an initial value of T 1 = 720 ms (the variance-weighted mean of the previous two measurements of the T 1 of lactate in this phantom) and b) the duration of the experiment constrained to 14 minutes, as for application of the prototype pulse sequence above. The TIs for the optimized measurements in the Braino phantom were 160, 942 and 942 ms, and the associated TR values were 1680, 2460 and 2460 ms for the three points, respectively. A similar numerical optimization algorithm was written for the standard IR sequence which constrained the time between the 2 nd refocusing pulse and the start of the next TR interval to equal 5T 1. For this sequence the number of TIs and the number of averages were allowed to vary while keeping the total experiment time equal to the experiment time of the prototype sequence. The optimal TIs were determined as 160, 897 and 897 ms and the associated TR values were 3909, 4646 and 4646 ms, respectively, with 64 averages performed at each TI.

85 71 For in vivo work, the prototype pulse sequence was used to measure T 1 with the optimization algorithm prescribing TI values of 160, 2011 and 2011 ms with TR values of 3454, 5304 and 5304 ms, respectively. (The larger prescribed in vivo TIs and TRs are due to the larger in vivo T 1 values that are expected in comparison to those of the Gadolinium-doped Braino phantom). Table 3.2: The TI, TR and total scan time values for all experiments. TI 1 (ms) TI 2 (ms) TI 3 (ms) TI 4 (ms) TR 1 (ms) TR 2 (ms) TR 3 (ms) TR 4 (ms) Total scan time (minutes) Braino IR Braino prototype Braino IR optimized Braino prototype optimized In vivo prototype optimized n/a n/a n/a n/a n/a n/a When performing MRS of patients, care was taken to maximize the amount of tumor tissue within the voxel by comparing the voxel placement with -weighted anatomical images acquired after administration of Gd-DTPA contrast agent from previous exams, which were available in 3 of the 6 patients. Care was also taken to avoid placing the voxel too close to the skull or ventricles. A representative anatomical image with overlaid voxel placement is shown in Figure 3.2.

86 Results Figure 3.3 shows the results of the four relaxation measurements (prototype sequence and IR-PRESS sequence with the same linearly-spaced values, the prototype sequence with optimized values, and the optimized IR sequence) for the four main metabolites in the Braino phantom. The measurements are in excellent agreement in all cases, as evident by observing the similar slopes of the plots (proportional to ) for each metabolite, and the Figure 3.2: T 1 weighted anatomical image with voxel placement (white square) overlaid for patient 5. The singlet and doublet spectra at both long and short TI are displayed in Figure 3.4 for this patient. differences are comparable to the measurement error. For display purposes, the amplitudes have been arbitrarily scaled to distinguish each line easily. However, the steady-state values for the prototype sequence versus the standard IR sequence are lower by 9%, 3%, 18% and 15%, for creatine, lactate, NAA and choline, respectively. The decrease observed for lactate is

87 73 substantially less than the other three metabolites despite its relatively large value due to the refocusing effect of BASING 129, as explained further in the discussion. The metabolite concentrations within the phantom were also estimated as described in the Methods section, using the values of Figure 3.3 as well as previously measured T 2 values. Values of mm, mm, mm, and mm were estimated for the concentrations of creatine, NAA, choline and lactate, respectively. The singlets are within approximately 10 % of the known concentrations 133 of 10 mm, 12.5 mm and 3 mm for creatine, NAA and choline, respectively, whereas the lactate doublet is within approximately 25 % of the known concentration of 5.0 mm. The lower estimate for lactate is likely due to residual anomalous J- modulation 24. Figure 3.3 also shows that the estimation error is largest for lactate, due to its lower concentration (and thus SNR) within the Braino phantom. The error on the estimated T 1 of lactate is reduced by a factor of 0.41 for the optimized prototype pulse sequence, compared to the error obtained when using the arbitrary linearly spaced values. The reduction factor predicted by the optimization algorithm is 0.47, in good agreement with this result. The error on the estimated T1 of lactate is reduced by a factor of 0.74 for the optimized prototype sequence compared to that obtained with the optimized IR sequence. The numerical optimization predicts a reduction factor of 0.82, again in good agreement. Overall, these results indicate a) that substantially improved precision of the estimate can be obtained if the value is known reasonably well a priori; and b) that by removing the constraint of large TR values, an improvement in precision can be gained for a constant experiment time. In addition, the technique developed was applied to probe the white matter of two healthy volunteers, producing the estimated values for choline, NAA and creatine shown in Table 3.3. Adequate agreement is obtained with previous estimates 122,131,134, with the present estimate slightly elevated for creatine. Using these values, the mean metabolite concentrations

88 74 Figure 3.3: Inversion recovery results for Braino phantom for the four major metabolites observed at TE = 144 ms (creatine, lactate, NAA, choline). The top line for each metabolite corresponds to the prototype pulse sequence applied with optimized choice of TI and TR. The second from the top line is the optimized interleaved IR technique. The second from the bottom line is the prototype pulse sequence with linearly spaced inversion times, and the bottom line is the standard interleaved IR technique applied with TR = 4000 ms. Amplitude values were scaled arbitrarily for display purposes. The acquisition time for both applications of the prototype pulse sequence and the optimized IR sequence was the same (approximately 14 minutes), and the acquisition for the linearly spaced IR sequence was approximately 34 minutes. The slope of the line is proportional to and the parameter estimates are also shown including error estimates. Excellent agreement is observed between measurements for all four metabolites. Substantially reduced error in estimating was obtained for both lactate and NAA when using the optimized TI and TRs for both the prototype and the standard IR sequence, as predicted by numerical simulation.

89 75 for the two healthy volunteers were estimated as mm, mm and mm for choline, NAA and creatine, respectively. The concentration estimates are within the range previously reported in the literature of 1-5 mm for choline, mm for NAA and 6-14 mm for creatine 135 and in excellent agreement with those reported using a very similar absolute quantitation scheme 35. No lactate was detected within the doublet spectra from the healthy volunteers, as expected. Table 3.3: T 1 values measured within the white matter in two healthy volunteers as well as the mean values obtained from healthy volunteers within the literature at 3 T. Subject Choline T 1 (ms) NAA T 1 (ms) Creatine T 1 (ms) 1 2 Chen, et al. 131 Li, et al. 122 Träber, et al. 134 (inversion recovery) Träber, et al. 134 (saturation recovery) Figure 3.4 shows the spectra obtained from a grade 3 glioma according to the voxel prescribed in Figure 3.2, for the optimized values of 160, 2011 and 2011 ms. There is good singlet suppression in the doublet spectra, consistent with previous work 132 (as shown by the significantly reduced amplitude of NAA, Cr and Cho), indicating negligible contamination from lipids in the vicinity of lactate. Table 3.4 lists the estimated T 1 values for lactate, choline, NAA and creatine across the group of patients. The T 1 estimates for choline and NAA agree well with those obtained previously from glioma patients 122, although the value presented here for creatine is slightly larger. Potential reasons for this discrepancy are given in the discussion. There is a significant difference between the T 1 of lactate and choline (P = 0.004) as well as lactate and NAA (P = 0.009). No significant difference is observed between the T 1 of lactate and

90 76 creatine (P = 0.537). Given the estimated T 1 of lactate, calculations indicate that is maximized for a standard PRESS sequence with TE = 144 ms or TE = 288 ms when TR = 2830 ms. Figure 3.4: Spectra obtained from patient 5 (from the voxel prescribed as shown in Figure 3.2). The top row shows singlet spectra (choline, creatine, NAA and lipids) whereas the bottom row shows doublet spectra (primarily lactate). Spectra in the left column were acquired with TI = 160 ms and those in the right column were acquired with TI = 2011 ms. Only two TI values are displayed, since the second and third acquisitions of the optimized prototype pulse sequence used the same TI value and the respective spectra differed only by noise. Note that there is some non-lactate signal in the doublet spectrum in the 2-3 ppm range, likely due to the coediting of NAA and glutamate. Table 3.5 displays the absolute concentrations for the four measured metabolites for all six glioma patients. Good agreement is observed between the present results and those previously estimate 35,136 by a very similar absolute quantification procedure. Most importantly, the lactate concentration estimate of ( ) mm is within experimental variation of the previously reported values of ( ) mm 35 and ( ) mm 136.

91 77 Table 3.4: Estimated T 1 values from six patients with high grade glioma. The measured spectra from patient 1 indicated very large lipid, lactate and water peaks with minimal other metabolites indicating that the voxel was placed primarily within a necrotic core; T 1 could only be measured for lactate in this patient. All patients were diagnosed with glioblastoma (grade 4), except patient 5 who had a grade 3 glioma. The third last row is the mean standard deviation across all patients. The second last row is a previous measurement of the T 1 values obtained from a population of glioma patients at 3 T. The last row is a previous measurement of the T 1 values obtained from a population of brain tumor patients at 1.5 T. Patient number Lactate T 1 (ms) Choline T 1 (ms) NAA T 1 (ms) Creatine T 1 (ms) 1* n/a n/a n/a Mean Li et al. 122 n/a Sijens et al. 123 (1.5 T)

92 78 Table 3.5: Estimated absolute concentration of metabolites from the same patients with high grade glioma as reported in Table 3.3. Spectra from patient 1 indicated very large lipid, lactate and water peaks with minimal other metabolites indicating that the voxel was placed primarily within a necrotic core. All patients were diagnosed with glioblastoma (grade 4), except patient 5 who had a grade 3 glioma. The second last row is the mean standard deviation across all patients. The bottom row is a previous measurement of the absolute concentration values obtained from a population of high grade glioma patients at 3 T. Patient number [Lac] (mm) [Choline] (mm) [NAA] (mm) [Creatine] (mm) 1* n/a n/a n/a Mean Madan, et al Discussion In the present work, a novel pulse sequence was developed for measuring of lowconcentration J-coupled species in a time-efficient manner. This sequence was then applied to a population of high grade glioma patients to measure the of the methyl group of lactate in vivo. A number of issues are worth discussion in relation to the pulse sequence that was developed. First, the numerical procedure for minimizing in a specific experiment duration (30 minutes in humans) prescribed that data should be acquired at a single low TI value, and

93 79 two identical high TI values. This prescription is not intuitive, however, it is understandable by thinking about simple linear least squares procedures for estimating the slope of a line. In such cases, the error on the slope has a dominator term equal to ( ), where x is the independent variable, is the mean, and the subscript i refers to each instance of the independent variable. The error on the slope is thus minimized if the values are spread widely apart in relation to. This accounts for the wide separation in TI values that was prescribed. In addition, the latter TI value has low SNR (as almost full recovery has occured) and so repeated measurements are prescribed to obtain a more precise estimate of the signal at this time point. A related issue concerns linearization of the monoexponential equation for which was performed to simplify computational aspects of optimizing TI and TR values for the prototype pulse sequence. For the TI values with low SNR, no correction was made for how the noise distribution was skewed by taking the natural logarithm. To check for potential systematic error due to this approach, T 1 estimates were re-calculated using nonlinear least squares fitting of the monoexponential function. The nonlinear fit results deviated by <1 % from the values listed in Table 3.3 and Table 3.4. Thus, linearization was useful in the present case, but it is not essential to the success of the method and may not be advisable for data acquired at lower SNR levels. The prototype pulse sequence was also found to be robust to experimental imperfections. Numerical simulation of the Bloch equations revealed that variation in the prescribed flip angle of the excitation and refocusing pulses perturbed a T 1 value of 2000 ms by only ms, well within the biological variation of the experimental results. No obvious signs of unwanted coherences were evident in the acquired spectra, possibly because decreased spoiling power is required for the coarse voxel size used here 26. More gradient spoiling could be added to the sequence in the future, if required. Slightly increased noise was consistently observed for the 2-3 ppm range in both the Braino phantom and volunteers, however (eg. See Figure 3.4). This noise did not affect quantification of lactate, and likely results from co-editing of J-coupled resonances of NAA and glutamate which are known to lie within the pass band of the BASING pulse 27. The effect of voxel shift due to chemical shift mis-

94 80 registration is also unlikely to be important because it can be reasonably assumed that all lactate originates from the tumor, which was typically larger than the prescribed MRS voxel. Lastly, water suppression could be achieved solely through BASING 9 by modifying the frequency scheme of the BASING pulses. This was not implemented here, as CHESS has been shown to be robust across a range of static magnetic field strengths, whereas simultaneous spectral editing and water suppression with BASING is challenging at 1.5 T due to spectral overlap effects with the pulses used here. However, sole use of BASING could reduce the minimum allowable TI to 7.6 ms (down from 160 ms), which could help to improve measurement precision. Overall, the quality of the spectra was judged to be similar to that obtained in previous work using the identical BASING scheme 132. The optimal choice of TI values has previously been investigated for MFIR 130. Similar results were obtained in comparison to the present work, with optimal results obtained when one low TI value and one high TI value were selected. The effect of low SNR motivating a repeated measurement at the high TI value was not considered. In contrast, Ogg and Kingsley 130 have suggested taking measurements with two additional intermediate TI values. Differences between the TI prescriptions are likely due to the differences in underlying mathematical model. The present work uses a two-parameter mono-exponential model which is appropriate under MRS conditions, whereas Ogg and Kingsley adopted a three-parameter model more appropriate for proton MRI with higher SNR 130. Although a priori knowledge of the T 1 is required for numerical minimization of the uncertainty on T 1, this is not a major limitation and is not a requirement for the monoexponential model of to hold. In practice, the initial input of T 1 for optimization did not have a strong impact on the prescription of optimized TI and TRs. If the actual value of varies from the input initial value of = 1725 ms by plus or minus 500 ms the result is an increase in the predicted uncertainty by a factor of 1.11 and 1.02, respectively. In any case, this is not a limiting issue. Some implicit knowledge of is always assumed when choosing TI values to sample recovery curves appropriately, as part of obtaining high quality results in inversion or saturation recovery experiments.

95 81 The MRS measurement precision in patients likely was also reduced compared to the data quality that is achievable in healthy humans 119. This is expected because of the lower signal from tumor tissue and the difficulty in maximizing the amount of tumor tissue within the voxel. These effects are general to the use of single voxel MRS and not specific to the pulse sequence. However, TI values were chosen to optimize T 1 measurements for lactate, which recovers in the longitudinal direction more slowly than some of the other metabolites, slightly compromising their measurement. Other MRS studies 134 measuring the longitudinal relaxation within tumors have achieved coefficients of variation (ratio of the standard deviation to the mean) for choline, creatine and NAA of approximately 20%, similar to the values observed here. The T 1 estimate for creatine was slightly larger than previously measured 122,123, which could be due to differences in the patient populations studied, voxel positioning or other sources of statistical variation. The discrepancy likely did not result from an imperfection in the model used here. Such a systematic bias likely would impact NAA and choline results as well, whereas these showed excellent agreement with the literature. With appropriate modification, the technique presented here could also be used in a variety of other measurement applications, such as to estimate the T 1 value of 2- Hydroxyglutarate 64. Furthermore, the technique is not constrained to single voxel applications. It could be incorporated in a typical MR spectroscopic imaging technique, or a multivoxel technique that avoids or minimizes k-space encoding, such as Hadamard encoding 137 or constrained source space MRS 138,139. This could be advantageous for measuring the value of metabolites in pathologies with large heterogeneous regions, or to expedite control measurements from regions of healthy tissue. The lactate-editing scheme chosen here is not the only available technique for disentangling lactate and overlapping lipid signals. The inversion sequence here could use the LASER (localization by adiabatic selective refocusing) method instead, which substantially reduces the chemical shift mis-registration, and the separation of lactate and lipid signals can be done using a multiple-quantum filter 140. Other alternatives are MEGA-SPECIAL 141, which adopts a similar editing technique referred to as MEGA for spectral separation and SPECIAL for spatial localization, or similarly MEGA-sLASER 142. These options could potentially improve SNR and, since the multiple-quantum filter is a single

96 82 shot technique, reduce sensitivity to motion at the cost of signals from the other metabolites. For BASING to provide perfect lipid suppression, the spectra in the two-cycle subtraction scheme must have identical phase and amplitude and thus there is the potential for motion to introduce errors. However, the present results suggest that such errors are small in practical circumstances. The lactate T 1 values reported for brain cancer patients in the present work agree well with those for rat gliomas at 4.7 T 60 but are substantially higher than those measured previously at 1.5 T in a separate population by another research group who did not include spectral editing 123. It is possible to add the signals from the lipid and lactate resonances in the present work, representing the scenario whereby measurements are made without use of BASING. This provides a estimate of ( ) ms that is within experimental uncertainty of the previous estimate of ( ) ms at 1.5 T 123, strongly suggesting that lipid contamination produces a substantial erroneous reduction in lactate. There is a significant difference between the of the lipid plus lactate compared to the lactate alone (P = 0.004). This discrepancy could also be partially due to the differences in field strengths used for measuring (3 T here vs 1.5 T previously 123 ), as in many biological compounds the value exhibits a field strength dependency. It should be noted that there exists a correlation between the T 1 relaxation times measured from Patients 2-6 between lactate and the other metabolites, as evident by the R 2 values of 0.45, 0.67 and 0.26 for NAA, Cr and Cho, respectively. It should also be mentioned that the estimates provided here are probably slightly different from the "true" values that would be obtained for each resonance in the absence of magnetization transfer and chemical exchange effects. Such effects likely occur at some level in the present experiments, for example due to use of CHESS pulses. This water suppression scheme is very common, and the vast majority of in vivo MRS work using this and other schemes does not account for exchange effects. Investigating the extent of perturbation due to magnetization transfer or chemical exchange is an interesting topic for future research which would likely benefit from the use of a time-efficient procedure for precisely measuring longitudinal relaxation, such as developed here. From a practical standpoint, the present work

97 83 makes the appropriate estimates that are required to correct for partial longitudinal recovery, as well as for optimizing in MRS experiments. The absolute concentration values that were estimated in the present work are also in good agreement with previous reports 35,136. Overall, the general trend was confirmed of increased lactate and choline, decreased NAA and roughly equal creatine concentration for glioma tissue as compared to healthy tissue 35. These estimates are based on the assumption that the water resonance has a constant concentration of 42.3 M 35,64, however, whereas the actual concentration within glioma tissue could vary from this value, as well as from patient to patient. This limitation can be removed by including an external reference sample in the measurement protocol and data analysis. For now, clinical MRS will continue to rely on interpreting MRS data using ratios of neurometabolite signals ratios with respect to creatine (which has been shown to vary substantially within a patient population 35 ). Irrespective of this, the use of reference samples, literature values for and for each spectral component (including the revised data for lactate reported here), enable absolute concentrations to be estimated for use in basic and clinical MRS research. In the future, such work may facilitate the use of lactate as a biomarker for improved cancer treatment and survival. 3.6 Conclusions A novel MRS technique was developed and validated at 3 T for time-efficient measurements of the methyl group of lactate without contamination from lipids. The resulting T 1 value of ( ) ms was obtained for a group of six glioma patients. After correcting for T 1 (and T 2 from literature values) the absolute lactate concentration was estimated as ( ) mm. Lactate T 1 exhibits similar variations as other major metabolites observable by MRS in high grade gliomas. The T 1 estimate provided here will be useful for future MRS studies that wish to optimize pulse sequence parameters, or to report relaxation-corrected estimates of lactate concentration as an objective tumor biomarker.

98 84 Chapter 4 Diffusion-Weighted J-Resolved Spectroscopy A paper published in Magnetic Resonance in Medicine [Epub ahead of print] by Karl Landheer, Rolf Schulte, Ben Geraghty, Christopher Hanstock, Christian Beaulieu, Albert P. Chen, Charles H. Cunningham, and Simon J. Graham 4.1 Introduction Proton magnetic resonance spectroscopy (MRS) is a powerful non-invasive technique used to measure biomarker activity within the brain and body. The diffusion characteristics of the spectral components can also be investigated by appending diffusion-sensitizing gradients to standard protocols such as Point Resolved Spectroscopy 4 (PRESS) and Stimulated Echo Acquisition Mode 113 (STEAM), as implemented by Posse et al. 101 These techniques, referred to as diffusion-weighted magnetic resonance spectroscopy (DW-MRS), provide novel information and allow metabolites and their microstructural environment to be probed noninvasively within the intracellular and extracellular space in vivo. The DW-MRS data features depend on factors such as active transport, cytosol viscosity and compartmentalization. With the exception of glucose and lactate, the metabolites that can be probed in this manner are predominantly intracellular 143. In principle, each individual metabolite offers specific information about the microstructural compartments where it resides. Previous DW-MRS results show that metabolites diffuse freely along cell fibers, suggesting that the metabolites are not confined inside cell bodies 103. The pathophysiological changes in DW-MRS signals have been measured for a range of disorders such as cancer, ischemia and excitotoxicity of the brain 143, in addition to glial reactivity in response to inflammation in systemic lupus erythematosus 106. Functional MR techniques have also been combined with DW-MRS to observe increased apparent diffusion of

99 85 metabolites during visual stimulation, 107 providing a unique tool for investigating physiological aspects of brain activity. To date, DW-MRS of the human brain has primarily focused on the N-aceytlaspartate (NAA), creatine (Cr) and choline (Cho) resonances due to their relatively high signal-to-noise ratio (SNR) and strong non-overlapping singlets. Other metabolites are of substantial interest, however. For example, glutamate (Glu) and gamma-aminobutyric acid (GABA) have important roles as the main excitatory and inhibitory neurotransmitters, respectively 46. Glutamate and GABA typically reside in the synaptic vesicles 29,46 within neurons, but during neurotransmission they are released into the synaptic cleft where they bind to postsynaptic receptors. To the authors knowledge, however, only three proton DW-MRS studies have investigated metabolites in the human brain beyond NAA, Cr and Cho: glutamate, glutamine (Gln) and N- acetyl aspartyl glutamate (NAAG) in healthy volunteers at 7 T 108, lactate in edema and tumors at 3 T 144 and myo-inositol (mi) in healthy volunteers at 3 T 145. The major difficulties in measuring such other metabolites are: 1) low SNR, necessitating long scan time; and 2) spectral overlap with larger resonances. These problems are particularly troublesome at field strengths of 3 T and below. Alternatively, using higher field strength systems for small animal MRI, the diffusion characteristics of up to 10 metabolites have been investigated in ischemic rat brains at 4.7 T 146 and 12 metabolites have been investigated similarly in healthy rat brain at 9.4 T 147. Several MRS techniques have been developed for accurately measuring smaller resonances in the absence of diffusion weighting. Spectral editing J-difference techniques have been developed on clinical-grade MRI systems for detection of Glu and Gln 8, GABA 148, lactate 129 and 2-Hydroxyglutarate 64, among others. These techniques have good efficacy but usually require the phase of two subsequent acquisitions to be consistent. It is well known that the phase varies greatly from one excitation to the next in DW-MRS due to involuntary subject motion, however, necessitating re-phasing of the spectra prior to summation 101. Re-phasing is a challenge under conditions of low SNR and this may negatively impact the ability to edit and quantify the smaller resonances of interest. A small deviation from the 180 phase difference requirement in spectral editing can lead to substantial error. In addition, spectral editing techniques often improve detection of specific resonances while disrupting other portions of

100 86 the spectrum. Two-cycle spectral editing is probably not ideal for measuring the diffusion properties of small resonances, therefore, in many cases. An alternative spectral editing scheme based on double-quantum coherence-transfer has been used to measure the diffusion of lactate in the presence of contaminating lipids , but discards information about other metabolites. Another approach uses biexponential fitting to estimate the apparent diffusion coefficient (ADC) of lactate within a tumor in the presence of lipids 152. This method is well suited to obtaining lactate ADC values, but would be challenging to apply to other metabolites such as glutamate due to spectral overlap, and the need for very high SNR to discern each metabolite properly. Small resonances can also be quantified at 3 T using localized two-dimensional (2D) J- resolved spectroscopy (JPRESS) 13,153, originally implemented in a half-echo acquisition mode. In JPRESS, a second spectral dimension is added by sequentially increasing the echo time for each spectroscopic data acquisition. As the initial phase of the signal collected from a J-coupled metabolite varies depending on the echo time, collecting data at a series of different echo times enables careful sampling of the dispersion in this second spectral dimension. Subsequent 2D Fourier transformation of the time domain data into the frequency domain enables quantification of some of the smaller resonances which are overlapped in traditional onedimensional (1D) spectroscopy. The efficacy of the JPRESS sequence has been demonstrated on clinical-grade 3 T MRI systems including acquisition of in vivo data, with a maximum echo sampling scheme to improve sensitivity 16. Using JPRESS and 2D fitting software referred to as ProFit 14,15, signals from 17 metabolites have been reliably measured in vivo at 3 T. Based on these promising initial developments, a novel technique called diffusion-weighted JPRESS (DW- JPRESS) is proposed here. The purpose of this study is to describe, characterize and validate use of DW-JPRESS to measure the ADCs of metabolites beyond NAA, Cr and Cho at 3 T. 4.2 Methods A prototype pulse sequence for DW-JPRESS was implemented using a MR750 3 T MRI system (General Electric Healthcare, Waukesha WI) with a standard 8-channel head coil receiver. The associated pulse sequence diagram is shown in (Figure 4.1), and includes three major

101 87 modifications from the basic JPRESS sequence. First, maximum-echo sampling was implemented, whereby sampling consistently commenced 1 ms after the last gradient pulse, instead of at the spin echo maximum as in typical MRS readouts. Maximum-echo sampling was used because it has been shown to increase SNR and decrease overlap of resonance tails 16. The 1 ms time delay following the last gradient pulse was included as a conservative measure to allow for dissipation of any fast decaying eddy currents that were potentially present, prior to commencing data collection. Second, diffusion-sensitizing gradients (DSGs) were added prior to the first crusher and after the last crusher in the three orthogonal directions simultaneously. Third, instead of automatically averaging the data from all identical excitations, all individual spectral traces for identical excitations were saved for rephasing prior to averaging, as necessary in DW-MRS 101. The time between the start times of the DSGs,, was set to be ms for the first TE value (74 ms), and incremented by = 1 ms for each TE step. The DSG width,, was ms with a rise time,, of 1 ms for all echo times (a slew rate of 50 T/s/m, ie. one quarter of the maximum value available on the MRI system, 200 T/s/m). For in vivo experiments, the amplitude of the DSG for the first TE value,, equaled 50 mt/m (the maximum allowable gradient amplitude) and 5 mt/m for diffusion-weighted spectra acquired with high and low b-values, respectively (see below for further details). The diffusion-weighting parameters were chosen to provide a sufficiently large b-value for adequate diffusion weighting while maintaining a short echo time. A non-zero b-value for the low b acquisition was used to assist in suppressing unwanted echo pathways. Outer volume suppression 154 and global water suppression via CHESS 19 were implemented using the standard pulse sequence components available. Outer volume suppression was used both to reduce lipid contamination from the scalp and for inner volume saturation 25 to reduce anomalous J-modulation effects. In each in vivo DW-JPRESS experiment, two data sets were collected with CHESS water suppression on: one with the DSG amplitude set to the high b-value, and the other with DSG set to the low b-value. In both cases, data were acquired with the number of excitations (NEX) set at 8 for each TE step, for signal averaging purposes. Two additional calibration data sets were collected with identical parameters except a NEX of 1 and water suppression off: one at high b- value and one at low b-value. All 4 data sets were acquired with a minimum TE value of 74 ms,

102 88 Figure 4.1: DW-JPRESS pulse sequence for the a) initial echo time and b) intermediate k th echo time. Shaded gradients are crushers. The large gradients played out in the three orthogonal directions are the diffusion-sensitizing gradients (DSGs). Acquisition begins approximately 1 ms after the end of the second DSG, for maximum echo-sampling. Note that the amplitude of the DSGs are reduced in b) compared to a) according to Equation 4.3 to keep the b-value constant across all echo steps. The reduction in amplitude is exaggerated for display purposes. The peak of the spin echo occurs at the echo time (TE) and is equal to and the second refocusing pulse in b) is played out at a time later than in a). Outer-volume suppression and global water suppression (CHESS) is executed prior to the 90 excitation pulse. Gradient amplitudes are not drawn to scale (crushers are substantially smaller than the DSGs for all TE values).

103 Hz receiver bandwidth (corresponding to the bandwidth of the F 2 dimension in the JPRESS spectra), the aforementioned of 2 ms (corresponding to a bandwidth of 500 Hz in the F 1 dimension) and 100 incremental TE steps. The water unsuppressed JPRESS spectra were used for eddy current correction 20 and estimation of coil sensitivity. Cardiac gating was also included to reduce motion-related errors in vivo due to cerebrospinal fluid pulsatility, with the TR value set to two R-R cycles (~2 sec) and a trigger delay of 300 ms 101. For the phantom experiments the TR was set to 1.5 s. For the phantom experiment performed on the BRAINO phantom, two additional intermediate b-values were also collected (both the water suppressed and water unsuppressed data). These data were subsequently used to compare ADCs estimated with four b-values to those estimated with only two b-values, as part of validating the latter approach. The signal processing of DW-JPRESS data was performed using specially-written scripts in MATLAB (the Mathworks, Inc., Natick, MA) using a pipeline as shown in Figure 4.2. The data from each coil were eddy-current corrected using the water-unsuppressed JPRESS spectrum 20, weighted by the coil sensitivity and then averaged over all eight coils. The coil-averaged signal was then multiplied by a novel streak correction factor to maintain the water resonance at constant amplitude across all NEX to correct any residual cardiac pulsatility artefacts not eliminated by cardiac gating. The streak correction algorithm is similar to the algorithm originally proposed by Posse et al. 101 to reject individual data traces that exhibit excessive signal losses. The algorithm used here first determined the excitation which produced the highest water resonance amplitude (ie. the least non-linear motion) for each of the 100 individual echo times. Results for the other seven excitations were then scaled to match this water resonance amplitude. In the absence of motion, the water resonance amplitudes for all 8 NEX had a comparatively small noise envelope and thus the streak correction had negligible impact. When non-linear motion was present, however, the algorithm substantially reduced the spurious fluctuations and subsequent streak artifacts in the 2D FID. The water resonance was then removed using Hankel singular value decomposition (HSVD). The signal was then Fourier transformed and automatically phase corrected for zero and first order phase terms 118 which were obtained from the water resonance prior to removal, inverse Fourier transformed and

104 90 Figure 4.2: Flow chart of the processing steps used to estimate ADCs from the raw DW-JPRESS data. The 2D free induction decay (FID) results are processed through two separate pipelines referred to as the 2D pipeline (left) and the 1D pipeline (right). The arrow connecting the 1D pipeline and the 2D pipeline indicates that the 1D Cr303 data are multiplied with the results from ProFit (because Profit outputs spectra as a ratio to Cr303), ensuring that the diffusion characteristics of Cr303 do not bias ADC estimates for all metabolites. The preprocessing steps are done for each TE value (ie. 100 times) with two repetitions: once for high diffusion and once for low diffusion. This produces two 2D FIDs which are then combined to calculate the ADCs in the bottom portion of the flow chart.

105 91 averaged over all NEX. These preprocessing steps were repeated for each echo step (100 times) for the data obtained at both high b-value and low b-value. The preprocessed FIDs were then submitted to two spectral analysis pipelines, subsequently referred to as the 2D and 1D pipelines (left and right columns in Figure 4.2, respectively). The 2D pipeline consisted of analysing the 2D spectra at both diffusion weightings with ProFit, using a basis set simulated from the complete density matrix with the General Approach to Magnetic resonance Mathematical Analysis (GAMMA) library 155 using the same metabolites as in the original ProFit implementation 14 minus glucose (due to its very small concentration). The basis set consisted of 19 metabolites: alanine (Ala), ascorbic acid (Asc), aspartate (Asp), Cr, phophorylcholine (PCh), GABA, Gln, Glu, glycine (Gly), glutathione (GSH), glycerophosphorylcholine (GPC), lactate (Lac), myo-insitol (mi), NAAG, phosphorylethanolamine (PE), scyllo-inositol (Scy) and taurine (Tau). For the work presented here, it was found that there was insufficient spectral resolution to separate NAAG from NAA and PCh from GPC. For this reason, the results from NAAG and NAA were summed and subsequently referred to as total NAA (tnaa), and the results from PCh and GPC were summed and referred to as total choline (tcho). Additionally, Cr was split into two separate metabolites, referred to as Cr303 and Cr391 for the two resonances at 3.03 ppm and 3.91 ppm, respectively, as is typical with ProFit 14. Because ProFit results are output as a ratio to the Cr303 peak, the 2D data were then multiplied by the Cr303 value obtained from the 1D pipeline (represented by the horizontal arrow connecting the two pipelines in Figure 4.2) to estimate ADCs using unscaled concentration values rather than ratios to Cr303. This processing step was important to remove bias, as otherwise the 2D spectral results at each b-value would be weighted by the specific diffusion characteristics of Cr303. The estimated diffusion characteristics for Cr303 were thus identical for both the 1D and 2D pipelines. The 1D pipeline consisted of separately analysing the data for each of all 100 TE steps with the freeware known as Totally Automatic Robust quantitation in NMR (TARQUIN 94 ). Because TARQUIN requires the onset of data acquisition to

106 92 occur at the echo maximum, all data acquired prior to the peak of each spin echo were discarded for this analysis. This corresponded to truncating the first ( ) samples for the k th line in the raw 2D FID. The average of the metabolite values obtained over the 100 individual lines was then used to estimate the 1D pipeline ADCs. The basis set was automatically generated in TARQUIN and contained identical in vivo metabolites to the basis set used in the 2D pipeline, as described above. In preliminary work, DW-JPRESS experiments were also conducted on the GE Healthcare "BRAINO" phantom that contains a restricted set of metabolites with known concentrations 133. In these cases, the basis set for the 1D and 2D pipelines was restricted according to a priori knowledge of the metabolite set (Cho, Cr, NAA, mi, Lac and Glu) to avoid overfitting. The 1D pipeline was also used for estimating the in vivo ADC values of NAA, Cr, Cho, mi and Glu. These results provided a useful comparison with the analogous estimates obtained from the 2D spectral analysis. The ADCs were estimated for both pipelines according to the standard equation [ ( ) ( )] (4.1) where ( ) is the peak area value obtained from the fitting software for each particular metabolite, m, from the spectra with b-value, and ( ) is the analogous metabolite peak area value from the signal with b-value. The uncertainties of ADC parameters estimated by the 1D pipeline were obtained by propagating the uncertainties in the concentration estimates from the 100 individual TE values. For the 2D pipeline, the analogous uncertainties were obtained from the uncertainty of the Cr303 values estimated by the 1D pipeline and the Cramer-Rao lower bounds outputted by ProFit, according to standard error propagation. The b- values were calculated according to the equation for a trapezoidal gradient: [ ( ) ] (4.2)

107 93 where is the gyromagnetic ratio for protons, and is the amplitude of the DSG at the first TE value. Because each TE step resulted in a different duration between the two DSGs, it was necessary to adjust the amplitude of the DSGs at each TE value to keep the b-value constant. This was achieved by the following equation: ( ) ( ) (4.3) where is the amplitude of the DSG at the k th TE step. The b-values were 2188 and 22 s/mm 2 (G 1 amplitude of 50 mt/m and 5 mt/m) for the high b and low b spectra for in vivo experiments, respectively. For the phantom experiments, the four b-values were 1012 s/mm 2, 1264 s/mm 2, 1544 s/mm 2 and 1852 s/mm 2 (G 1 amplitude of 34 mt/m, 38 mt/m, 42 mt/m and 46 mt/m), respectively, reflecting the change in material properties. A smaller maximum b- value was used in the latter case because the ADC values were known to be substantially higher in the phantom than in vivo. For the same reason, a larger minimum b-value was used to assist in water suppression in the phantom. To investigate the efficacy of using Equation 4.3 to modify the amplitude of the DSGs for each TE step, ADCs were calculated and compared for the first 15 and last 15 TE values in the phantom experiment. To investigate the potential for bias between the two data processing pipelines, the ADCs from both pipelines for tnaa, tcho, Glx and mi were compared using a Mann-Whitney U Test, with the threshold for statistical significance set according to a Type 1 error of. Additionally, to quantify the deviation between the two pipeline ADC estimates for tnaa, tcho, Glx and mi, the root mean square relative difference, calculated: for each metabolite, m, was ( ) (4.4)

108 94 where and are the estimates from the 2D and 1D pipeline for metabolite m and the i th subject, respectively (N subjects in total). This value was not calculated for Cr303 because the values from both pipelines were identical, as described above. Once the DW-JPRESS pulse sequence was debugged and validated using the BRAINO phantom, experiments were subsequently conducted in 8 young healthy adult volunteers free from previous or existing neurological or psychological deficits. All volunteers participated with free and informed consent and with the approval of the Research Ethics Board at Sunnybrook Health Sciences Centre. One dataset was discarded due to poor shim, and another due to motion that resulted in negative ADCs. Thus the data for 6 volunteers are presented (one female) with an age range of 23 to 35 years. For the phantom experiment, the voxel was placed within the middle of the BRAINO phantom and was 2.53 cm by 2.67 cm by 2.44 cm in size (16.5 cm 3 ). In vivo, voxels were consistently placed in predominantly parietal white matter with sizes that ranged from 4.76 cm by 1.86 cm by 2.29 cm (20.3 cm 3 ) to 4.54 cm by 2.78 cm by 2.54 cm (32.1 cm 3 ) in the anterior/posterior, right/left and superior/inferior directions, respectively. Figure 4.3 shows a representative voxel overlaid on top of axial and coronal anatomical images. The total experiment time for each subject was approximately 75 minutes, which included a localizer and T 1 -weighted anatomical imaging (FSPGR IR, 256 by 256 pixels, pixel size = 0.86 mm by 0.86 mm, TR/TE = 8.2/3.2 ms, flip angle = 8 ). Each individual water-suppressed JPRESS spectra was acquired in approximately 26 minutes, although due to the cardiac gating procedure, this depended on the heart rate of the subject. 4.3 Results Table 4.1 lists the ADCs estimated from the BRAINO phantom using both the 1D and 2D pipelines. The measured temperature within the bore of the magnet was 19 C and, for comparison with literature values typically given at 20 C, the data from the phantom were thus scaled assuming equal activation energy between water and the metabolites 156 using cubic interpolation of the water ADC values from Sacco et al. 157 The values listed in Table 4.1 include an increase of approximately 3 % above the unscaled values due to this temperature correction

109 95 Figure 4.3: a) Axial prescription and b) coronal prescription of the DW-JPRESS voxel for Subject 3. DW- JPRESS spectra for this subject are displayed in Figure 4.4. factor. The ADC of water, as estimated from the residual water signal after water suppression, yielded a value corrected to 20 C of x10-3 mm 2 /s using four b-values. The analogous corrected value was x10-3 mm 2 /s using the lowest and highest b-values only, as subsequently used in vivo. These estimates agree well with each other and the ADC values reported in the literature for water at room temperature, which range between 1.95 x10-3 mm 2 /s and 2.1 x10-3 mm 2 /s 101,102,108,157. Table 4.1 also shows excellent agreement between ADC estimates for both pipelines for the three metabolites typically measured by DW- MRS: Cr (both components at 3.03 and 3.91 ppm), choline and NAA. The measured percent difference of the ADC estimated from the first 15 TE values compared to the last 15 TE values of the 2D data set, using the b-values of 1012 s/mm 2 and 1852 s/mm 2, was ( ) %, ( ) %, ( ) %, ( ) %, ( ) %, ( ) % and

110 96 ( ) % for Cr303, Cr391, tnaa, Cho, Lac, Glu, and mi, respectively. Negligible differences were Table 4.1: ADC estimates obtained from the BRAINO phantom for the 2D and 1D pipelines scaled to 20 C. For each pipeline, results are listed for fitting data acquired at 4 b-values (1012 s/mm 2, 1264 s/mm 2, 1544 s/mm 2, 1852 s/mm 2 ) to Equation 1 using linear least squares, as well as for fitting with 2 b- values (1012 s/mm 2, and 1852 s/mm 2 ). Metabolite Cr303 Cr391 NAA Cho Glu Lac mi* 2D-pipeline ADC (x 10-3 mm 2 /s) 4 b-values 2D-pipeline ADC (x 10-3 mm 2 /s) 2 b-values 1D-pipeline ADC (x 10-3 mm 2 /s) 4 b-values 1D-pipeline ADC (x 10-3 mm 2 /s) 2 b-values *Because of rapid T 2 relaxation, only the first 10 TE steps were used in this case. observed between ADC pairs in all cases except Cr391, verifying that it was acceptable to use Equation 4.3 to maintain a constant b-value for all TE values. It can also be seen Table 4.1 that the ADCs estimated using two b-values are in excellent agreement to those obtained using 4 b- values for both pipelines, validating the use of two b-values for the in vivo experiments. Figure 4.4 shows typical in vivo 2D JPRESS spectra obtained with both high b-values and low b-values, including the spectral fitting and residual results obtained from ProFit. Similar fit quality is obtained in both conditions, indicating that the large DSGs have negligible impact on the quality of the spectral data (eg. linewidth). Table 4.2 lists the ADCs estimated from both pipelines for 6 healthy volunteers. The mean was calculated using only values which were physically realistic (ADC value 0.80 x 10-3 mm 2 /s, the mean ADC of water in brain measured here, which the metabolites should not surpass, and 0.09 x 10-3 mm 2 /s, which is the lowest measured ADC in healthy tissue of any metabolite previously reported 109 ). Some of the weakest resonances were not reliably quantified by ProFit (as observed by extremely large Cramer-Rao bounds or by non-physical

111 97 Figure 4.4: Water-suppressed JPRESS spectra obtained from Subject 3 with voxel prescription as shown in Figure 4.3. The real spectra (top), fits (middle) and residuals (bottom) are plotted on a logarithmic color scale. High b value weighting is shown in the left column of plots, with low b value weighting shown in the right column. Note that due to the scaling performed by ProFit the amplitude appears to be the same; however, the high b spectrum has its signal amplitude reduced by ~35 %. As can be seen from the comparable residuals, similar quality fits are obtained for both low and high b-values. The subfigures are logarithmically scaled and window and levelled consistently throughout, with negative values depicted in blue. negative ADC values) and were therefore excluded. The metabolites Ala, Asp, Asc, Pe, GABA, Gln, Gly, and Tau were found to have physically unrealistic ADCs (either negative or several times larger than water) for at least one subject. As expected, a wide range in ADC estimates is observed across the remaining resonances, with the highest mean ADC observed for Tau (although this result may not be reliable), and the lowest for mi and tcho. These results suggest that knowledge of the ADC values for some of these other metabolites beyond Cr, tnaa and tcho may provide additional valuable information.

112 98 Table 4.2: ADCs estimated from 6 subjects for 2D and 1D pipelines. 2D Pipeline ADC (x 10-3 mm 2 /s) Metab olite Cr303 Cr391 tnaa tcho Subject 1 Subject 2 Subject 3 Subject 4 Subject 5 Subject 6 Mean Ala Asp Asc GABA - - Glu Gln Glx Gsh Gly - Lac - - mi Pe Scy Tau - - 1D Pipeline ADC (x 10-3 mm 2 /s) Cr303 tnaa tcho Glx mi Water

113 99 No significant difference is observed between the median ADC values estimated from the two pipelines for tnaa (P = 0.82), tcho (P = 0.39), Glx (P = 0.82) and mi (P = 0.70). Figure 4.5 demonstrates the correlation between the 1D and 2D pipeline estimates for tnaa, tcho, Glx, mi across the six subjects. The measured D rms,m values were ( ) %, ( ) %, ( ) %, and ( ) %, for tnaa, tcho, Glx and mi, respectively. The larger variation for Glx and mi, as well as reduced precision, is likely due to the difficulties in estimating these resonances using traditional 1D spectroscopy. Figure 4.5: Plot of ADCs estimated from the 2D pipeline versus those estimated from the 1D pipeline. Strongest agreement is observed for tnaa, followed by tcho; poorest agreement is observed for Glx and mi.

114 Discussion The quality of the spectra shown in Figure 4.4 was obtained by carefully controlling for the effects of eddy currents. A previous study found that a single water unsuppressed spectrum was sufficient for eddy current correction in typical JPRESS spectra 16 because the majority of the eddy currents arose from the last set of gradients applied. However, preliminary experiments related to the present work (not shown here) found that water-unsuppressed spectra acquired at a single TE value were insufficient to remove eddy current effects in DW- JPRESS spectra for all TE steps, as apparent by distortions in the lineshapes. This is likely due to the fact that substantial eddy currents result from the very large DSGs, which have modified timing for each TE step. Differences in gradient coil hardware characteristics between the research MRI system used here and that used in the previous work 16 could also be an important factor. Irrespective of the cause, one full water-unsuppressed JPRESS spectra was acquired for each b-value to correct for eddy currents with good efficacy across all TE steps. The eddy current correction was done for each individual coil element prior to averaging, as shown in Figure 4.2, because in principle each may be sensitive to slightly different eddy currents. Due to its simplicity, Equation 4.3 was used at each TE step to calculate the amplitude of the DSGs. This equation neglects the small effect of crushers, however, which at the larger TE values produce a slightly larger b-value than the nominal b-value listed. The b-value for each echo step was also calculated using the alternate approach of integrating the square of the k- space trajectory mapped out by the gradient waveforms, which included all DSGs and crushers. It was found that the estimate of the b-value through this technique was approximately 0.5 % greater for the last echo than the first echo, indicating a negligible change for the precision of the experiments presented here. This was corroborated by the negligible changes observed in the phantom experiment when comparing ADC values calculated from the first 15 TE values to those calculated from the last 15 TE values. As part of these observations, the very large uncertainties in the ADC difference values for Glu and mi are due to the relatively low concentrations as well as the low T 2 values of these metabolites in the phantom (resulting in large variations in the ADCs estimated at larger TE values), whereas the large uncertainty observed for Cr391 is due to contamination from the water peak, as explained further below.

115 101 It is also important to emphasize that the present work does not provide rotationally invariant estimates of ADCs, as DSGs were applied in all three orthogonal directions simultaneously. The rotationally invariant estimate is usually achieved by acquiring diffusionweighted spectra from gradients successively applied in three orthogonal directions, but this was impractical in the present work due to experiment time constraints and the need to generate high b-values while keeping the TE values relatively low. The initial DW-JPRESS data from the BRAINO phantom (Table 4.1) confirmed that both the 1D and 2D pipelines produced ADC estimates in good agreement with each other for all metabolites except mi. The discrepancy observed for mi was likely due to quantification difficulties using 1D spectroscopy, and the small T 2 value of this metabolite in the phantom. The results also agree with ADC values previously estimated from an identical phantom as x10-3 mm 2 /s, x10-3 mm 2 /s, and x10-3 mm 2 /s for tnaa, creatine and choline, respectively, using a DW-MRS PRESS sequence at 7 T 100, whereas the values obtained from the 2D pipeline were x10-3 mm 2 /s, x10-3 mm 2 /s and x10-3 mm 2 /s. The previously measured ADC of glutamate within a glutamateonly phantom was x10-3 mm 2 /s at 7 T 108, which is about 20 % larger than the value presented here of x10-3 mm 2 /s for the two b-value estimate. This discrepancy could be due to differences in the temperature at which these values were measured, differences in eddy current correction schemes or other differences in the data processing pipelines between studies, such as the confounding overlap of glutamate and NAA at 2.03 ppm. For the other metabolites (NAA, Cho and Lac) the difference between the ADCs values estimated by both pipelines is comparable to the experimental uncertainty. The 2D pipeline provides substantially improved precision, however, likely because of the improved fitting capability that arises from introducing a second spectral dimension. Overall, these results indicate that the 2D pipeline can be used to extract ADC estimates in agreement with those obtained at higher field strengths in phantom experiments. Due to the difficulty in quantifying smaller resonances using 1D MRS at 3 T, no attempt was made to quantify ADCs beyond tnaa, Cr, Cho, Glx and mi using the 1D pipeline for in vivo data (which exhibit much broader linewidths and lower SNR than the phantom data).

116 102 Previously reported ADC values for tcho, tnaa and Cr in white matter 108 are x10-3 m 2 /s, x10-3 mm 2 /s and x10-3 mm 2 /s, respectively. The mean values for tcho, tnaa and Cr303 from the 2D pipeline used in the present work are mm 2 /s, mm 2 /s and mm 2 /s, respectively. The present mean ADC value estimated for tcho is slightly elevated compared to the previous finding. However, the results between 2D and 1D pipelines are in excellent agreement for all subjects except Subject 1, for which the tcho estimate for the 2D pipeline was slightly elevated, although this was still within experimental uncertainty. This observation notwithstanding, no statistically significant differences were observed between the two pipelines for tnaa, tcho, Glx or mi ADC estimates across all subjects (Cr was not tested because it was identical for the 2 pipelines, as described in the Methods). There is, however, an increase in the standard deviation across all 6 patients from the 2D pipeline as compared to the 1D pipeline. This is due to the uncertainty on the 2D ADC estimates being derived from the uncertainty from both the 1D pipeline Cr303 and the uncertainty on the 2D individual metabolites from ProFit. It should also be mentioned that due to the inherent variation in diffusion time as well as TE value within this DW-JPRESS, possible correlations between relaxation and diffusion-weighted signals may impact the estimated ADC values. It has previously been suggested that no correlation between relaxation and diffusion properties exist for mouse brain 158, however a significant correlation was found for NAA and Cr within human brains 159 (although the effect was small). The present results are also consistent with a small effect, given that the estimated ADC values agree well with previous estimates obtained with standard 1D DW-MRS. Nevertheless, mitigation strategies should be considered for future studies (such as use of a smaller value for ). Future work will investigate removing the Cr303 scaling by ProFit, which in turn will make it unnecessary to perform the processing step of multiplying DW-JPRESS results by Cr303 values obtained from the 1D pipeline. The net result should be improved precision on the ADC values estimated by DW-JPRESS. The estimated ADC of water obtained here across all six subjects of x10-3 mm 2 /s agrees well with the previous invariant trace/3 ADC estimate in healthy white matter at 3 T 102 of x10-3 mm 2 /s. The values obtained within the present work for Cr, NAA, Cho lie in the range previously reported for rat

117 103 brain 146,147, However, The estimates obtained here for mi, Gln and GSH (which reside in glial cells) and Glu (which resides in axons) are elevated compared to rat studies 146,147, suggesting a possible differences in the compartments within the respective cells, physiological differences between species, or differences in acquisition and analysis schemes. Furthermore, the effects of restricted diffusion have been completely neglected in the present work due to the minimum number of b-values chosen, as well as the relatively small maximum b-value used. Future studies may separate the fast and slow-diffusing components using more b-values and a biexponential fit, which can be used to estimate the intra-extracellular distribution of metabolites, as has previously been done in rat brains 147. Possible causes of the slightly elevated tcho ADC estimates in the present work, compared to previous reports, include residual errors from cardiac pulsatility and T 1 recovery. The effects of cardiac pulsatility were elevated by use of a somewhat large MRS voxel to improve SNR in DW-JPRESS. Although the "streak-removal" procedure was effective at suppressing pulsatility effects that remained present even in the presence of cardiac gating, close inspection of the data indicated that a small amount of pulsatility artifact still remained. In addition, cardiac gating introduced a variability in the TR interval that created small signal fluctuations related to differences in the extent of T 1 recovery for each of the resonances. The former issue can be addressed by moving to a smaller voxel (see below) or, for example, by implementing navigator-based reacquisition of corrupted data 100. The T 1 recovery effect can be addressed by increasing the diffusion-weighting, which would likely improve the ADC precision, or by increasing the TR so that small variations in TRs have less impact, at the expense of increased experiment time. It is possible that tcho was most affected by small variations in TR values because it exhibits a shorter T 1 value than Cr or tnaa 119. It is also important to mention that the present work is particularly sensitive to bulk tissue motion due to the relatively long experiment time, and the use of large diffusion sensitizing gradients to detect molecular displacements. It is likely that this sensitivity can be reduced by future technical development, for example by implementing a new version of the DW-JPRESS pulse sequence optimized for newer MRI systems with enhanced SNR and gradient amplitude. Additionally the voxel used was predominantly white matter, as it allowed for the largest voxel possible, although due to

118 104 the relatively higher concentration of metabolites in grey matter than white matter in future implementations it may be possible to increase the SNR by moving to a smaller voxel placed in grey matter. Previously reported ADC values for Glu, Gln and Glx (Glu+Gln) in parietal white matter of healthy volunteers are x10-3 mm 2 /s, x10-3 mm 2 /s and x10-3 mm 2 /s, respectively, using a DW-MRS PRESS sequence at 7.0 T 108. For comparison, the present work obtained values of x10-3 mm 2 /s, x10-3 mm 2 /s and x10-3 mm 2 /s, respectively, in good agreement. The one notable exception involved Subject 5, for which the ADC estimated for Gln was uncharacteristically low. This anomalous result was likely due to the inability of ProFit to distinguish between the two glutamatecontaining moieties. Thus, the reliability of DW-JPRESS to separate Glu from Gln reliably at 3 T remains an open question and likely depends on the available SNR as well as shim quality. Additionally, the value for Glu obtained here agrees well with a previous value of x10-3 mm 2 /s which was obtained in a monkey brain using Carbon-13 labelled glutamate 164. The 2D pipeline ADC estimate for mi was x10-3 mm 2 /s, in good agreement with previous results obtained in an anaesthetized monkey 165 ( x10-3 mm 2 /s), and in healthy volunteers using diffusion-tensor spectroscopy 145 ( x10-3 mm 2 /s). Interestingly, the ADC value for mi was among the lowest of all metabolites that were studied (along with tcho). It was also observed that the ADC of mi (which primarily resides within glial cells) was smaller than Scy, despite an equal molecular weight. This suggests that there is a potential difference in either cellular localization or compartmentalization of these molecules. This difference was close to statistically significant (P = 0.06). Although the estimate for the ADC of Scy was anomalously high for Subject 1, even when excluding this subject a difference trend was observed between the ADC estimate for Scy and mi (P = 0.08). There was a weak correlation (R 2 = 0.13) between the ADC and the square root of the molecular weight. This indicates that although some of the variation in the ADCs can be attributed to size of the molecules, most is due to various compartmentalization factors.

119 105 The remaining metabolites of interest were probed less reliably by the prototype implementation of DW-JPRESS. Only Subjects 3 and 4 had a coefficient of variation below 25 % for GABA. The T 2 of GABA is approximately 88 ms 166, similar to the initial TE value of 74 ms which ensures appreciable T 2 -weighting of the DW-JPRESS results. Furthermore, GABA has a relatively low concentration and strong overlap with larger resonances. The ADC values for Ala, Pe and Tau were not reliable in any subjects, likely for similar reasons. Future work to reduce the minimum TE value could help to alleviate this problem (using an MRI system with higher gradient strength) and allow ADCs to be estimated reliably for a larger range of biomolecules than was achieved in the present work. It would also be interesting to investigate the implementation of DW-JPRESS at 7 T where there is improved SNR and decreased overlap between resonances. In principle, identical ADC values should be estimated for Cr303 and Cr391 using the 2D pipeline. The results listed in Table 4.2 show consistently higher in vivo values for Cr391 than for Cr303, however (except for Subjects 5 and 6 where the estimate is markedly low). This effect likely arises from use of the HSVD method to remove water signal, which affects the Cr391 resonance because it is near the HSVD cut-off frequency. Conversely, the phantom experiments provided very similar ADC estimates for Cr303 and Cr391 for both pipelines because of substantially reduced linewidths in comparison to in vivo conditions, and thus reduced effect from water contaminating the Cr391 peak. A relatively large voxel size was used in this proof-of-principle work, even in the context of single voxel experiments. In general, JPRESS requires a large voxel size for accurate detection of the smaller coupled resonances, and the diffusion-weighting introduces an additional reduction in SNR of ~35%. The b-value used for the in vivo measurements was 2188 s/mm 2, whereas the b-value that minimizes the standard deviation of Equation 4.1 is approximately 80% of 1/ADC. It is therefore possible that the optimal b-value which minimizes the expected uncertainty on the ADCs is somewhat higher, which is corroborated by Ellegood et al. 167 although care must be taken due to the potential of increased weighting from the restricted

120 106 diffusion regime at higher b-values. With the gradients used here this would necessitate increasing the gradient duration,, which would increase TE values, increase the effects of eddy currents and bring the sequence further away from the q-space condition of instantaneous diffusion, resulting in artificially inflated ADCs. Improvements can likely be obtained by optimizing diffusion sensitization, choice of TR as well as the number of TE steps. Typical 1D DW-MRS has previously been optimized at 3 T, where a recommendation of 13 minutes duration was prescribed 105. A similar reproducibility study should be done to determine optimal DW-JPRESS measurement parameters to obtain reliable ADC estimates with low variability. This will be investigated in the future, and it is likely that optimized implementations of DW-JPRESS can significantly reduce the total scan time or voxel size while keeping a similar precision on the ADCs obtained here. In addition, bipolar gradient schemes 109 have been shown to reduce eddy currents 108 and their implementation should be investigated for DW-JPRESS. In principle DW-JPRESS could be combined with parallel imaging to measure the change in ADCs in two or more voxels simultaneously 138, which would be critical in reducing experiment times for future DW-MRS applications such as those that compare results between healthy and diseased tissues. However, care must be taken to avoid the possibility of introducing artefacts from a multivoxel reconstruction. 4.5 Conclusions A novel technique which combines JPRESS with DW-MRS was developed to measure the ADCs of metabolites beyond NAA, Cr and Cho at 3 T. The proposed technique was found to provide consistent estimates for the ADCs of tnaa, Cr and tcho when compared to a typical DW-MRS pipeline. Additionally the new technique provided realistic estimates for the ADCs of glutamate + glutamine, and myo-inositol in all subjects and additionally glutathione and scyllo-inositol in all but one subject. With further technical development to address the main limitation of long acquisition times, DW-JPRESS will become more practical and may provide useful information about the diffusion characteristics of metabolites beyond NAA, Cr and Cho at 3 T.

121 107 Conclusion Chapter 5 The most common in vivo MRS sequences are PRESS 4 and STEAM 5 which were developed almost 30 years ago and, in principle, remain identical to their initial inception. Despite its mature status, however, MRS continues to find new applications due to its underlying ability to non-invasively measure physiological information to supplement anatomical information from MRI. What follows is a discussion of the outcomes of the thesis, as well as recommended future work. It is evident that there remains considerable scope for further development of in vivo MRS technology. It will be interesting to see how the field of in vivo MRS evolves as the translation of in vitro techniques becomes increasingly possible, due to ongoing improvements in hardware such as increased field strength, improved high order shimming, and increased gradient amplitude and slew rate. 5.1 Summary In Chapter 1, a brief overview was presented of the necessary physics to understand the work developed in the thesis. In particular, the quantum mechanical basis for proton MRS was explained and the product operator formalism was introduced. The basics of in vivo MRS were explained including the metabolites observable in the brain, how the signal is spatially localized, as well as topics such as parallel imaging, absolute MRS and diffusion-weighted MRS, that were relevant for the work that was undertaken. In addition, the present status of MRS as applied to brain cancer and brain cancer treatment was also discussed. Within Chapter 2 a study was presented which extended SVS to include multiple voxels through amplitude modulation of the excitation RF pulses and use of localized multi-channel coil sensitivity to reconstruct the individual voxels. By this approach, referred to as constrained source space MRS (CSSMRS), it was shown that high quality data from two voxels, with relatively few artefacts and very little bleed from one voxel to another. In addition, the increase in noise due to the geometry of the head coil was investigated as a function of

122 108 distance between the two voxels, which was necessary to determine whether there is a time benefit in using CSSMRS. Based on the positive results of this experiment, the CSSMRS technique was applied to a cohort of brain cancer patients. This was undertaken because SVS is often used in that particular clinical setting to differentiate between neoplastic and nonneoplastic lesions, typically with additional data acquisition from a contralateral brain region as a control. Positive results were again obtained and it was concluded that CSSMRS could potentially halve the duration of clinical MRS protocols where spectra are measured from both lesion and control locations. Within Chapter 3 a novel pulse sequence was developed which was a hybrid of fast IR and saturation recovery used it to estimate the longitudinal relaxation time of lactate, filling a gap in the in vivo MRS literature. The sequence was similar to a standard IR experiment except that the inversion pulse was interleaved on and off successively, and the total repetition time (TR) was linked to the inversion time (TI). By making these two changes: 1) the difference signal at each TI value followed a monoexponential function of T 1, enabling simple fitting procedures to estimate the relaxation time; and 2) the consistent need for long TR values (as required in standard IR) was removed, providing increased time efficiency. The predicted uncertainty on the estimated T 1 of lactate was then numerically minimized by finding the optimal TI and TR pairs to use within fixed measurement time. Spectral editing pulses were used to separate lactate from the contaminating lipid signals and the first lipid-free estimates of lactate T 1 were thus reported in vivo. From specific validation experiments in phantoms, the technique was found to provide approximately 25 % improvement in measurement precision over standard IR. The mean lactate T 1 value was subsequently determined to be ( of 6 patients with high grade glioma. ) ms over a group In Chapter 4 a novel technique was developed which combines a diffusion-weighting module with the 2D JPRESS technique. Typical DW-MRS experiments at 3 Tesla only investigate the diffusion of NAA, choline and creatine due to their relative ease of measurement. JPRESS, however, allows for resolving smaller J-coupled resonances because of the introduction of a second spectral dimension. By combining these two techniques a more accurate measurement of the diffusion characteristics of glutamate + glutamine, myo-inositol, glutathione and scyllo-

123 109 inositol was obtained. Good agreement was observed between the two techniques estimates for the typical metabolites diffusion characteristics, namely NAA, creatine and choline in both phantom and healthy volunteer experiments. Optimization of this technique may allow for the estimation of additional metabolites beyond those mentioned above. From these collective research milestones, multiple avenues of future research are possible. Several examples are provided in the following sections. 5.2 Future Directions for CSSMRS The CSSMRS work developed in this thesis focused exclusively on acquired spectral information from two voxels simultaneously, as it was the simplest extension of SVS. However, extension to a larger number of voxels is desirable in certain applications, such as when multiple disease foci are present (eg. brain metastases). There are two main issues to address when extending CSSMRS beyond two voxels: 1) how to perform appropriate spatial localization; and 2) whether advantages are maintained due to the increase in noise from the condition number of the reconstruction matrix. Considering the first issue, the simple localization scheme presented in Chapter 2 does not enable additional voxels to be positioned arbitrarily. One alternative is to make a small pulse sequence modification to cosine modulate one of the refocusing RF pulses, which then enables four voxels to be localized. Three of these four voxels can then be arbitrarily positioned (subject to the condition that the three voxels cannot lie along a single line), although the position of the fourth voxel becomes very constrained. This was implemented in preliminary experiments, as shown in Figure 5.1. This approach could also be extended further by modulating both of the refocusing pulses, which would allow four out of a total of eight voxels to be arbitrarily localized (subject to the condition that the four voxels cannot lie in one plane). In principle this implementation is straightforward, but the cosine modulation has the effect of reducing the bandwidth of the pulses by a factor of two (assuming the refocusing pulses are played out at the physical maximum allowed B 1 amplitude). The bandwidth

124 110 Figure 5.1: Four voxel profile overlaid on an anatomical axial MR image. Three of the four voxels were positioned and the fourth voxel was localized based on an algorithm that made the voxels as square as possible. reduction results in greater chemical shift displacement and, for J-coupled chemical species, a reduction in the measured signal amplitude due to partial cancellation at the borders of the voxel. A more robust solution is the arbitrary excitation of multiple voxels through the excitation k-space approach 72. Mapping out excitation k-space is typically quite slow, however, so it is likely that a parallel excitation approach utilizing an array of transmit coils 168 such as Transmit SENSE 169 (also known as parallel RF transmission ) is needed to reduce the duration of the excitation pulse. Considering now the second issue, acquiring more voxels with CSSMRS while using the same multi-channel receiver coil is expected to increase the g-factor, and because CSSMRS is only beneficial when the g-factor is less than the square root of the number of voxels, future multi-voxel implementations will need to investigate the g-factor dependence in detail. The g- factor increase relates to the increase in the condition number of the matrix ( ) in