Diffusion-Weighted Magnetic Resonance Spectroscopy

Transcription

1 Diffusion-Weighted Magnetic Resonance Spectroscopy Itamar Ronen 1 & Julien Valette 2 1 Leiden University Medical Center, Leiden, The Netherlands 2 Molecular Imaging Research Center, Commissariat àl énergie atomique, Fontenay-aux-Roses, France Diffusion-weighted magnetic resonance spectroscopy (DW-MRS) is a unique tool for the noninvasive exploration of the structure and physiology of the intracellular space in vivo. The method combines sensitization to diffusion using magnetic field gradients with a variety of localized MRS sequences, and thus provides the means to measure and quantify the diffusion properties of intracellular metabolites in various tissues, most commonly in the brain and in skeletal muscle. As several metabolites are preferentially found in different cell types, an investigation of the intracellular space using DW-MRS also provides cell-specific information. Information obtained from DW-MRS experiments is relevant to the assessment of the fundamental properties of the intracellular space, contributes to the understanding of diffusion-weighted MR imaging (DWI), and provides valuable information for the characterization of different pathological mechanisms in several diseases. DW-MRS measurements are extremely challenging, both from the acquisition perspective as well as from the analysis and quantification standpoint. In this article, we will present the background and motivation for performing DW-MRS studies, the various methods that have been developed thus far for the robust acquisition and analysis of DW-MRS data, and survey the variety of applications in which DW-MRS has been used to date. Keywords: diffusion, metabolites, intracellular space, tissue microstructure, brain, skeletal muscle, 1 H magnetic resonance spectroscopy, 31 P magnetic resonance spectroscopy How to cite this article: emagres, 215, Vol 4: DOI 1.12/ emrstm1471 Introduction The effect of diffusion on the relaxation properties of the NMR signal has been known since the early days of NMR. 1 3 It was, however, with the introduction of the Stejskal Tanner technique, 4 which uses magnetic field gradient (MFG) pulses to sensitize the NMR signal to diffusion, that diffusion measurements became a frequently used NMR tool to probe nuclear spin mobility in a variety of environments. In this scheme, the sensitization to diffusion in a given direction, i, is achieved through a pair of MFG pulses applied in that direction. The combination of these gradients and the RF pulses in the sequence generates a dephasing and a subsequent rephasing of the transverse magnetization, M XY, so that the loss in M XY at the end of the sequence reflects the overall loss of coherent phase owing to the movement of the spins in a strongly inhomogeneous magnetic field. In the case of nonrestricted or Gaussian diffusion, the effect of the diffusion-weighted (DW) MFG is an exponential attenuation of the signal S: S(b i ) = S()e b id i (1) where i denotes the direction in which the gradient is applied, D i is the diffusion coefficient of the observed spins in that direction, and b i,ortheb-factor in the i-direction, is a combined factor linked to the exact application of the gradients during the Stejskal Tanner sequence. Upon implementation in a spin-echo sequence, it can be analytically shown that ( b = γ 2 g 2 δ 2 Δ δ ) (2) 3 where γ is the gyromagnetic ratio of the observed nucleus, g the gradient amplitude, δ the gradient duration, and Δ the time between the onset of the dephasing and the rephrasing gradients. Initially, experiments were mostly applied to physical investigations in, for example, porous media, but diffusion measurements in biological tissues soon followed, generally focusing on the most abundant NMR-visible molecule in tissue, i.e., water. As the diffusion of water in tissue reflects the microstructural environment in which the water diffuses, the utility of such measurements for the characterization of the tissue microstructure is immense, as exemplified by the incredibly large number of applications of diffusion measurements in humans, animals, and plants. When diffusion occurs in a complex medium, e.g., in living tissue, where the mobility of the observed particles is obstructed and hindered by structural features such as cell membranes and intracellular organelles, it deviates from the simple Gaussian model and the attenuation of the NMR signal is no longer monoexponentially dependent on b. Yet, in most applications, the DW signal, typically performed in more than one diffusion-weighting gradient direction, is treated according to equation (1) which remains essentially valid for low b values, and a phenomenological diffusion coefficient, or an apparent diffusion coefficient (ADC), is used to describe the average Volume 4, John Wiley & Sons, Ltd. 733

2 IRonen&JValette diffusion rate in the direction of the gradient. In the simplest case, where one b value is used for diffusion-weighting and is applied in n different directions, the ADC can be estimated from the diffusion measurements as follows: i ( ) S(bi ) ln S() b i ADC = (3) n where the index i runs over all n diffusion-weighting directions. ADC measurements are particularly common in conjunction with diffusion-weighted magnetic resonance imaging (DW- MRI). Since its inception and its first applications on clinical MRI scanners, 5 DW-MRI has become an extremely successful technique, playing a central role in both clinical and basic investigations of tissue microstructure. 6 In this article, we present in vivo diffusion measurements of spin species other than water protons, and, in particular, those of small metabolites. We will provide a background for the motivation to measure diffusion properties of metabolites in the brain and in muscle with DW magnetic resonance spectroscopy (DW-MRS) and expand on the methods used to perform these measurements and their current applications in fundamental and clinical research. These metabolites are typically present in the body in concentrations in the millimolar range, i.e., about four orders of magnitude less concentrated than water. This dictates a necessarily lower detection sensitivity than that of DW-MRI, and an extreme sensitivity to errors and artifacts, and thus, the accurate measurement and quantification of the diffusion of metabolites poses a significant challenge. It is hoped that this article will convince the reader that these challenging measurements provide unique, highly specific information and that they are extremely useful for investigating the fundamental properties of tissue, as well as contributing to the understanding of pathological mechanisms in a variety of diseases in which DWI provides only partial or confounded information. Diffusion of Metabolites: Specific Probes of the Intracellular Space Water molecules are ubiquitous, being present in all cellular compartments, as well as in the extracellular space. In addition, cell membranes are relatively permeable to water molecules at the timescale of typical diffusion measurements, so that water molecules cannot be assigned a well-defined compartment. This complicates any attempt to interpret the mechanisms underlying DW-MRI measurements. In contrast, most metabolites detected by MRS are almost exclusively intracellular. Even neurotransmitters, such as the excitatory neurotransmitter glutamate, have an overall extremely low concentration in the extracellular space, even with the transient local increase in extracellular glutamate that occurs in the synaptic cleft during glutamatergic neuronal activity. The few known exceptions are substrates of energy metabolism, such as glucose, lactate, and acetate. In addition, biological membranes are typically 1 3 times more impermeable to metabolites than to water; thus, metabolites tend to remain in a well-defined cellular compartment. Finally, in the particular case of the brain and the central nervous system, it is commonly accepted that metabolites are not equally concentrated in all cell types (for review see Ref. 7). Within the brain, N-acetyl-aspartate (NAA) and glutamate (Glu) are generally considered to be almost exclusively neuronal, while myo-inositol (Ins) and, probably, to a lesser degree, choline compounds (tcho = phosphocholine PC + glycerophosphocholine GPC) are believed to be preferentially localized in glial cells. Total creatine (tcr = creatine Cr + phosphocreatine PCr) is thought to exhibit no preferential compartmentalization. The main motivation to study metabolite diffusion by DW- MRS is, therefore, the possibility of monitoring a large set of molecular probes traveling in the intracellular space in a celltype-specific manner. All phenomena related to the extracellular space, such as potential flow of the cerebrospinal fluid (CSF), extracellular volume fraction, diffusivity, and tortuosity in the extracellular space, while contributing to water diffusion, can be neglected when interpreting and modeling such metabolite diffusion. Intracellular Phenomena Affecting Metabolite Diffusion The diffusion process describes a thermally driven random displacement of molecules, resulting in a displacement variance that increases linearly with an observation time, denoted by the diffusion time t d, i.e.: (r r ) 2 =6D free t d (4) In the above equation, triangular brackets denote the ensemble average, and r and r are the initial (at t = ) and final (after t d ) positions of the molecules, while D free is the free diffusion coefficient. This random displacement lies at the origin of the NMR signal attenuation, as measured by DW-MRS; therefore, any phenomenon affecting this average displacement may influence measurement outcomes and derived quantities, such as the ADC. Free Translational Diffusion in the Cytosol (Including Molecular Crowding). Generally speaking, the free translational diffusion coefficient, D free, of a molecular species in an aqueous solution such as the cytosol depends on a driving term, k B T,wherek B is the Boltzmann constant and T the absolute temperature of the solution; and on a drag term, f, in opposition to the motion, as expressed in the Stokes Einstein equation: D free = k B T f In the simplest case of a chemically inert molecule in a dilute solution, the drag term is simply proportional to the hydrodynamic radius, R H, of the molecule and the viscosity, η, of the solution: f = 6πηR H (6) Molecular Crowding. Molecular crowding refers to a situation where the solution contains a high concentration of additional (5) John Wiley & Sons, Ltd. Volume 4, 215

3 Diffusion-Weighted Magnetic Resonance Spectroscopy molecules, including, e.g., metabolites or macromolecules that cannot be neglected when compared to the solvent concentration. These other cytosolic molecules occupy a volume fraction, φ, of the cytosol, and the drag term accordingly modifies to: f = 6π( φ)ηR H (7) Equation (7) implies that viscosity cannot be distinguished from molecular crowding when considering translational diffusion. Tortuosity. Numerous obstacles exist within the intracellular space, such as the cytoskeleton and various organelles, which may potentially result in the cytosol becoming a tortuous space. More precisely, the tortuosity, T, refers to the effect of hindrances imposed by various obstacles in the medium on the path that diffusing molecules can take. Such hindrances affect the minimal pathway between two points so that, rather than a straight line, the pathway becomes tortuous. In this case, the shortest pathway between two points is increased, on average, by a factor T ( 1), compared to a straight line connecting these points. At very short diffusion times, during which the displacement variance is very small compared to the square of the typical distance between obstacles, tortuosity will not affect molecular displacement, and the diffusion process will appear free. At longer diffusion times, one has: (r r ) 2 6 D free T 2 t d (8) Equivalently, the ADC measured at long t d converges to: ADC D free T 2 (9) Restriction. The confinement of metabolites within a given compartment, such as within organelles or even inside the whole intracellular space, will also impose an upper limit to the displacement variance. While this restriction effect is again negligible at very short t d, as the displacement variance is very small compared to the square of the typical distance between diffusion barriers, at long t d, the restriction effect will strongly influence the diffusion process. For example, in a situation of perfect restriction, i.e., without a possible escape for diffusing molecules, the ADC will converge to with increasing t d. Active Transport. Active transport mechanisms are also present in the intracellular space and are essential for the mobilization of large objects such as organelles and large proteins, for which diffusion is a very inefficient transport mechanism. Many active transport mechanisms are based on motor proteins conveying their cargoes (often vesicles) on microtubules. Convection of the cytosol, also known as cytoplasmic streaming or cyclosis (which is occasioned by gel sol transitions of actin, actin flow, myosin contraction, or syneresis), is well established in plants and amoeboids, and has been occasionally reported in mammalian cells (e.g., cancer cells 8 and oocytes 9 ). Agutter and Wheatley have even argued that cytoplasmic streaming is a fundamental characteristic of life, and is the dominant mechanism by which metabolites and proteins are transported inside all cells, 1,11 although there is little experimental evidence supporting this hypothesis. While the highest reported speed for cytoplasmic streaming is 7 μm s 1 in characean algal cells, it is, in general, one order of magnitude slower in higher plants, 12 and most certainly less than.1 μm s 1 (when existing) in animals, 9 although quantitative measurements for the latter case are rare. Hence, in animals at least, the distance traveled by molecules under the effect of cytoplasmic streaming is presumably negligible compared to the distance traveled by diffusion at the timescales of the measurement. Thus, active transport does not appear to significantly contribute to DW-MRS signal attenuation. Moreover, as the characteristic distance traveled under the effect of diffusion scales only as the square root of t d, it is expected that as t d becomes shorter, the effect of active transport would become negligible compared to diffusion. Chemical Reactions. Metabolites are not inert molecules, but are engaged in a wide range of chemical reactions, from interactions with other small molecules to binding to membranes or macromolecules. If these reactions significantly affect the physical properties of metabolites during t d, they can potentially affect DW-MRS measurements, e.g., by modifying the drag term, f, in equation (5) in the case where chemical interactions are fast compared to t 13 d. In the more general case of arbitrary exchange rates between two pools both characterized by Gaussian diffusion, evolution of the magnetization is described by the Kärger model 14 and signal decay is no longer monoexponential. This model has been refined to account for exchange between restricted pools. 15,16 Although it is difficult to foresee the actual impact of such reactions on DW-MRS in vivo, it is possible to compare some typical reaction rates to typical values of t d. Many major metabolic fluxes, such as the TCA cycle rate, or the intercellular glutamate glutamine flux, are less than 1 μmol g 1 min 1, as measured by 13 C MRS, 17 or.1 μmol g 1 s 1, while typical metabolite concentrations are in the range of 1 1 μmol g 1. Taken together, this corresponds to reaction rates of.1.1 s 1. This means that only a minor fraction (.1 1%) of each metabolic pool is transformed during 1 s, which is longer than t d in most DW-MRS experiments. The impact of metabolic reactions is thus expected to be very minor in most situations. One possible exception is the Cr/PCr couple, which is exchanged through creatine kinase (CK) activity at a rate of.2.4 s 1 in the muscle or in the brain, as measured by 31 P MRS. 18 In 31 P DW-MRS, diffusion of adenosine triphosphate (ATP) is also certainly affected by the high reaction rates of the CK and ATPase reactions, as well as by binding with macromolecules. Finally, it is worth mentioning the very fast exchange of amine and amide protons between water and metabolites, such as glutamate and glutamine (with reaction rates up to 2 s 1 ), 19 which may impact the diffusion attenuation of some of the upfield metabolite resonances, although these resonances are usually not quantified in DW- MRS, because their signal becomes very weak when water suppression is applied, owing to the rapid exchange. Volume 4, John Wiley & Sons, Ltd. 735

4 IRonen&JValette Methods for Measuring Metabolite Diffusion Introduction From the acquisition standpoint, the addition of a diffusionweighting pulse sequence module based on the classic Stejskal Tanner diffusion-weighting scheme 4 is straightforward, both in the case of nonlocalized MRS sequences and in the case where spatial localization is required. As will be explained, the flexibility in choosing a pulse sequence for the DW-MRS experiment, as well as in the choice of diffusionweighting parameters, allows for a large variety of experiments from which metabolite diffusion information can be drawn. The challenges associated with the acquisition of robust and reproducible DW-MRS data and their subsequent processing and quantification stem not from the implementation of diffusion-weighting in spectroscopic sequences, but rather from the extreme sensitivity of the DW metabolite signal to a variety of factors, which must be taken into consideration in the acquisition stage as well as in the preprocessing and the analysis stages. This section begins with an introduction to the experimental strategies for the acquisition of localized DW-MRS data: pulse sequences, diffusion-weighting strategies, and tailoring the DW-MRS experiment to fit the desired information and the experimental circumstances. The unique challenges in both single-volume localization and in spatially encoded (MRSI) experiments will be emphasized. The main sources of artifacts that contribute to bias or to increased variance in metabolite diffusion properties will be discussed, as well as the efforts to minimize their effect on the acquired data. Subsequently, factors that affect the quantification of DW-MRS spectra will be discussed, and strategies for accurate quantification will be suggested. Single-Volume Diffusion-Weighted MRS: The Sequences Spatial localization or volume selectivity in MRS is primarily achieved via the combined use of RF pulses and MFGs for subsequent selection of intersecting planes. The most commonly used techniques are (a) point-resolved spectroscopy or PRESS, 2 stimulated echo acquisition mode (STEAM), 21 and localization by adiabatic selective refocusing (LASER) 22 and its variants. Other techniques, based on outer volume suppression, will not be discussed here. All the sequences mentioned above can be easily transformed into DW-MRS sequences via the addition of single or multiple diffusion-weighting modules. Point-Resolved Spectroscopy (PRESS). PRESS is a three-pulse sequence that generates a T 2 -weighted localized echo. 2 The selectivity is achieved through gradients applied simultaneously with the RF pulses in three orthogonal directions. Spurious transverse magnetization generated by imperfect 18 pulses is typically suppressed by the use of strong crusher gradients positioned symmetrically around these pulses. Figure 1 shows a variety of possible implementations of the Stejskal Tanner method in combination with the PRESS sequence. In the figure (top),theechotimete= 2(τ 1 + τ 2 ). The flexibility in choosing the position of the diffusion-weighting gradients allows coping RF g (a) (b) (c) π/2 π π τ 1 τ 1 τ 2 τ Echo 2 δ δ δ/2 Δ Δ Δ Figure 1. Possible methods for the incorporation of diffusion-weighting schemes in the PRESS sequence with different scenarios and optimizing the sequence for the desired information. For example, option a of Figure 1 allows for relatively short diffusion times, and the delay between the MFG pulses and the acquired echo acts to diminish the effect of eddy currents generated by the MFG pulses. Option b allows for longer diffusion times of the order of the sequence TE, and, if the condition δ Δ (the short gradient pulse condition) is obeyed, then data for the generation of the displacement distribution functions of intracellular metabolites can be collected and a quantitative q-space analysis of metabolite diffusion data is possible. 23 If adherence to the short gradient pulse condition is not a priority, then a full bipolar sequence (option c) offers a robust diffusion-weighting scheme with a wide range of advantages. The application of bipolar gradients throughout the sequence minimizes the resulting eddy currents, 24 which significantly corrupt the resulting DW spectra, especially at high b values. Moreover, the interaction or cross-terms, between the diffusion gradients and the background gradients, which reflect the inhomogeneity of B on various spatial scales, is minimized. 25 The bipolar scheme also allows the diffusion gradients to occupy most of the available TE, thus maximizing the b value for a given TE. This last point is particularly important on clinical scanners, where the maximum available gradient strength is much lower than in high-resolution or small-bore, preclinical scanners. The maximum diffusion time in the fully bipolar case is TE/2. An interesting variant of a fully bipolar diffusion-weighting scheme that enables a single-shot isotropic diffusion-weighting was suggested by De Graaf et al. 26 In this variant, the diffusion time is much shorter. When using the PRESS sequence for DW-MRS, a number of disadvantages must be considered, some linked directly to diffusion measurements. First is the large chemical shift displacement in the localization of the various metabolites, engendered by the relatively low bandwidth achievable by the 18 selective pulses owing to the available RF power or specific absorption rate (SAR) limits (a problem more prominent in human experiments). This means that significant errors in the τ John Wiley & Sons, Ltd. Volume 4, 215

5 Diffusion-Weighted Magnetic Resonance Spectroscopy π/2 π/2 π/2 π/2 π π/2 π/2 Echo π Echo RF RF TE/2 Tm TE/2 TE/2 Tm TE/2 g g (a) (b) Figure 2. Possible methods for the incorporation of diffusion-weighting schemes in the STEAM sequence. (a) Standard STEAM; (b) 13-delay STEAM diffusion properties of metabolites being measured along, say, a specific white-matter tract, could result from the displacement of the VOI of those metabolites whose peaks are farther away from the pulse s carrier frequency. Second, the T 2 dependence of the PRESS signal at time TE limits the maximum diffusion time that can be used without a significant penalty in SNR. The T 2 of brain metabolites, especially the strong singlet peaks of NAA, tcr, and tcho, tend to be longer than those of water, 27 but the initial low SNR of the metabolite signal, coupled with the error propagation in the calculation of properties such as ADC and diffusion tensor imaging (DTI) quantities, necessitates a careful consideration of SNR. 28 The Diffusion-Weighted STEAM Sequence. Figure 2 shows the incorporation of diffusion-weighting schemes into the STEAM sequence. The versions shown here select the positive echo, whereas inversion of the polarity of the refocusing gradient group (dark gray) will select the anti-echo, where static B inhomogeneity and chemical shift are not refocused. 29 The simpler version in (a) is easy to implement, but suffers from strong cross-terms between the DW-MFGs and background gradients. 25 The sequence on the right, the so-called 13-delay STEAM sequence, is much more immune to interactions or cross-terms, with the background gradients, and is more benign with respect to eddy currents, owing to the fully bipolar scheme employed here. Additional variations can further improve the insensitivity to spatially varying background gradients. 3 The additional 18 pulses increase the SAR of the sequence, thus limiting, e.g., the shortest repetition period, TR, that can be used in human scanners. In addition, these pulses may generate spurious echoes that corrupt the principal echo. The main advantage of the STEAM sequence, with respect to spectroscopic diffusion measurements, is the greater flexibility in choosing a diffusion time without much of a penalty in SNR. The diffusion time can be built around the STEAM mixing time, during which the magnetization is stored on the Z-axis and thus relaxes according to T 1, which is much longer than T 2 in most cases. A typical example is 31 P-DW-MRS in muscle. In this case, the T 2 of several of the metabolites is relatively short (in particular, the γ, α, andβ-ntp (nucleoside triphosphate) phosphorus signals, with, e.g., T 2 < 1 ms at 3 T), 31 while the T 1 is well over 3 s. The relatively large bandwidth of the 9 pulses in the sequence mitigates the chemical shift displacement, and the two additional 18 pulses in the 13- delay sequence can be applied without spatial selectivity, thus not adding additional shift. The most significant drawback with the use of STEAM is the loss of 5% of the signal owing to the collection of a single coherence pathway. In standard MRS, this drawback is typically compensated by the possibility of achieving an extremely short TE. In DW-MRS, a longer echo time is needed to accommodate the diffusion-weighting gradients, which typically results in lower SNR for the STEAM DW-MRS compared to PRESS DW-MRS at the lower range of diffusion times. As mentioned before, at longer diffusion times, the possibility of storing the magnetization along the z-axis makes STEAM the sequence of choice compared with the spin-echo-based sequences. Diffusion-Weighted LASER and slaser: Diffusion-Weighting in the Presence of Adiabatic RF Pulses. In a situation where the B 1 field is highly inhomogeneous, e.g., when RF surface coils are used, or in situations where the RF wavelength is short with respect to the observed body part or object, adiabatic RF pulses become highly advantageous. 22 Their inclusion in localized in vivo MRS has been realized mostly through the fully adiabatic LASER 22 and partially adiabatic slaser 32 sequences, which can be transformed into DW sequences. One sequence, shown in Figure 3, provides a single-shot isotropic diffusion-weighting, as well as an efficient nulling of the crossterms with background and other imaging gradients, 33 while another incorporates oscillating diffusion-weighting gradients for ultrashort diffusion times. 34 Diffusion-Weighted Magnetic Resonance Spectroscopic Imaging (DW-MRSI). The extension of the concept of DW-MRS to spatially encoded methods seems rather straightforward, and soon after single-volume DW-MRS was introduced, the first attempts at DW-MRSI were performed on phantoms. 35 The impetus to devise a robust DW-MRSI sequence for in vivo research is understandably strong: for example, combining high-resolution water diffusion data from DTI experiments with spatially encoded DW information on metabolites in the brain can provide invaluable information about the link between water diffusion properties, such as fractional anisotropy and ADC, and the cellular composition of tissue within a voxel. In disease, the potential for co-visualization and analysis of water-based data and metabolite diffusion maps can help disentangle various pathological mechanisms that affect water diffusion and relaxation properties in a nonspecific manner, but which differentially affect the diffusion properties of different metabolites. However, very few implementations of in vivo DW-MRSI have been published as yet. The main reasons for this will be discussed in detail in the next section, where Volume 4, John Wiley & Sons, Ltd. 737

6 IRonen&JValette 9 18 RF G X G Y G Z (a) RF G X G Y G Z (b) Figure 3. (a) An isotropic, fully adiabatic DW-MRS sequence, based on the LASER sequence. Gray: slice selection gradients; black: crusher gradients; white: diffusion-weighting gradients (Reproduced with permission from Ref. 33. John Wiley & Sons, Ltd., 212); (b) LASER-based DW-MRS sequence with oscillating diffusion-weighting gradients. (Reproduced with permission from Ref. 34. Nature Publishing Group, 212) the various sources of artifacts in DW-MRS are introduced. Volume preselection using PRESS, STEAM, or slaser before spatial encoding enables the use of the same diffusion-weighting schemes as shown previously. The spatial encoding that follows can be done using the standard MRSI method employing multiple phase-encoding gradient steps, 36 or with the echo-planar spectroscopic imaging (EPSI) method. 37 Artifacts in DW-MRS and Possible Countermeasures Accurate quantification of in vivo MRS data poses considerable challenges. To begin with, the typical signal-to-noise ratio (SNR) for spectra acquired in realistic conditions, especially in humans, is relatively low. Data typically result from time averaging of several acquisitions, introducing time-dependent error sources, such as frequency and phase drifts and fluctuations. Each individual spectrum consists of multiple metabolite peaks and the overlap among them in the in vivo spectrum complicates the quantification of each individual contribution. In addition, macromolecular (MM) structures in tissue contribute broad resonances to the baseline of in vivo spectra, thus adding a potential bias to the metabolite estimation. All of these factors are present and significantly exacerbated in DW-MRS, in which the spectra are further corrupted by the adverse effects of the strong diffusion-weighting gradients. To add to this, the end goal of DW-MRS is the evaluation of the diffusion properties (e.g., ADC) of metabolites. These quantities are calculated from several measurements at different diffusion-weighting conditions, and error propagation during their calculation can significantly amplify the effect of error sources present in the actual measurements. In this section, some of these error sources and their effect on the estimation of metabolite diffusion properties will be discussed, and some potential solutions and guidelines for error minimization will be proposed. Phase and Amplitude Fluctuations Acquisition in Physiological Conditions. The DW-MFG pulses sensitize the NMR signal to the displacement of spins. Hence, any type of bulk motion affects the signal as well. Simple translation, owing to, e.g., a small amount of linear motion during the diffusion time, will result in an added phase to the measured signal. In DW imaging, data acquisition is typically performed in the singleshot, echo-planar imaging (SE-EPI) mode and magnitude data are collected, so this phase shift is of relatively minor consequence. In DW-MRS, where several data acquisitions are performed for each DW condition and then averaged, phase variations during the experiment will result in signal loss upon averaging, and thus in overestimation of the metabolite ADC values. It is thus crucial to individually phase-correct spectra before averaging. Panels (a) and (b) in Figure 4 exemplify the phase variability of the NAA peak, and the effect of individual phase correction based on the residual water peak in each spectrum. Phase correction is preferably performed in the frequency domain following Fourier transformation of each free induction decay (FID). It is important that the spectra have at least one peak with sufficient SNR, and it is recommended that the integral (or at least several points) of the reference peak be used for the phase correction procedure. 39 Amplitude fluctuations are far more insidious than phase variations, and they can be caused by any non-purely translational motion that occurs during the diffusion time. For example, even a small rotation, by a fraction of a degree, can cause a significant reduction in signal. 4 Another significant source of amplitude fluctuation is compressive motion due to cardiac and CSF pulsation. The latter can be significantly John Wiley & Sons, Ltd. Volume 4, 215

7 Diffusion-Weighted Magnetic Resonance Spectroscopy Intensity (a) Intensity (b) (c) (d) Figure 4. Physiological effects on in vivo DW-MRS spectra. Data were acquired from a 5 cc voxel of interest (VOI) on the anterior body of the human corpus callosum at 3 T. (a) Enlarged portion of a DW-MRS data set, showing 64 spectra zoomed on the NAA peak at 2 ppm. Data are shown before phasing of the individual spectra; (b) same spectra, after individual phasing using the residual water peak. (c) The water peak in the eight reference spectra (no water suppression) acquired for the same experiment. Individual phasing has been performed, and the data were acquired without cardiac triggering; (d) reference spectra acquired under the same conditions as in (c), with cardiac triggering obtained using the pulse peripheral unit (PPU) and a trigger delay of 3 ms. (Reproduced with permission from Ref. 38. John Wiley & Sons, Ltd., 27.) mitigated by synchronizing the acquisition to the cardiac cycle with the use of a pulse peripheral unit or an ECG (electrocardiograph) device. With an appropriate choice of trigger delay, the amplitude fluctuations can be mostly controlled (see panels c and d of Figure 4). In order to further remove the detrimental effect of amplitude fluctuations, individual FIDs that fall below a certain threshold can be retrospectively removed, given enough redundancy in the number of acquisitions. Eddy Currents and Their Correction. The detrimental effect of gradient-induced eddy currents on the line shape of MRS peaks is not exclusive to DW-MRS, but the application of strong diffusion gradients significantly increases the magnitude of their effect on the resulting spectra. Sequences that employ bipolar diffusion-weighting schemes, such as the 13-delay STEAM and the bipolar DW-PRESS, have better eddy current profiles than single-polarity diffusion schemes, 24 but data acquired with these sequences still require careful eddy-current correction (ECC). Simple ECC assumes that the phase at each sampling pointofthefidatatimetis the sum of the native phase of the FID and an additional phase term caused by the eddy currents: ϕ(t) = ϕ FID (t) + ϕ EC (t) (1) The correction typically entails a separate acquisition under the same diffusion-weighting condition of an FID of the water signal from the same voxel of interest, VOI (i.e., the FID with the same diffusion-weighting, performed without water suppression). Assuming a single resonance, ϕ EC (t), is estimated from the water measurement, and the ECC is achieved by removing the eddy-current (EC) phase from the original FID: FID ECC (t) = FID(t)/e iϕ EC(t) (11) An example of the effects of eddy currents induced by diffusion gradients on the spectrum, and the same spectrum after ECC using water data from the same volume, is shown in Figure 5. Alternatively, if there is a strong peak present in the spectrum (e.g., the residual water peak), it is possible to filter the time-domain signal of that peak, e.g., using a linear-prediction singular value decomposition (LPSVD) algorithm, 41 to derive ϕ EC (t). Eddy currents typically have a strong spatiotemporal dependence, and thus, in the case of strong chemical shift displacement among metabolites, the procedure can have varying efficacy on different metabolite peaks in a VOI. In addition, the higher ADC of water compared with the typical ADC of metabolites (about fivefold) may result in low SNR for the water FIDs at very high b values.thisinturnwillresultina noisy ϕ EC (t), and an additional loss of signal in the DW spectrum following ECC. A synthetic ϕ EC (t) obtained by applying an LPSVD procedure to the water FID can mitigate this effect. Volume 4, John Wiley & Sons, Ltd. 739

8 IRonen&JValette 2 25 tcho tnaa 15 2 tcr S (a.u.) 1 5 S (a.u.) 15 1 tcr 5 5 (a) Frequency (ppm) (b) Frequency (ppm) Figure 5. The effect of eddy currents generated by the diffusion-weighting gradients. Data were acquired at 7 T from a 9 cc VOI in parietal white matter. The sequence used was PRESS with bipolar diffusion gradients and b 32 s mm 2. (a) The spectrum before eddy-current correction; (b) same spectrum after correction. tnaa, total NAA = NAA + NAAG; tcr, total creatine = Cr + PCr; tcho, total choline compounds = Cho + PCho + GPC Biases due to Macromolecular Resonances. A potentially significant source of bias in the measurement of metabolite diffusion is the presence of broad peaks in the spectrum, assigned to resonances with very short T 2 that originate from MM structures (e.g., proteins, cell membranes) present in tissue. The typical diffusion coefficient of MMs has been estimated to be about.6 μm 2 ms 1, 42 and thus, the contribution of this diffusion coefficient to the DW spectrum remains roughly the same at typical b values used for DW-MRS (e.g., 1% attenuation at b = 2 s mm 2 ). Thus, if MMs are not accounted for in the spectral analysis, the resulting metabolite ADC will be underestimated. This bias is particularly strong in preclinical measurements, where the strong gradients allow for relatively short echo times, resulting in a significant MM contribution to the spectrum. Figure 6 shows the proper inclusion of an experimentally measured MM spectrum (black line) and an LCModel built-in estimation of the contribution of MMs to the spectral analysis of a DW-MRS data set at b = smm 2 (left) and at b = 3 s mm 2 (right). As the built-in MM spectrum in the LCModel software consists of a group of independent broad contributions, the inclusion of an experimentally derived MM spectrum is advantageous, because the ratio between the various MM resonances is not expected to change among different diffusion-weighting conditions, and the excessive freedom in fitting the built-in MM contributions may otherwise generate an additional bias or variability. Accuracy in b Value and the Effect of Cross-Terms with Background Gradients. Diffusion measurements with NMR must take into consideration the effect of all MFGs operating on the spins in the observed region during the pulse sequence, including the diffusion-weighting gradients, G diff,andallother gradients, G other. The latter are either generated by the pulse sequence, e.g., by slice selection gradients and crushers, or by inhomogeneity in the static magnetic field B as a result of, e.g., magnetic susceptibility effects and/or suboptimal shimming. The estimation of the actual diffusion-weighting in a DW sequence is given by: T seq b act. = γ 2 dt t 2 ( ( G diff t ) + G other (t )) dt (12) where γ is the gyromagnetic ratio and T seq thetimebetween excitation and the beginning of the acquisition. 25 Equation (12) gives rise to three types of integral terms involving (i) G 2 diff (t ), which yields the desired b value that results from the applied diffusion-weighting; (ii) G 2 other (t ), which accounts for the constant contribution of the background and sequence gradients present at any diffusion-weighting; and (iii) G diff (t ) G other, which are the cross-terms between the diffusion and the other gradients. The cross-terms are nonvanishing and lead to a significant error in the estimation of the ADC if not properly accounted for. One method of eliminating the effect of the cross-terms is to perform two sets of measurements in each DW direction, one with the positive polarity gradients, G + diff, and one with negative polarity gradients, G diff. The geometric average of the resulting measurements, S = S(G + diff ) S(G diff ), will depend only on G 2 diff (t ) and on G 2 other (t ). 43 As the effect of G 2 other (t ) is constant and adds in the same way to all DW conditions (including to the b = smm 2 condition), the ADC calculation will not depend on it. Diffusion-weighting using bipolar schemes suffers much less from cross-terms with the background gradients, and, in several instances, when these gradients are constant, the cross-terms are eliminated altogether. 25 Still, it is important to properly evaluate, either numerically or analytically, the effect of the sequence gradients, which can significantly contribute to the b value and to the direction of the resulting diffusion-weighting John Wiley & Sons, Ltd. Volume 4, 215

9 Diffusion-Weighted Magnetic Resonance Spectroscopy b = s mm 2 b = 2 s mm 2 tcr tnaa 3 2 ppm 1 tcho Glx Built-in MM estimated by LCModel Experimental MM spectrum estimated by LCModel Figure 6. The inclusion of MM and lipids in DW-MRS. Red: DW spectra acquired from a rat brain at 7 T, at b = smm 2 (left) and at b = 2 s mm 2 (right). Spectra were processed by LCModel using the built-in MM + lipid portion of the basis set (blue) and the experimental MM + lipid spectrum acquired in situ (black). The experimentally acquired MM spectrum remained identical in the two diffusion-weighting conditions, whereas slight variations can be seen in the built-in spectrum (arrows). The built-in MM + lipid spectra, estimated by LCModel for the data acquired at b = smm 2 (red) and that acquired at b = 2 s mm 2 (black), are shown in the insert in the left panel. Error Propagation and Diffusion Estimates. The error in the estimation of diffusion measures, such as ADC, is directly related to the accuracy in the spectral quantification and the choice of diffusion-weighting. In the simplest case, the ADC of a certain metabolite can be simply calculated from two measurementsattwo different b values, one performed, e.g., at b = smm 2 and the other at a higher value, b diff. Assuming an exponential attenuation of the DW signal, the ADC can be expressed in terms of) the result of these two measurements: ADC = 1 b ln ( S(bdiff ) S(b=) ADC is then given by: σ ADC 2 1 b 2 (. The variance in the estimation of the 1 [ ( )] 2 + SNR bdiff ) 1 [SNR(b = )] 2 This is a function of the SNR of the signal measured at b = andatb diff, typically expressed as the Cramèr Rao lower bounds (CRLB) for the peak estimation, as well as of the b value chosen for the experiment. The minimum of this function occurs roughly at b 1/ADC. More complex considerations are necessary when multiple b values are used, as well as when the duration of the experiment is set as constant. Diffusion-Weighted MRSI The Challenges All the challenges with single-volume DW-MRS are present in the acquisition and processing of DW-MRSI data. An additional complication specific to DW-MRSI is that the timedomain data are acquired along with spatial encoding, typically involving a shot-by-shot variation in a phase-encoding gradient acting in one, two, or three directions (depending on the desired dimensionality of the spatial encoding). Thus, The DW-MRSI pulse sequence has to be designed to account for both the shot-by-shot phase and amplitude variations, of both the phase-encoding and MFG pulses. An example of such a design is given in Ref. 36. In this particular example, two echoes are acquired after each excitation. The phase-encoding gradient is performed after the diffusion-weighting scheme, leaving a small time window to acquire data points affected by the DW-MFGs but not the phase-encoding gradients. This short time-domain data set serves as a navigator, whose phase is used to correct for diffusion-induced phase fluctuations. A similar navigator is also acquired before the second echo. The amplitude of the navigator data is used to set an amplitude threshold that prospectively determines whether re-acquisition of k-space data is required. The procedure for real-time use of the navigator for re-acquisition of k-space data is fully described in Ref. 36, as well as in Ref. 37. Figure 7 shows the NAA map at b = smm 2 (a), the DW-NAA map without any correction (b), the effect of phase correction using the phase of the navigator (c), and the use of re-acquired data using the navigator (d). The challenge of performing proper ECC in DW-MRSI is also shown here. ECC was performed using the residual water peak in each voxel. As the water preselected volume (dotted rectangle) is significantly displaced from the preselected NAA volume due to the chemical shift offset (white rectangle), proper ECC could be performed only in the intersection between the two volumes. Examples of a voxel with a successful ECC (denoted 1 in Figure 7d) and an unsuccessful ECC (denoted 2) are given in the spectra shown (Figure 7, panels e and f). The full procedure of obtaining the ADC map for NAA is shown in Figure 8. Applications of DW-MRS: Insights, Diseases, Microstructures, and Physiology Fundamental Insights We list here the accumulated insight gained using DW-MRS on the fundamentals of cellular physiology and microanatomy. Skeletal Muscle. Metabolite diffusion in skeletal muscle was the first in vivo application of DW-MRS, which began in the early 199s. Most experiments were performed with 31 P DW-MRS and provided precious insight about the Volume 4, John Wiley & Sons, Ltd. 741

10 IRonen&JValette (a) (b) 2 1 (c) (d) b = s mm 2 b = s mm 2 4 b = 287 s mm 2 4 b = 287 s mm S (a.u.) 2 S (a.u.) (e) Frequency (ppm) (f) Frequency (ppm) Figure 7. Artifacts in DW-MRSI and their correction. Data were acquired at 7 T from a supracallosal axial slice with a preselected VOI of mm 3 (Figure 8). (a) tnaa map at b = smm 2 ; (b) same map, at b = 287 s mm 2. No phase correction was performed, nor use of re-acquired k-space data; (c) same map with phase correction based on navigator phase; (d) same map with phase correction and use of navigator-based re-acquired data. White rectangle: preselected NAA VOI; dotted rectangle: the shifted VOI at the water resonance. (e) Spectra obtained from position 1, showing successful ECC; (b) spectra from position 2, where ECC failed due to the lack of residual water signal. (Reproduced with permission from Ref. 36. John Wiley & Sons, Ltd., 214.) compartmentalization and microstructure of muscle fibers. 31 P DW-MRS experiments are challenging, both due to the fact that metabolite 31 P-T 2 values are relatively short (except for PCr) and because the gyromagnetic ratio of 31 P is significantly lower than that of 1 H, thus lowering the efficacy of the diffusion-weighting gradients, which is proportional to γ 2. The advantage of measuring 31 P DW-MRS in muscle is the complete avoidance of the strong lipid signal in and around muscles, which can significantly hamper accurate metabolite quantification in 1 H spectra. Conversely, 1 H DW-MRS in muscle is the preferred method with which to study the diffusion of intramyocellular lipid droplets John Wiley & Sons, Ltd. Volume 4, 215

11 Diffusion-Weighted Magnetic Resonance Spectroscopy S (a.u.) b = s mm 2 Gdir 1 Gdir 2 Gdir 3 tcho tcr Glx tnaa Frequency (ppm) b= d1 d2 d3 Figure 8. The full process of obtaining a metabolite ADC map. Maps for b = smm 2 and the three diffusion-weighted directions acquired at b = 287 s mm 2 are calculated from LCModel data. The ADC map is then calculated for each metabolite. Shown is the ADC(tNAA) map, overlaid on the corresponding anatomical image. Note the lower ADC(tNAA) in the gray matter region than in the medial region. (Reproduced with permission from Ref. 36. John Wiley & Sons, Ltd., 214.) Evidence for the Low Viscosity of the Cytosol. ADC measurement of PCr and ATP using 31 P DW-MRS at relatively short t d (in the range of 1 15 ms), sometimes combined with modeling of metabolite diffusion inside cylinders, has allowed estimation of the D free of metabolites inside the cytosol of animal and human muscle cells. Reported ADC values were approximately 5 15% lower than those measured in aqueous solution This finding has also been reported in excised muscles of goldfish 52 and lobster, 53 using 31 P DW-MRS. The results strongly suggest that the effective viscosity of the cytosol, i.e., including molecular crowding [see equation (7)], is only 5 15% higher than that of water. Cell Internal Structure and Metabolite Compartmentalization. The various studies performed with 31 P DW-MRS provide evidence that metabolite diffusion along muscle fibers is essentially free, i.e., the ADC parallel to fibers does not depend on t d. This means that, for the most part, metabolites are not highly confined to subcellular organelles, such as mitochondria. As expected, metabolite diffusion perpendicular to fibers was shown to be restricted. The diameter of the restricting cylindrical compartment, as estimated by modeling the t d - dependency of ADC perpendicular to fibers, was found to be 2 μm. 45,47 This estimate is much smaller than the actual cell diameter ( 8 μm). These results, again complemented by studies of excised goldfish and lobster muscle, 52,53 suggest that most of the hindrance to metabolite diffusion may result from the sarcoplasmic reticulum and mitochondria all exhibiting a longitudinal orientation in muscle fibers, rather than the cell membrane itself. As pointed out by Kinsey et al., 53 as the sarcoplasmic reticulum and mitochondria do not constitute a perfectly impermeable barrier to radial diffusion, modeling with impermeable cylinders would not yield the correct diameter for the sarcoplasmic reticulum and associated myofibrils. Volume 4, John Wiley & Sons, Ltd. 743

12 IRonen&JValette ADC/ μm 2 ms NAA tcho tcr Diffusion time t d /ms Figure 9. ADC values for NAA, tcr, and tcho as a function of t d in the range 1 1 ms. Measurements were performed on rats at 7 T, with a DW-MRS sequence based on the LASER sequence. Ultrashort t d values were achieved using a diffusion-weighting scheme based on oscillating gradients. The sharp drop in ADC is caused by the transition from D free to D intra, which includes intracellular tortuosity effects. (Reproduced with permission from Ref. 34. Nature Publishing Group, 212.) In the Brain. The first DW-MRS measurements in the brain were performed as early as 1993, in rats 54 and in humans. 55 Unlike in muscles, all the work in brain to date has been performed using 1 H DW-MRS, where spectral quality allows accurate metabolite quantification. Listed here are some of the most interesting fundamental insights accrued over more than 2 years of brain DW-MRS. Absence of Significant Cytoplasmic Streaming. Interestingly enough, the potential existence of cytoplasmic streaming in brain cells has been frequently evoked in the DW-MRS literature, in particular, to explain a consistently-observed decrease in metabolite ADC during ischemia DW-MRS itself, however, provides strong arguments against the significance of cytoplasmic streaming as a determinant of metabolite diffusion. The first argument is the stability of the macromolecule (MM) signals, whose ADC has been consistently measured to be close to (e.g., see Ref. 42 for an early, clean measurement of MM ADC in the rat brain). If the mobility of MM, whose large hydrodynamic radius is expected to result in a very small D free compared to metabolites, were indeed affected by cytoplasmic streaming, then the ADC of MM would be similar to metabolite ADC. Another argument stems from the strong decrease in metabolite ADC when t d is increased in the range of 1 1ms 34 (Figure 9). At this range of diffusion times, the ADC of metabolites transition from being very close to D free to being influenced by intracellular tortuosity/restrictions. This leads, indeed, to a decrease in ADC, whereas cytoplasmic streaming and active transport would, in general, result in an increase of ADC with t d. Viscosity of the Cytosol. Measurements performed in conditions where tortuosity and restriction effects are assumed to become negligible, i.e., at ultrashort t d using oscillating gradients, 34 have estimated values of metabolite D free in the range of 5% to 8% of the D for those metabolites in aqueous solution. This suggests a cytosolic viscosity (including molecular crowding) that is, at most, twice the value of water. For example, in this work, the D free of NAA in a VOI that contained a mixture of gray and white matter was estimated by combining experimental data and modeling at.59 μm 2 s 1 (at 37 C), while the D of NAA in aqueous solution at 2 Cis.7 μm 2 s 1 (e.g., Ref. 61). For the purely neuronal/axonal metabolite NAA, it is possible to estimate D intra, the intra-axonal diffusion coefficient, at longer t d values, based on DW-MRS measurements in an organized white-matter tract and geometric modeling. D intra includes the effect of tortuosity, as estimated at t d values for which the characteristic displacement is on the order of several micrometer. In one study, the parallel diffusivity, i.e., the diffusivity along the fibers of the posterior parts of the corpus callosum, was reported to be.3 μm 2 s 1, and, based on a local anisotropy model, D intra was estimated at.36 μm 2 s Very similar empirical results for the parallel diffusivity of NAA in the corpus callosum were reported elsewhere. 38,63,64 In a more recent study performed at 7 T, a smaller VOI was used and a higher parallel diffusivity of about.34 μm 2 s 1 reported. 65 On the basis of a model that included the curvature of the callosal fibers within the VOI and the dispersion in axonal orientation, D intra was estimated at.51 μm 2 s 1. A very similar value of the D intra of NAA in axons was obtained independently with DW-MRS measurements performed at very long t d values of 72 ms. 66 In the latter study, the isotropic ADC of NAA in parietal white matter was reported as.15 μm 2 s 1,and, assuming a neurite model, where the entire content of NAA is in long fibers, D intra = 3 ADC =.45 μm 2 s 1. Cell Internal Structure and Metabolite Subcellular Compartmentalization. The strong decrease in metabolite ADC as t d is increased from 1msto 1 ms suggests that metabolite diffusion in brain cells is hindered by obstacles that are typically separated by distances of 2 μm. 34 This is a much shorter scale than that reported for muscle. These obstacles could be either organelles or structures of the cytoskeleton, or simply the membranes of fibers extending from the cell bodies of neurons and glial cells (axons, dendrites, astrocytic processes). In contrast, metabolite ADCs appear to be fairly stable in the monkey brain in the range of t d values between 75 ms and 1 s. This demonstrates that metabolites are, for the most part, not confined inside small subcellular structures, such as organelles or cell bodies, but are, rather, free to diffuse along the long fibers characteristic of neurons and astrocytes. 67 The ADC perpendicular to white-matter fibers quickly drops to, as seen in human white matter at t d > 65 ms. 65 Metabolite ADC stability has also been confirmed separately in human gray and white matter for t d between 1 and 72 ms. 67 Figure 1 shows the ADC for NAA measured in a mostly gray matter volume at three different t d values. The three lines correspond to three different models diffusion in organelles, diffusion in neuronal cell bodies, and diffusion along the entire neuronal structure, including the long processes (axons, dendrites). The only one of these models that fits this data requires diffusion along long fibers John Wiley & Sons, Ltd. Volume 4, 215