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NMR IN BIOMEDICINE NMR Biomed. 2001;14:94­111 DOI:10.1002/nbm.686

Review Article

Diffusion NMR spectroscopy

Klaas Nicolay,1* Kees P. J. Braun,1,2 Robin A. de Graaf,1 Rick M. Dijkhuizen1,3 and Marijn J. Kruiskamp1

1 2

Department of Experimental In Vivo NMR, Image Sciences Institute, University Medical Center, Utrecht, Utrecht, The Netherlands Department of Neurology, University Medical Center Utrecht, Utrecht, The Netherlands 3 Department of Neurosurgery, University Medical Center Utrecht, Utrecht, The Netherlands

Received 28 January 2000; revised 25 October 2000; accepted 1 November 2000

ABSTRACT: MR offers unique tools for measuring molecular diffusion. This review focuses on the use of diffusionweighted MR spectroscopy (DW-MRS) to non-invasively quantitate the translational displacement of endogenous metabolites in intact mammalian tissues. Most of the metabolites that are observed by in vivo MRS are predominantly located in the intracellular compartment. DW-MRS is of fundamental interest because it enables one to probe the in situ status of the intracellular space from the diffusion characteristics of the metabolites, while at the same time providing information on the intrinsic diffusion properties of the metabolites themselves. Alternative techniques require the introduction of exogenous probe molecules, which involves invasive procedures, and are also unable to measure molecular diffusion in and throughout intact tissues. The length scale of the process(es) probed by MR is in the micrometer range which is of the same order as the dimensions of many intracellular entities. DW-MRS has been used to estimate the dimensions of the cellular elements that restrict intracellular metabolite diffusion in muscle and nerve tissue. In addition, it has been shown that DW-MRS can provide novel information on the cellular response to pathophysiological changes in relation to a range of disorders, including ischemia and excitotoxicity of the brain and cancer. Copyright 2001 John Wiley & Sons, Ltd. KEYWORDS: diffusion; restriction; tortuosity; anisotropy; brain; muscle; ischemia; excitotoxicity

INTRODUCTION

MR is well known for its ability to accurately measure the diffusion coefficients of solutes and solvents in isotropic liquids. To date diffusion MR imaging and spectroscopy have found a broad range of applications in physics, chemistry, biology and medicine. This review focuses on in vivo measurements of metabolite diffusion in mammalian tissues, using diffusion-weighted MR spectroscopy (DW-MRS). 1H-MRS studies of water diffusion are excluded from the overview

*Correspondence to: K. Nicolay, Department of Experimental In Vivo NMR, Image Sciences Institute, University Medical Center Utrecht, Bolognalaan 50, 3584 CJ Utrecht, The Netherlands. E-mail: [email protected] Present address: MRC, Yale University, New Haven, USA. Present address: MGH-NMR Center, Harvard Medical School, Charlestown, USA. Contract/grant sponsor: Netherlands Organization for Scientific Research (Medical Sciences, Earth and Life Sciences); contract grant number: 902-37-113, 805.09.101. Abbreviations used: ADC, apparent diffusion coefficient; ADP, adenosine diphosphate; Cho, choline-containing compounds; DW, diffusion-weighted; 2FDG-6P, 2-fluoro-2-deoxyglucose-6-phosphate; geMQC, gradient-enhanced, multiple-quantum coherence; NAA, Nacetylaspartate; PCr, phosphocreatine; PFG, pulsed field gradient; PRESS, point-resolved spectroscopy; STEAM, stimulated-echo acquisition mode; tCr, total creatine/phosphocreatine. Copyright 2001 John Wiley & Sons, Ltd.

while biomedical applications of diffusion MRI are covered elsewhere in this issue. The relatively rapid exchange of water across biological membranes implies that water diffusivity as a rule reports on more than one tissue compartment which complicates the interpretation of water diffusion data. The transport of metabolites across cellular boundaries, however, is slow on the time scale of the DW-MRS experiment, preventing the confounding effects of exchange on data interpretation. This review is organized as follows. A brief outline of the physicochemical concept of diffusion is followed by a synopsis of current insights in the diffusion characteristics of the intracellular and extracellular compartments of the mammalian cell. The basis of the MR measurement of diffusion and pulse sequences for DW-MRS is presented next, followed by examples of the application of the technique in fundamental biological and biochemical research for cell structure and function. Finally, the opportunities for DW-MRS in pathophysiological studies are described.

THE DIFFUSION PROCESS

Diffusion is the random translational (or Brownian) motion of molecules or ions that is driven by internal

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position r at time t. For ordinary, isotropic diffusion, the `propagator' P(rojr,t) also obeys eqn. (3),6 leading to eqn. (4): @Pro jr; [email protected] Dr2 Pro jr; t 4

Figure 1. Schematic representation of diffusive transport in the case of an initial concentration gradient. (A) Initial boundary of solute diffusion into pure solvent; (B) solute distribution after a certain time; (C) variation of concentration with distance; (D) gaussian-shaped concentration gradients after successive times. Curve 1: initial boundary; curves 2±4, alternative representations of the solute distribution after successive times

In the case of unbounded diffusion and for the starting condition P(rojr,0) = (ro À r) (indicating that as t 0, c = 0 everywhere except at the origin r = 0) and the boundary condition P(rojr,t) 0 for r ?, the solution of eqn. (4) yields the dependence of the probability P on the displacement: Pro jr; t 4DtÀ3=2 expÀr À ro 2 =4Dt 5

thermal energy. Translational diffusion is the basic mechanism by which molecules are distributed in space1 and is considered to play a central role in any chemical reaction since the reacting species have to collide before the reaction can occur2. Classically, the mathematics of the diffusion process (i.e. Fick's first and second law of diffusion3­5) has been worked out for systems in which an initial concentration gradient is established. As an example, Fig. 1 shows two compartments, one containing a solute at a certain finite concentration and one with solvent only. Connecting the two compartments initiates a macroscopic diffusive flux across the compartment boundary, in the direction of decreasing chemical potential of the solute. The net diffusive transport proceeds until the concentration gradient has vanished. Thereafter, the diffusion process evidently continues but no longer involves net solute transport. Diffusion has the dimension of area per unit time and is typically expressed as m2 sÀ1 in the SI-unit system. The diffusion equations are readily solved for various initial concentration profiles and boundary conditions.3­5 The description below uses the nomenclature as presented by Johnson.5 The flux of particles J at position r is directly proportional to the concentration gradient rc: Jr; t ÀDrcr; t 1

Equation (5) indicates that the probability distribution P has a Gaussian shape, as is also evident from Fig. 1(D). It should be noted that the distribution function in eqn. (5) depends on the displacement of the molecule but not on its initial position. Since diffusion is a random process and the displacements are equally probable in all directions, the net (or mean) molecular displacement [i.e. k(r À ro)l] is zero. Therefore, the molecular displacements associated with three-dimensional diffusion are calculated from eqn (5) as average square displacements, which gives the Einstein­Smoluchowski equation: hr À ro 2 i 6Dt 6

Equation (6) demonstrates that displacement resulting from diffusion is simply related to the diffusion coefficient and that, for the case of unhindered diffusion, the average square displacement increases linearly with the diffusion time, t. Equation (6) corresponds to the second moment of the displacement distribution function of eqn (5). Deviations from the Gaussian distribution function will arise if the translational displacements are restricted by geometrical constraints. It should be noted that in most MR diffusion experiments the molecular displacement is only probed in a single direction at the time. The probability density function of eqn (5) then becomes: Px; t 4DtÀ1=2 expÀx2 =4Dt 7

in which D is the diffusion coefficient and c(r,t) is the solute concentration. Conservation of mass is expressed by eqn (2): @cr; [email protected] Àr Á Jr; t 2

Combining eqns (1) and (2) leads to Fick's second law of diffusion: @cr; [email protected] Dr2 cr; t 3

D is assumed to be essentially independent of the solute concentration, which is presumed to be low. It is appropriate to introduce the probability P(rojr,t) that a solute molecule, which is initially at ro will be at

Copyright 2001 John Wiley & Sons, Ltd.

In analogy to eqn (6), the one-dimensional average square displacement is given by 2Dt. Classical approaches towards measuring molecular self-diffusion typically employ radioactive or fluorescent tracers, or ions that can be probed with ion-specific microelectrodes. Tracer techniques span the mm to mm range of length scales and have been successfully applied to a variety of biological systems, including the brain.7­9 However, because of the inherent invasiveness of the use of exogenous tracers (they have to be introduced into the system of interest), these methods cannot be used to study diffusion in human tissues in vivo. The MR-based measurement of diffusion is fundamentally different

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from that using tracers: MR is able to utilize endogenous molecules and capable of monitoring the diffusion process itself, i.e. the random motions of an ensemble of particles,4 and therefore does not rely on a concentration gradient to probe diffusion. MR is also able to measure diffusion phenomena related to the intermingling of initially separated components.6 This aspect of diffusion MRS is not covered in this review. In isotropic solutions, under well-defined in vitro conditions, diffusion is closely related to the size of molecules, according to the Stokes­Einstein equation: D k T=f 8

DIFFUSION IN THE INTRA- AND EXTRACELLULAR COMPARTMENTS

In isotropic aqueous solutions, the diffusion of metabolites is quantitatively understood in terms of the physicochemical properties of the molecules themselves and those of the solvent. The diffusion coefficients as measured by MRS under these conditions are in excellent agreement with data obtained by other techniques.15 Because of its non-invasive nature, MR is also uniquely suited to assessing the diffusion characteristics of molecules in intact tissue. The molecular diffusion in the tissue compartments is potentially influenced by a number of factors that are of no relevance in vitro,16­20 including: . . . . non-specific adsorption and desorption events; specific binding; the availability of cell water as a solvent; the relative and absolute dimensions of the aqueous phase and intervening immobile structures; and . cytoplasmic streaming, caused by gel­sol transitions in cytoplasmic actin or by myosin movements along actin fibrils,21 or by syneresis. These factors clearly challenge the diffusion model of random Brownian motion and suggest that the classical diffusion theory will be unable to provide a complete explanation for intracellullar metabolite displacements at the molecular level.16 The classical diffusion model requires, among others, that the following conditions are met: (a) the time period over which diffusion is sampled is orders of magnitude longer than the average duration of a random movement of the molecule; (b) collisions of a solute molecule with solvent molecules are equally probable from all spatial directions (this condition only holds for relatively dilute solutions); (c) molecular interactions of the solute with other components are insignificant; and (d) the system exhibits no bulk directional flow of solvent. As indicated above, Agutter et al.16 have recently argued that the latter four conditions do not hold for the intracellular compartment. The cytoplasmic space of eukaryotic cells can be considered homogeneous only over relatively short length scales, causing conditions (a) and (b) to be at risk of violation. Condition (c) is known not to hold for several small solute molecules such as ATP and ADP that are to some extent bound to cytoplasmic proteins. With respect to condition (d), the situation is equally complex. There are indications that cytoplasmic streaming occurs and that this process is energy-dependent (for review see Wheatley20). The evidence for bulk flow in the cell interior primarily originates from studies on isolated mammalian cells

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in which D is the molecular self-diffusion coefficient, k the Boltzmann constant, T the absolute temperature and f the friction coefficient. For spherical entities the friction factor f is given by eqn (9): f 6R H 9

in which Z is the viscosity of the solution and R H the hydrodynamic (or Stokes) radius of the particle. Generally, however, the shape of molecules that are of interest to diffusion-weighted MRS is non-spherical and may be affected by factors such as hydration. The friction factor f must then be modified accordingly.2 Consequently, quantitative measurements of the effective diffusivity provide information on the shape and the interactions of the diffusing molecule. This property is widely exploited in in vitro MRS studies of biomolecules in solution to assess various biophysical and biochemical parameters, including the hydrodynamics and the folding/unfolding of proteins,10 proton exchange with biomacromolecules,11 the oligomerization state of biomacromolecules12 and protein­ligand interactions.13 Equation (8) shows that diffusion strongly depends on temperature which should therefore ideally be kept constant throughout the diffusion measurement, unless temperature per se is the parameter of interest. The diffusion coefficient D exhibits a non-linear dependence on the temperature T because the viscosity Z in eqn (9) is strongly affected by T. This results in an exponential dependence of D on T: D DI e

ÀEa =kT

10

in which Ea is the activation energy associated with translational diffusion. For water, Ea is ca 0.18 eV, corresponding to the energy required for breaking hydrogen bonds. Similar activation energies have been reported for the in vitro diffusion of N-acetyl-D-aspartate (NAA) and choline-containing compounds (Cho) in aqueous solutions.14 This suggests that in vitro the mechanism of diffusion for these metabolites is the same as that for water (i.e. temperature-induced activation through dissociation and reassociation of hydrogen bonds).

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using microinjection of fluorescent-tagged protein. The distribution of the labeled protein appeared to proceed much faster than expected on the basis of its molecular size. If the concept of cytoplasmic circulation is correct, this implies that under normal physiological conditions molecules are both coherently moved by external forces and incoherently move by translational diffusion. Using fluorescence techniques on isolated tissue culture cells microinjected with fluorophores, the viscosity of the aqueous domain of the cell cytoplasm was estimated to be 1.2­1.4 times that of water (see Nicolay et al.15 and references cited therein). This will cause a reduction in the diffusion coefficient of metabolites, as evident from eqns (8) and (9). The intracellular milieu is characterized by a high density of globular proteins, cytoskeletal elements and subcellular organelles. The above considerations are therefore most relevant for the cell internum. The major fraction of the metabolites that contribute to in vivo MR spectra also resides inside the cell. A limited number of DW-MR studies has dealt with the measurement of metabolite diffusivity in the extracellular compartment, particularly of rat brain. The extracellular diffusion space of the brain has been thoroughly studied using invasive optical and micro-electrode techniques.8,9,22 It was shown that the cerebral extracellular space resembles foam. The diffusing probe molecules execute random movements that cause their collisions with membranes and affect their concentration distribution. By measuring this distribution and computer fitting of modified diffusion equations, the extracellular space volume fraction (a) and the tortuosity () can be estimated.9 The volume fraction a represents the relative volume of the extracellular space while the extracellular tortuosity is a measure of the hindrance imposed by cellular obstructions and extracellular matrix components. The tortuosity is assumed to be an important determinant of the effective intracellular diffusion coefficient as well.15,16,23 The tortuosity is related to the ADC and the intrinsic diffusion coefficient D8,9 by: ADC D=2 11

For the above reasons, an interpretation of in vivo diffusion data in terms of random translational motion only is dubious. One measures an effective diffusivity that is usually called an apparent diffusion coefficient (ADC) and that tends to be lower than the diffusion coefficients expected without these influences.15 Such effects differ among metabolites and therefore it is anticipated that the difference between the intrinsic diffusion coefficient and the measured effective ADC also differs among metabolites. Since MR-based measurements of metabolite diffusion make use of linear magnetic field gradients, diffusion is sampled along discrete spatial directions. This opens up opportunities for assessing the potential directional dependence (or anisotropy) of diffusion. If the diffusion anisotropy as such is of no interest measures should be taken to eliminate the orientational dependence of the measured ADC values. These points are discussed in detail below. The complexity of mammalian cells in terms of their subcellular compartmentation (e.g. the spaces enclosed by the nuclear and mitochondrial membranes) has been ignored thus far. To date the DW-MRS technology is unable to do justice to this intricacy. Using PFG methods, Garcia-Perez et al.26 have recently shown that there is a ´ ´ ´ significant diffusional heterogeneity among small metabolites within different intracellular organelles. It is obvious that realistic models of in vivo diffusion will have to account for the cytoarchitecture of the eukaryotic cell. In summary, the in vivo translational displacement of metabolites is influenced by a variety of factors, especially in the cytoplasmic compartment. Data interpretation exclusively in terms of the classical diffusion model is questionable. One therefore measures an effective diffusivity or apparent diffusion coefficient. While the MRS measurement can in principle provide information on each of the additional factors involved in metabolite dislocation, it is difficult to single out individual factors.

It should be noted that eqn (11) only holds for situations where the tortuosity is a dominating factor in reducing the diffusion coefficient from its intrinsic value. This situation appears to hold for most of the probe molecules that have been used to assess the diffusion characteristics of the extracellular compartment. The protein content of the extracellular space is low and therefore metabolite binding and absorption play a minor role as compared to the cell internum. There are strong indications for longdistance fluid pathways in the extracellular compartment that are probably of importance for volume transmission of chemical signals.9,24,25 It is unlikely that the extracellular diffusive transport is driven by an active process, in contrast to the situation for the cell interior.

Copyright 2001 John Wiley & Sons, Ltd.

DIFFUSION MRS TECHNIQUES

Basic principles of the pulsed-®eld gradient technique There are two main ways in which MR may be used to measure self-diffusion coefficients, i.e. analysis of relaxation data27 and pulsed-field gradient (PFG) NMR.28 In the first method, T1 relaxation data are analyzed to determine the rotational correlation times of a probe molecule, which can ultimately be related to the translational diffusion coefficient. The relaxation approach relies on a number of serious assumptions that probably are violated (or at least very difficult to verify)

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by moving from r0 to r1 is given by: Ár1 À r0 g Á r1 À r0 13

Figure 2. Basic diffusion-sensitized spin-echo sequence. (A) The 90° excitation and 180° refocusing pulses form a spinecho at the echo-time TE. (B,C) The pulse sequence of (A) can be sensitized for diffusion by applying a pair of pulsed®eld gradients, with amplitude g, surrounding the 180° pulse. Constant (B) and half-sine (C) gradient wave forms are most commonly used. The de®nition of the gradient pulse duration, , and the time separation between gradient pulses, D, is indicated

under in vivo conditions.27 The relaxation technique will not be further discussed. In the PFG method, the attenuation of the MR signal resulting from the dephasing of the nuclear spins due to the combined effect of the translational motion and the imposition of spatially well-defined gradient pulses is used to measure molecular motion. Although in principle both B0- and B1- (i.e. radiofrequency) gradients can be used, the present article is restricted to the use of B0gradients. The PFG method was first introduced by Stejskal and Tanner,28 who incorporated a pair of diffusion-sensitizing linear magnetic field gradients into a Hahn spin-echo sequence (Fig. 2). The purpose of the gradient pulses is to magnetically label the transverse magnetization of spins within a molecule as a function of spatial position. The gradient causes the Larmor frequency of the nuclear spins to become spatially dependent with respect to the gradient direction. The phase effect f of a gradient pulse g of duration [and constant amplitude, as shown in Fig. 2(B)] on a spin at position r is given by: r g Á r 12

In the absence of diffusion, the phase difference Df is zero since the two identical gradient pulses exert an equal phase effect. The phase effect of the gradient pulses is cancelled out in that case because of the fact that the 180° refocusing pulse in the spin-echo sequence (Fig. 2) reverses the sign of the phase angle. This causes the static spins to be all in phase, which gives a maximum echo signal. Obviously, the intensity of the Hahn spin-echo in Fig. 2 is inevitably affected by T2 relaxation. Equation (13) implies that the dephasing efficiency of a gradient pulse depends on the type of nucleus (the higher the g, the stronger the dephasing effect will be), the strength and duration of the gradient pulse, and the displacement of the spin along the gradient direction. Although the example of eqns (12) and (13) assumes a constant gradient amplitude [Fig. 2(B)], the gradient itself may be a function of time and not merely a rectangular pulse [Fig. 2(C) depicts a sine-shaped gradient]. The integral of the gradient pulse and not its amplitude per se determines its dephasing efficacy. In order to appreciate the effects of diffusion on the signal intensity from an ensemble of nuclear spins, it is necessary to consider the probability of a spin starting at r0 to move to r1 in the time D. This probability is given by P(r0jr1,t) as before [see eqn (5)]. The measured spin-echo signal results from the ensemble of spins and therefore we must integrate over all possible starting and finishing positions to obtain the total signal as a superposition of transverse magnetization vectors, in which each phase term is weighted by the above probability: Z Z Sg=S0 Pro jr1 ; t expi g Á r1 À ro dro dr1 14

in which S (g) represents the echo intensity for the case of a diffusion time D and a gradient g, and S (0) is the signal intensity without diffusion weighting. From eqns (7) and (14), it can be deduced27 that: Sg=S0 expÀ 2 g2 D2 Á 15

In eqn (12), the scalar product arises because only motion parallel to the direction of the gradient will cause a change in the phase of the spin. It should be noted that eqn (12) ignores the effects of displacement during the gradient pulse (the so-called short gradient pulse limit). Experimentally, this condition is approximated by keeping ( D (Fig. 2), but this assumption does not generally apply in practical cases. If we consider the phase of a spin that was at position r0 during the first gradient pulse and at position r1 during the second, then the change in phase of this individual nuclear spin, Df,

Copyright 2001 John Wiley & Sons, Ltd.

for the case of a gradient g with constant amplitude. This derivation of the pulsed-field gradient diffusion attenuation applies to the case of unrestricted, isotropic diffusion and under the assumption that diffusion during the gradient pulse itself can be neglected. In practice, however, we also need to consider diffusion displacement during the gradient pulse. Equation (15) must then be modified to account for the finite width of the gradient pulse and, for the case of a rectangular gradient pulse,

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becomes: Sg=S0 expÀ 2 g2 D2 Á À =3 16

The term (D À /3) is usually referred to as the diffusion time, tdiff. Often, eqn (16) is presented in the form: Sb=S0 expÀbD; or lnSb=S0 ÀbD 17 in which b is the so-called b-factor that is used to indicate the strength of the diffusion weighting (typically given in units of s mmÀ2). For the case of the half-sine gradients [Fig. 2(C)], the b-factor is given by: b 4= g Á À =4

2 2 2 2

reference. In the principle axes system of the cell frame of reference, the diffusion tensor D' is given by 1 0 H 0 Dxx 0 C B 20 DH @ 0 DHyy 0 A 0 0 DHzz

However, the cell frame of reference almost never coincides with the laboratory frame. The diffusion tensor D in the laboratory frame is related to D' by: D RÀ1 DH R 21

18

The above formulas for the gradient-induced attenuation of the MR signal could have been equally well derived by taking the macroscopic approach based on the Bloch equations, modified to accommodate diffusion effects.27,28 The displacement of nuclear spins that is associated with macroscopic flow or bulk motion will lead to net changes in the phase of the measured (ensemble averaged) signal in PFG MR studies.15 This is due to the fact that net displacement of spins occurs in the presence of the magnetic field gradients. This is principally different from diffusion where the net displacement is zero and the ensemble average phase shift is also zero. Hence, the absence or presence of net phase shifts in diffusion-weighted MR spectra is a means by which pure diffusion can be distinguished from macroscopic displacements.15 Up to this point only isotropic diffusion has been considered, and this implies a scalar diffusion coefficient, D. However, the above framework also applies to those cases where diffusion is anisotropic (i.e. unequal in different directions) and has to be described as a tensor.4,29 The diffusion tensor D is a rank two (i.e. three by three) tensor and is given by: 1 0 Dxx Dxy Dxz C B 19 D @ Dyx Dyy Dyz A Dzx Dzy Dzz

in which R is a rotation matrix. When the cell frame of reference differs from the laboratory frame, the offdiagonal elements in D are non-zero and have to be taken into account for a complete description of anisotropic diffusion. For uncharged particles, such as water, the diffusion tensor D is symmetric. Using the formalism of the diffusion tensor, the Stejskal­Tanner relationship of eqn (17) can be rewritten as: lnSb=S0 À

3 3 XX i1 j1

bij Dij

22

where bij is a component of the b matrix and Dij is a component of the diffusion tensor D. Note that crossterms between perpendicular gradients appear in bij components for which i j. In order to quantitatively describe anisotropic diffusion at least seven experiments need to be performed [to obtain Dxx, Dxy, Dxz, Dyy, Dyz, Dzz and S(0)], in which diffusion gradients are applied in various oblique directions. For example, to measure signal attenuation related to diffusion in the x-direction and to obtain Dxx, a pulse sequence should be used with only diffusion gradients along x, so that b11 = bxx 0. The echo attenuation is then given by: lnSb=S0 Àbxx Dxx 23

The diagonal elements Dxx, Dyy and Dzz represent the diffusion along the x, y and z axes in the laboratory frame, i.e. the frame in which the pulsed-field gradients are applied. The off-diagonal elements represent the correlation between the diffusion in perpendicular directions. For isotropic diffusion, there is no correlation between diffusion in orthogonal directions and the off-diagonal elements are zero. Furthermore, Dxx = Dyy = Dzz = D. For anisotropic diffusion one has to consider how the laboratory frame relates to the principle axes (i.e. the axes that coincide with the three main orthogonal directions of diffusion) of the cell (or tissue) frame of

Copyright 2001 John Wiley & Sons, Ltd.

Obviously, for localized MRS experiments the requirement of only having a gradient along x is not feasible, resulting in a more complex expression with more components of b and D. In the generalized case, the echo attenuation is caused by all of the diagonal and all of the off-diagonal components of D simultaneously, resulting in an echo attenuation given by: lnSb=S0 À bxx Dxx byy Dyy bzz Dzz 2bxy Dxy 2bxz Dxz 2byz Dyz 24 Note that for isotropic diffusion, i.e. Dij = 0 for i j and Dij = D for i = j, eqn (24) reduces to the classical Stejskal­Tanner equation [eqn (18)] with b = (bxx byy bzz)/3, demonstrating that the two models are equivalent. Knowledge of the complete diffusion tensor provides insight into the orientational dependence of diffusion.

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Figure 3. Diffusion-sensitized pulse sequences for localized MRS. For simplicity, the slice-selection gradients for volume selection are omitted and the sinusoidal diffusion gradients are shown along a single axis only. (A) PRESS sequence. As an example, two pairs of diffusion gradients are positioned symmetrically around the two 180° refocusing pulses. This doubles the b-factor as compared to the use of a single pulsed-®eld gradient pair. (B) STEAM sequence. Diffusion gradients are placed in the two TE/2 periods. For de®nition of symbols see the legend to Fig. 2

However, for many applications this is of no interest and knowledge of the scalar diffusion coefficient suffices. For these cases, one can make use of the fact that the trace of the diffusion tensor is invariant to rotations: TrDH DHxx DHyy DHzz Dxx Dyy Dzz TrD 3Dav 25

Dav can be obtained by three separate measurements of Dxx, Dyy and Dzz. Several methods to measure the trace of the diffusion tensor in a single experiment by using particular combinations of gradient pulses have been proposed for MRI.30,31 We have recently adapted a similar approach for DW-MRS, which can be employed to extract quantitative, orientation-independent information from metabolite diffusion experiments in a timeefficient manner.32 Pulse sequences for diffusion MRS Basically any MRS pulse sequence that makes use of echo formation can be simply sensitized for diffusion effects by incorporation of one or more pairs of pulsedfield gradients.4,15 Diffusion-weighted 1H-MRS is usually carried out in volume-selective mode, using either PRESS [Fig. 3(A)] or STEAM [Fig. 3(B)] (see review by Nicolay et al.15). In most cases, DW-MRS on other nuclei is conducted with a simple spin-echo sequence, without localization.

Copyright 2001 John Wiley & Sons, Ltd.

PRESS [Fig. 3(A)] is primarily used for DW-MRS studies on components with a relatively long T2 (e.g. brain metabolites in 1H-MRS) since T2 relaxation is operative throughout the sequence. This hampers experiments in which the time separation between the gradient pulses, D, is varied to assess the diffusion timedependence of the MR signal the TE should be kept constant in order to avoid the complication of changes in the degree of T2-weighting of the signal. The STEAM sequence [Fig. 3(B)] is better suited for diffusion timedependent studies since the mixing time TM can be prolonged without concomitantly increasing the echotime TE. Increasing diffusion weighting is obtained at a constant T2-weighting, at the expense of a slightly increased signal loss via T1 relaxation. The main disadvantage of STEAM is that the stimulated-echo is only 50% of the maximally obtainable signal. The above diffusion-sensitive MRS sequences can be readily extended to incorporate additional features. As an example, Sotak et al.33,34 have used multiple-quantum filtering techniques for the measurement of lactic acid diffusion in tumor tissue. The rationale behind this approach is that the filtering technique enables a strong suppression of unwanted resonances that might interfere with the detection of the resonance of interest. Metabolite diffusion measurements are considerably more demanding than water diffusion measurements, mainly because: (a) metabolite levels are several orders of magnitude lower than those of water; and (b) metabolite diffusivity is substantially slower than water diffusion, requiring

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Figure 4. Single-shot diffusion trace sequence for localized DW-MRS32, based on PRESS [Fig. 3(A)]. Narrow and broad sinusoidal gradients depict crusher and diffusion gradients, respectively. The sequence uses four pairs of bipolar gradients to achieve diffusion weighting. The diffusion gradients have speci®c relative signs and are simultaneously executed in all three orthogonal directions. The crux of the sequence is that the indicated combination of 12 gradient pairs eliminates the off-diagonal elements of the diffusion tensor [eqn (19)] and constructively adds up the diagonal elements [eqn (20)]. The sequence has the additional advantage that it achieves single-shot cancellation of crossterms between static magnetic ®eld gradients and the diffusion-sensitizing gradients. For 1H-MRS the sequence is typically preceded by CHESS water suppression, while for 1HMRI it can readily be extended with imaging gradients

Figure 5. 31P-MRS of the anisotropy of ATP and phosphocreatine (PCr) diffusion in rat hindleg skeletal muscle, as measured at 4.7 T. Diffusion weighting was performed (A) in the z-direction (largely parallel to the muscle ®bers) and (B) in the x-direction (approximately perpendicular to the long axis of the muscle ®bers). Numbers indicate the amplitude of the diffusion-sensitizing gradients (duration , 9.3 ms; separation D, 95 ms). The spectra were acquired using a 2.5 cm diameter surface coil and a selective stimulated-echo sequence70 that refocuses the J-evolution of the spin±spin coupled resonances of g- and a-ATP. The b-ATP resonance is not visible because of the frequency selectivity of the adiabatic radio-frequency pulses. All spectra were subject to the same phase correction. Other parameters: TR, 5s; TE, 20 ms; TM, 75 ms; nt, 128; b-factor, ca 100±4000 s mmÀ2 (reproduced with permission from De Graaf et al.,40)

higher gradient amplitudes and/or longer diffusion times to achieve sufficient diffusion-dependent signal attenuation. These considerations especially apply to nuclei having a low gyromagnetic ratio. In 31P-MR, for example, gradient pulses should be 2.5 Â stronger than in 1H-MR to get a similar signal attenuation, assuming the remaining parameters to be equal [see eqn (16)]. Since strong diffusion-sensitizing gradient pulses are required, metabolite diffusion studies may be subject to experimental artifacts. Gradient performance should be excellent in that the diffusion gradient pairs (Figs 2 and 3) are well balanced and induce minimal Eddy currents. Sample motion should be minimized since net displacement of spins in the presence of linear magnetic field gradients will cause changes in the phase of the MR signal, which may lead to amplitude losses on top of those related to diffusion. During signal averaging the phase shifts may appear incoherent from acquisition to acquisition and thereby lead to signal attenuation. More complex motional patterns (e.g. bulk rotations) lead to phase errors that are incompletely refocussed in individual acquisitions and, consequently, are accompanied by signal loss in individual scans. In in vivo applications, the macroscopic motion-related signal losses are superimposed on the diffusion-dependent signal losses and therefore cause an overestimation of the diffusion

Copyright 2001 John Wiley & Sons, Ltd.

coefficients.15 Posse et al.35 have proposed a correction strategy for macroscopic motion-related signal losses in 1 H-MRS studies of metabolite diffusion by storing each FID signal separately, followed by individual phase correction and signal averaging. Non-translational motion, like for example cardiac cycle-related CSF pulsations in brain,36 is more difficult to compensate for. In principle, it is possible to employ gradient moment nulling techniques to eliminate the effects of certain types of motions.37 However, the nature of in vivo movements requires complex compensation schemes which severely diminish diffusion sensitization. In view of the pronounced sensitivity of diffusion to temperature [eqns (8)­(10)], special care should be taken for temperature control of the object. This necessitates the careful recording and stabilization of body temperature in anesthetized animals. Depending on the information one wants to obtain, the diffusion-sensitizing gradients can be executed in different ways. In order to achieve sufficient sensitization for slowly diffusing molecules at reasonable diffusion times, the diffusion gradients can be positioned around both 180° pulses in the case of PRESS or in all three directions simultaneously (in the case of PRESS and STEAM). It should be realized that although this is in principle a legitimate procedure, it excludes the objective assessment of the directional dependence of metabolite diffusion. Furthermore, the measured metabolite ADCs will depend on the orientation of the object in the coordinate system of the magnet in the case of diffusion anisotropy. We have recently proposed a PRESS-based pulse sequence32 for localized MRS (Fig. 4) that eliminates this orientation dependence in single-shot

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fitting the peak integrals to eqn (17). More advanced experiments and the information that they provide will be discussed in the subsequent sections.

DW-MRS AND CELL STRUCTURE AND FUNCTION

In vivo diffusion-weighted metabolite MRS can be used to provide both functional and structural information. The first application focuses on the biophysical properties of the intracellular metabolites. Measurements of ATP diffusivity, for example, give insights into the capacity of diffusion-related free-energy transport that is of relevance to the regulation of in vivo bio-energetics. The structural studies exploit the fact that the signal attenuation in DW-MRS is related to the mean displacement of the molecule involved rather than to its intrinsic diffusion coefficient. When the diffusion path lengths are in the order of the dimensions of cellular constituents that constrain the diffusional displacements, the diffusion time-dependence of the signal attenuation can be used to non-invasively probe the dimensions of the restricting elements. Both the functional and structural usage of metabolite DW-MRS is illustrated below. Skeletal muscle

Figure 6. In vivo diffusion of phosphocreatine in rat skeletal muscle. (A) Trace diffusion coef®cient Dav for PCr as a function of TM (which is proportional to the diffusion time). Each data point represents the average Æ SD (n = 6). The solid line represents the best ®t to a cylindrical restriction model, according to Van Gelderen et al.39 (B) `Trace mean square displacement' 2av for PCr as a function of TM. 2av was calculated from the (time-dependent) `trace diffusion coef®cient' Dav (A), according to eqn (6). The solid lines are the best ®t to the experimental data. The dotted lines indicate the mean square displacement when the unbounded diffusion coef®cient Dav(0), as obtained from the modeling, is used in eqn (6). The difference between the dotted and solid lines is again indicative of diffusion restriction (reproduced with permission from De Graaf et al.).40

mode by weighting along the trace of the diffusion tensor (see above). The sequence is adapted from the pulse scheme developed by Mori and Van Zijl for trace diffusion-weighted MRI30 that makes use of a primary Hahn spin-echo. The specific features of the trace DW-MRS pulse sequence are described in the legend to Fig. 4. The majority of the DW-MRS studies reported to date were aimed at quantifying the metabolite apparent diffusion coefficient by using step-wise increases in the gradient amplitude at fixed timing of the gradient pulses. ADCs can be calculated from such a series of spectra by

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Figure 5 shows a series of 31P-MR spectra that were measured in rat hindleg skeletal muscle. Six spectra were acquired with different gradient strengths (at a fixed diffusion time) while the magnetic field gradient direction was approximately parallel [Fig. 5(A)] or perpendicular [Fig. 5(B)] to the muscle fiber direction. Signal attenuation is more prominent in Fig. 5(A) than in Fig. 5(B), which is a manifestation of the anisotropy of metabolite diffusion in muscle.38,39 The effect is both evident for the phosphocreatine (PCr) resonance and the a- and g-ATP resonances. De Graaf et al.40 have performed such measurements for three orthogonal directions [yielding Dxx, Dyy and Dzz and, from these, Dav; see eqn (25)] and as a function of the diffusion time (yielding the dependence of Dav on the diffusion time). Examples of the outcome of these measurements for PCr are depicted in Fig. 6. The diffusion restriction is evident from the decrease of Dav with increasing diffusion times. The solid lines in Fig. 6(A) represent the best fit of the experimental data to a diffusion model39 that assumes a cylinder-shaped compartment, as inspired by the macroscopic and microscopic structural features of skeletal muscle,41 in which diffusion is restricted in the radial but not in the axial dimension. The modeling yields estimates of the unbounded diffusion coefficients Df of PCr and ATP as well as the limiting radius of the cylindrical diffusion space. The in vivo Df of PCr and ATP amounts to 0.64 Æ 0.07 and 0.50 Æ 0.08 Â 10À9 m2 sÀ1 while the

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Figure 7. Serial diffusion measurements on N-acetyl-D-aspartate (NAA) in excised rat brain tissue (A), bovine optic nerve parallel (B) and perpendicular (C) to the PFG direction, as a function of gradient strength. The diffusion gradients were incremented from 0 (®rst row) to 27 G cmÀ1 in 14 equal steps. The diffusion time was 125 ms. Note that the attenuation of the NAA signal in optic nerve shows a pronounced directional dependence (reproduced with permission from Assaf and Cohen).48

radii are estimated at 10.7 Æ 0.9 and 8.5 Æ 1.0 mm, respectively. The main implications of these findings are that: (a) the unbounded diffusion coefficients of PCr and ATP are very similar to their in vitro values at 37°C which amount to 0.74 Æ 0.04 and 0.53 Æ 0.06 Â 10À9 m2 sÀ1, respectively;40 (b) the radial dimensions of the restricting compartment in skeletal muscle as deduced from the MRS data are much smaller than the crosssectional radii of muscle fibers in rat hindleg which range from 30 to 40 mm.42 The latter finding suggests that the diffusional anisotropy in rat muscle results from intracellular barriers well within the boundaries of the sarcolemma. Kinsey et al.43 have recently studied PCr diffusion anisotropy in isolated ex vivo goldfish muscle. Their data also provide convincing evidence that the radial restriction does not essentially involve the cell membrane. Kinsey et al.43 hypothesize that the sarcoplasmic reticulum and mitochondria are the principal intracellular structures that restrict diffusional transport of PCr in an orientation-dependent manner. Both have dimensions on the mm scale and have a structural

organization that is compatible with the observed anisotropy. The above 31P-data on PCr diffusion have been confirmed by Kruiskamp et al.44 using localized diffusion-weighted 1H-MRS of the creatine/phosphocreatine signal from rat and mouse skeletal muscle. The 1 H-MRS studies yield essentially the same values for the unbounded diffusion coefficient as that of PCr measured via 31P-MRS, as expected. Brain The majority of the metabolite diffusion measurements has been carried out on nervous tissue, primarily in vivo rat brain. Nakada et al.45 have studied the diffusivity of PCr in relation to brain maturation, by performing 31P PFG spin-echo measurements in newborn rat pups and in adult rats. These authors found that the ADC of cerebral PCr increases from 0.36 to 0.94 Â 10À9 m2 sÀ1 from the neonatal stage into adulthood. The developmental facilitation of PCr diffusivity was hypothesized to be primarily due to a decline in the concentration of the amino acid taurine and not to alterations in the tissue microstructure. These 31P-MRS findings are at variance with 1H-MRS data of metabolite ADCs in rat brain where a general decrease with age is observed while the PCr ADCs as such are also very high as compared to those found for tCr in 1H-MR studies. The reason for this apparent discrepancy is unclear. Cohen and coworkers46­48 have made fundamentally important contributions to the field of DW-MRS by their systematic studies in brain and nerve tissue. These authors have primarily focussed on the diffusional characteristics of N-acetyl-D-aspartate (NAA), using a large range of b-factors (up to 35 Â 104 s mmÀ2) and diffusion times (up to 300 ms). Examples of diffusionweighted 1H-MR spectra in rat brain and in bovine optical nerve at a diffusion time of 125 ms are shown in Fig. 7. The NAA signal attenuation curves are nonNMR Biomed. 2001;14:94­111

Figure 8. Displacement distribution pro®les of the choline signal in rat brain (dashed line), bovine optic nerve (k) (continuous line) and nerve (c) (dotted line) at a diffusion time of 125 ms (reproduced with permission from Assaf and Cohen).48

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Figure 9. Diffusion-weighted 1H-MRS of rat brain. (A, B) Series of localized 1H-MR spectra at increasing diffusion weighting. In the region 0.7±2.2 ppm (A) the dominant NAA signal is attenuated by approximately 40%, whereas the macromolecular resonances (MM) show no signi®cant attenuation as indicated by the dotted line (bmax, 5 Â 103 s mmÀ2). (B) The diffusion attenuation of the 1H-a-glucose resonance at 5.23 ppm suggests that a signi®cant fraction of cerebral glucose in vivo is located intracellularly where it exhibits diffusion restriction (bmax, 49.2 Â 103 s mmÀ2; tdiff, 118 ms; TE, 20 ms; TR, 4 s; volume, 100 ml; nt, 240 or 320; 1.5 and 3 Hz gaussian linebroadening). (C) Signal intensities of NAA (^), glucose (&) and lactate (Â). The measurements of the ADCs were performed at b < 5 Â 103 s mmÀ2 (C) and up to 50 Â 103 s mmÀ2 (D). The latter series illustrates the bi-exponential decay of the three metabolites. The ADCs of glucose and lactate are larger than that of NAA and most other metabolites. Note the equal slope at large b but different intercepts at b = 0, consistent with the different volume fraction of glucose and lactate as compared to NAA. Data were normalized to the signals without diffusion weighting. The error bars indicate the inter-assay variation in the log±linear plot, which are small for NAA. The data points from (C) are replotted in (D). The straight lines (dotted for NAA, solid for glucose, and dashed for lactate) indicate log±linear regression (reproduced with permission from Pfeuffer et al.).50

monoexponential and are adequately fitted to a biexponential decay (for NAA ADCs of 0.21 and 0.0047 Â 10À9 m2 sÀ1 were found at a diffusion time of 125 ms while the estimated fractions of the fast and slow diffusing components amounted to 47 and 53%, respectively). The ADCs decrease with increasing diffusion time. The relative population of the slow diffusing component decreases with increasing diffusion time. Both the slow and fast diffusing fractions of NAA show a considerable restriction in rat brain from which two compartments, one of 7­8 mm and one of ca 1 mm, were calculated with the Einstein­Smoluchowski equation [eqn (6)]. It was proposed that the two compartments represent the cell bodies and the intra-axonal space, respectively. Similar findings have been reported for choline and creatine. Measurements of this type underscore the potential of

Copyright 2001 John Wiley & Sons, Ltd.

metabolite diffusion measurements to non-invasively probe neuronal cell structure. Recently, Assaf et al.48 have reported the use of the qspace analysis49 as a promising means to extract structural information from DW-MRS. In the q-space approach, the displacement profile [i.e. the probability of the molecular translational displacement; equivalent to eqn (7)] is determined directly by Fourier transformation of the attenuation of the MR signal (at fixed PFG timing) with respect to q, the spatial wave number. The q-vector that is defined as (gg)/2p (in units of cmÀ1), determines the value of the diffusion-induced phase shift [see eqn (13)]. This type of analysis enables the estimation of the existence of restricted diffusion and the estimation of the compartment size. Restricted diffusion is immediately evident from the displacement curve as a deviation from

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a gaussian distribution function. An example of q-space analysis is depicted in Fig. 8, which shows the displacement probabilities for choline in rat brain and bovine optic nerve in two orientations. The graph shows that there are two compartments, one with a narrow and one with a broad displacement profile. The latter is less well defined because of the superimposed wiggles that are caused by insufficient signal loss in the raw data. The narrow displacement profiles are very similar in brain and optic nerve, the main difference being the relative size of narrow and broad displacement profiles. It is to be expected that the q-space approach is going to provide important novel information on the diffusion space for a variety of in vivo systems. Pfeuffer et al.50 have recently reported 9.4 T diffusionweighted 1H-MRS of rat brain, using b-factors up to 50 Â 103 s mmÀ2. Exploiting the excellent sensitivity and spectral resolution afforded by the high field strength, these authors were able to assess the diffusivity of 13 different cerebral metabolites. Figure 9(A) and (B) shows examples of 1H-MR spectra as a function of b-factor while a graphical representation of the measured attenuation curves is shown in Fig. 9(C) and (D). Both NAA (known to be localized in the intracellular compartment) and glucose and lactate display biexponential diffusion characteristics. Pfeuffer et al.50 found that in the high b-factor range the ADCs of glucose and lactate are similar to those of intracellular metabolites such as NAA, creatine and glutamate (0.025­ 0.030 Â 10À9 m2 sÀ1 for the slow diffusing component in the bi-exponential fit). This suggests that, at strong weighting, the glucose and lactate resonances predominantly originate from the intracellular space. This concept was used to estimate the distribution of glucose and lactate between the intra- and extracellular compartments and has provided evidence for an even distribution of glucose between these two tissue spaces. The fast diffusing components of the bi-exponential fits yield ADCs of the intracellular metabolites around 0.3 Â 10À9 m2 sÀ1. When the signal attenuation curves were fitted mono-exponentially,50 using only data points from the low b-factor range, the corresponding ADCs range from 0.10 to 0.14 Â 10À9 m2 sÀ1. Dreher et al.51,52 have achieved an improved spectral resolution at 4.7 T through the CT-PRESS technique that effectively results in homonuclear decoupling and greatly facilitates the measurement of strongly coupled resonances. They were able to quantitate the ADCs of 10 different metabolites in normal rat brain, using b-factors up to 5.5 Â 103 s mmÀ2. The measured ADCs of NAA, tCr and Cho are around 0.16­0.17 Â 10À9 m2 sÀ1, which is very similar to values reported previously by others for measurements with a similar b-factor range.15,53­55 An extensive DW-MRS study on human brain has been performed by Posse et al.35 at 1.5 T. In white matter, the effective diffusivities of NAA, tCr and Cho amounted to 0.18 Æ 0.02, 0.15 Æ 0.03 and 0.13 Æ 0.03 Â 10À9 m2

Copyright 2001 John Wiley & Sons, Ltd.

sÀ1, respectively. These values are very similar to the numbers quoted above for normal rat brain when similar parameters for diffusion weighting are utilized. As indicated earlier [eqn (6)], the diffusion coefficient is directly proportional to the mean square displacement in a certain direction. Typical pulse sequence parameters that have been reported in literature for collection of DWMRS, and the measured ADCs correspond to a root mean square displacement of about 2.5­3.0 mm for the major metabolites in rat brain.15,56 This is considerably shorter than the perikaryal diameter of neurons (ranging from 6 to 80 mm in human brain). Nevertheless, restrictions imposed by intracellular structures and the effects of tortuous diffusion pathways apparently cause the effective diffusion coefficients of the metabolites to be considerably lower than their in vitro values.

DW-MRS AND PATHOPHYSIOLOGY

Most of the recent in vivo DW-MRS studies have been carried out on tissues in the rat (primarily brain and to a lesser extent skeletal muscle and tumors) and were related to pathophysiological processes, such as ischemia,23,52,54­57 excitotoxicity,56 hydrocephalus58 and apoptosis.59,60 These pathophysiological studies have proven to provide valuable information on the biophysical processes that are sampled with in vivo diffusion MRS. Cerebral Ischemia and Excitotoxicity Quantitative diffusion-weighted 1H-MRS on cerebral ischemia and excitotoxicity has primarily been prompted by the well-known observation that the ADC of brain tissue water decreases rapidly following the initiation of ischemic stroke and excitotoxic injury (and several other acute forms of brain injury). Both ischemic and excitotoxic brain injury are acutely accompanied by cell swelling (cytotoxic edema) which leads to an expansion of the intracellular space at the expense of the extracellular compartment. Despite the widespread use of DW-MRI in experimental and clinical studies, the pathophysiological mechanisms underlying the water ADC changes remain poorly understood. Water is both present in the extra- and intracellular space and, most importantly, exhibits a rapid exchange between these two compartments by virtue of its ability to permeate cell membranes. This implies that the water ADC decrease could be due to the change in extra- vs intracellular volume ratio, to alterations in the intracellular compartment, the extracellular space or in the permeability of the cell membrane to water, or to combinations of these factors. This lack of mechanistic understanding of the water ADC change following acute cerebral injury has created a strong need for compartment-specific measureNMR Biomed. 2001;14:94­111

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ments of the extra- and intracellular diffusion space. The most abundant metabolites that are detected by 1H-MRS are primarily located in the intracellular compartment of the brain and therefore diffusion-weighted 1H-MRS offers excellent tools to specifically measure the intracellular response to cerebral injury. The ADC of cerebral metabolites decreases upon induction of focal and global ischemia. This has been observed in neonatal56 and adult rat brain,23,52,54,55 using localized 1H-MRS. Focal ischemia in adult rat brain typically results in a reduction in the ADCs of the major metabolites NAA, tCr and Cho from 0.14­0.16 Â 10À9 m2 sÀ1 to 0.10­0.12 Â 10À9 m2 sÀ1. The absolute ADC reductions induced by focal brain ischemia differ somewhat among the metabolites but the relative ADC reductions are remarkably similar, amounting to 25­30 % of the control values. The water ADC is reduced by ca 40% under the same experimental conditions. Global ischemia of the brain is accompanied by slightly stronger reductions in metabolite ADCs.15,54­56 Henriksen et al.61 have reported that the ADC of NAA is increased in human brain from 0.24 Æ 0.16 to 0.57 Æ 0.26 Â 10À9 m2 sÀ1 in the first days following stroke and remains elevated up to 60 days after the insult. To the best of our knowledge, this is the only human study related to pathology using DW-MRS of cerebral metabolites. The reason for the apparent discrepancy between the metabolite ADC findings in focal ischemia in animal studies and in Henriksen's study in man is unclear. Studies in animal models also show a trend towards a secondary increase in metabolite ADCs with development of tissue necrosis but the ADC values have never been observed to exceed control values.55,56 It is obvious that the interesting findings on reduced metabolite diffusivity in the early phase of experimental cerebral ischemia need to be carefully interpreted and that macroscopic changes induced by the insult should be ruled out prior to interpreting the ADC alterations in light of a microscopic intracellular response. Temperature effects do not significantly contribute to the ADC decrease.56,57 Similarly, the virtual absence of blood flow in focal ischemia and the complete perfusion arrest in global ischemia have been shown not to be directly relevant for the ADC reduction. The neonatal NMDAinduced excitotoxicity model of cell swelling is associated with similar metabolite ADC changes and yet exhibits an uncompromised cerebral perfusion.56 These observations in the neonatal rat also exclude the possibility that ischemia-induced tissue deoxygenation contributes to the metabolite ADC reduction via a misinterpretation of the diffusion-weighting b-factor.55 Rosenbaum et al.62 have found, by measuring the extracellular levels of NAA via microdialysis, that the DW-MRS assay of NAA diffusivity measures the displacements of intracellular NAA in the early phase of focal cerebral ischemia in the rat: the extracellular

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levels of NAA were negligible. Hence, alterations in the distribution of NAA between the extra- and intracellular compartment in brain are insignificant and therefore play no role in the reduced NAA ADC observed in acute ischemia. Dijkhuizen et al.56 have performed extensive studies in neonatal rats, using NMDA-receptor (over)activation as a means to pharmacologically induce a state of cell swelling. Intracerebral NMDA injection resulted in a pronounced reduction in the ADC of intracellular metabolites. Treatment of the NMDA-injected animals with the non-competitive NMDA receptor antagonist MK-801 led to a rapid normalization of the water ADC. Interestingly, the metabolite ADCs remained reduced for up to 2 h after MK-801 injection. At 72 h after MK-801 treatment the ADCs of all metabolites had returned to control levels. A similar diversion between the behavior of the ADCs of water and metabolites has been noted by Wick et al.54 using a model of transient global ischemia. The metabolite ADC decline partly persisted upon reperfusion (initiated 20 min after the onset of ischemia) while the water ADC readily recovered to baseline values. This suggests that the diffusion characteristics of intracellular metabolites are affected by a semi-permanent ischemia- or excitotoxin-induced cellular response that is not manifested in the water ADC. Duong et al.23 have recently performed ingenious diffusion-weighted 19F-MRS studies of rat brain in which they made use of the introduction of exogenous compounds to sample the intracellular as well as the extracellular diffusion space using the same molecule, i.e. 2-[19F]luoro-2-deoxyglucose-6-phosphate (2FDG6P). Through a judicious choice of routes of administration, 2FDG-6P was either confined to the extracellular or the intracellular space. Localization of 2FDG-6P in the extracellular space is achieved when it is administered directly via intraventricular infusion. The 2FDG-6P molecule can be confined to the intracellular compartment when its non-phosphorylated precursor, 2-[19F]luoro-2-deoxyglucose, is delivered via intravenous infusion. The rationale of this approach was to create compartment-specific indices of ADC changes in cerebral ischemia. The extra- and intracellular ADCs of 2FDG-6P amounted to 0.144 Æ 0.018 and 0.157 Æ 0.028 Â 10À9 m2 sÀ1, respectively, in vivo and were reduced to 0.086 Æ 0.012 and 0.099 Æ 0.021 Â 10À9 m2 sÀ1, respectively, in globally ischemic brain.23 Ischemia resulted in a 40% decrease in water ADC. The extracellular ADC reduction is in agreement with invasive microelectrode recordings of tetramethylammonium ion diffusion in the extracellular compartment.63 The 2FDG-6P data led Duong et al.23 to conclude that the intrinsic diffusion characteristics of the intra- and extracellular space of rat brain are virtually identical, as is its response to tissue ischemia. Neil et al.57 have used non-localized, surface coil 133Cs-MRS to assess the effects of acute ischemia on the diffusion of Cs, a K NMR Biomed. 2001;14:94­111

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Figure 10. Single-shot 1H-MRS trace ADC measurements in dead hydrocephalic rat brain. The PRESS-based MRS sequence depicted in Fig. 4 was used. A rat with kaolin-induced hydrocephalus was euthanized and measured 45 min later, using a 240 ml voxel that was placed around the enlarged ventricles. (A) Series of diffusion-weighted spectra, showing the resonances of NAA and lactate. Further parameters: D, 20 ms; , 6 ms; nt, 32; b-factors, up to 6.0 Â 103 s mmÀ2. NAA exhibits a monotonous decay, while the lactate signal decrease was ®tted adequately as a bi-exponential decay (B). The component with the rapid decay [labeled 2 in Fig. 10(B)] re¯ects lactate in the ventricles, while the slowly decaying component (labeled 1) represents tissue lactate (K. P. J. Braun, R. A. de Graaf and K. Nicolay, unpublished data)

analog that was introduced via the drinking water. This study reports on a ca 30% decrease in the ADC of intracellular Cs ions upon induction of global ischemia (from 0.90 to 0.65 Â 10À9 m2 sÀ1), in line with the above 1 H-MRS studies on metabolite diffusion. In a similar approach, Ramaprasad64 has introduced 7Li-ions into rat brain in order to establish the feasibility of diffusionweighted 7Li-MRS. This technique might be of value for studies on the assessment of lithium therapy. The ADC of Li-ions was found to be 0.25 Æ 0.05 Â 10À9 m2 sÀ1 in normal rat brain. Studies of tissue pathology using 7Li-MRS have not been reported as yet. What do the metabolite ADC changes that are consistently seen upon induction of ischemic and excitotoxic brain injury, report on? At present one can only speculate, and conclusive answers have to await further experimentation. The dynamic decrease in cerebral water ADC related to ischemia and excitotoxicity proceeds in essence in parallel to cell swelling.63 It is therefore appropriate to consider the possible consequences of an increased fractional volume of the intracellular compartment for the ADC of water and metabolites. A cell volume increase might reduce the influence of restriction effects on intracellular diffusion pathways which is expected to cause an ADC increase. The net influx of water (which forms the basis of cytotoxic cell swelling) might lead to a reduction in the viscosity of the cytoplasmic fluid phase. The viscosity argument also predicts an increase in metabolite ADCs rather than the observed ADC decrease. It seems plausible that the cell swelling argument does explain the reduction in the ADC of extracellular 2FDG-6P that was noted by Duong et al.23 Shrinkage of the extracellular space is accompanied by an increase in the

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tortuosity of the extracellular diffusion paths63 and this leads to a reduced ADC [see eqn (11)]. Possibly increased restriction effects also contribute to the drop of the extracellular metabolite ADC.23 It has been argued that ischemia- and excitotoxininduced cell swelling leads to an increased intracellular tortuosity,54,56 thus explaining the increased metabolite ADC. Swelling of cell organelles, disaggregation of polyribosomes, an increase in the number of cytoplasmic fibrillary structures (partly caused by fragmentation of the microtrabecular lattice and the cytoskeleton) and other factors65 have been put forward as possible causes for this effect. The intriguing finding that renormalization of the water ADC upon intervention in ischemia and excitotoxicity models is not directly followed by renormalization of the metabolite ADCs suggests that metabolite diffusivity is more sensitive to the above factors than water diffusivity. A final factor that has been mentioned as a possible contributor to the metabolite ADC reduction is the inhibition of cytoplasmic streaming (or `assisted' diffusion).16,19,20 This process may be interrupted by factors that cause cell injury and associated impairment of the energy status. Such a generalized, energy-dependent phenomenon would explain the reduction of the ADC of both intracelllular water and metabolites. Furthermore, it might provide a clue as to why the ADCs of the intracellular metabolites (at least those measured by 1HMRS in mammalian brain) have almost identical values. If `assisted' diffusion rather than random Brownian motion is the overriding process by which the intracellular displacements of these molecules occur, the diversity in their intrinsic diffusion coefficients as observed in vitro may be eliminated in vivo.

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Figure 11. Diffusion-weighted MRI of lactate in a RG2 glioma, using spectral editing via gradient-enhanced, multiple-quantum coherence (geMQC) ®ltering. (A) MR image of a subcutaneous RG2 glioma (matrix: 256 Â 128; FOV, 5 Â 5 cm2; slice thickness, 4 mm; TE, 100 ms; TR, 3 s) measured with adiabatic radiofrequency pulses and a single surface coil (diameter 2 cm). (B) Lactate image of the same slice (matrix, 32 Â 32) obtained using geMQC editing with adiabatic RF pulses. (C) ADC map of lactate as calculated from ®ve diffusion-weighted lactate images as in (B), using b-factors of 250, 1300, 2300, 3400 and 4500 s mmÀ2. Calculated ADC values range from 0.12 to 0.18 Â 10À3 mm2/s. (D) A MRS experiment on the same slice with the same diffusionweighting that certi®es that the lactate images are not contaminated by residual signal from water or lipid. The lactate ADC was estimated at 0.17 Â 10À9 m2 sÀ1. Note the excellent water (and lipid) suppression as is required for MRI studies of lactate distribution (F. A. Howe, and R. A. de Graaf, unpublished data)

The evidence presently available strongly suggests that the pronounced reduction in the ADC of water in cerebral ischemia is due to diminished translational displacements in both the extra- and intracellular compartment. Hydrocephalus Hydrocephalus is a pathologic condition that is most probably associated with diffuse tissue ischemia. Kaolininduced hydrocephalus in the rat is indeed accompanied by a prominent resonance from lactate (the end product of anaerobic glycolysis) in localized 1H-MR spectra.66,67 Braun et al.58 have made use of diffusion-weighted 1HMRS to assess the compartmentation of the cerebral lactate pool which is relevant for the understanding of the pathophysiology of hydrocephalus. The spectral data in their in vivo experiments were acquired with the singleshot trace DW-MRS pulse sequence illustrated in Fig. 4, using b-factors up to 6.0 Â 10À3 s mmÀ2. This sequence

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eliminates any ambiguity with respect to the orientational dependence of the diffusion attenuation.32 Extensive pilot studies had shown that metabolite ADCs in rat brain gray matter exhibit a significant degree of directional anisotropy, which is efficiently removed with the trace pulse sequence.32 The quantitative analysis of the attenuation curves of the NAA and lactate peaks in living hydrocephalic rat brain demonstrated that both NAA and lactate display a mono-exponential decay. The lactate ADC was six times higher than that of NAA, providing convincing evidence for the intraventricular CSF localization of lactate. Figure 10(A) shows a series of increasingly diffusion-weighted 1H-MR spectra of dead hydrocephalic rat brain, shortly after the animal had been euthanized. For clarity, only the NAA and lactate peaks are depicted. In this situation, NAA and lactate display a mono- and bi-exponential decay, respectively, as delineated in Fig. 10(B) for lactate. The ADC of NAA amounts to 0.11 Â 10À9 m2 sÀ1, which is reduced as a consequence of death, induced by anoxia. The two

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distinct lactate ADCs are estimated at 1.10 and 0.13 Â 10À9 m2 sÀ1. These numbers are essentially identical to the in vitro diffusion coefficient of lactate at 37°C and the in vivo ADC of intracellular metabolites, respectively. The former pool of lactate most probably resides in the cerebrospinal fluid present in the strongly enlarged ventricles. The slowly diffusing pool of lactate results from global ischemia-induced anaerobic glycolysis (since this fraction is absent in the live animal) and consequently is mainly present in the tissue, inside the cells. These data demonstrate the unique capability of DW-MRS to non-invasively assess the compartmentation of endogenous metabolites in situ. The studies by Pfeuffer et al.50 on glucose and lactate compartmentation in normal rat brain have been described in the previous section. Tumor tissue A limited number of DW-MRS studies has dealt with malignant tissue. Sotak et al.33,34 have performed pioneering studies with the use of zero and double quantum coherence MR spectroscopy for lactate editing. This procedure was used in order to eliminate the strong 1 H-MR signals from lipid molecules that are intrinsic to many tumors and basically co-resonate with the 1.3 ppm methyl protons from lactate. The coherence pathway selection procedure enabled the clean detection of lactate and the assessment of its diffusion characteristics. The lactate ADC was estimated at 0.21­0.23 Â 10À9 m2 sÀ1 in an H-MESO-1 human tumor xenograft implanted subcutaneously in a mouse.33 Lactate levels in tumor tissue may become sufficiently high to enable the imaging of lactate distribution and thus the spatially resolved measurement of the lactate ADC, using a MRI sequence combined with multiple-quantum coherence editing.68 An example of this potentially interesting approach is shown in Fig. 11, illustrating data that were collected from a subcutaneous RG2 glioma growing in a rat. It was assured that the 1H-MRS signal from the tumor only originated from the lactate CH3-protons. This was done using gradient-enhanced, multiple-quantum filtering.68 Figure 11(D) shows that this indeed results in a strong 1H-peak at 1.3 ppm and that residual water at 4.7 ppm (and overlapping lipids at 1.3 ppm) has a negligible intensity. This makes it possible to visualize the distribution of lactate by combining the editing sequence with spin-echo MRI (note that MRI and not spectroscopic imaging was used; the signal was sampled in the presence of a read-out gradient), thus providing a reasonably time- efficient experiment. A typical result of the lactate MR imaging is shown in Fig. 11(B). A series of diffusion-weighted lactate images was used to estimate a lactate ADC map [Fig. 11(C)], yielding ADCs ranging from 0.12 to 0.18 Â 10À9 m2 sÀ1. A series of DW-MR spectra from the entire slice [Fig. 11(D)] resulted in an

Copyright 2001 John Wiley & Sons, Ltd.

average lactate ADC of 0.17 Â 10À9 m2 sÀ1. Studies of this type may prove valuable for the monitoring of the distribution and the biophysical status of the lactate pool in tumor tissue. Remy et al.69 have studied the mobile lipid component in rat brain C6 glioma, using diffusion-weighted 1HMRS. The ADC of the lipids was found to be 0.046 Æ 0.017 Â 10À9 m2 sÀ1, which is orders of magnitude higher than the ADC expected for lipids present in plasma membrane microdomains. This led the authors to conclude that the mobile lipid pool detected by 1H-MRS is located in large lipid droplets, associated with tumor necrosis. Hakumaki et al.59,60 have studied BT4C glioma tumors ¨ in rat brain, using diffusion-weighted 1H-MRS. These authors have investigated the effects of thymidine kinasemediated gene therapy using treatment with ganciclovir. This approach has proven feasible for the therapy of various experimental malignancies. The cell damaging effect is most probably mediated by apoptosis that will ultimately lead to eradication of tumor tissue. The development of apoptosis-specific in vivo MR assays would represent a major step forward since the noninvasive monitoring of this mode of (programmed) cell death has not been achieved so far. A major morphological hallmark of apoptosis is cell shrinkage, while necrotic cell death is accompanied by cell swelling. Ganciclovir treatment caused profound changes in the status of water, metabolites and macromolecules in the tumor, as became evident using quantitative DW-MRS. The normal, non-tumor tissue remained unaffected by drug treatment. Water diffusion attenuation curves were analyzed with bi-exponential fitting. The rapidly diffusing water fraction increased from 87 to 94% while the corresponding ADC of this water pool increased by 219%. The ADC of the slowly diffusing water pool and macromolecules remained unaltered. Interestingly, the ADC of the choline-containing compounds decreased by 50% from its pre-treatment value of 0.14 Æ 0.01 Â 10À9 m2 sÀ1.59,60 Hakumaki et al.60 have performed extensive ¨ (non-MR) assays for apoptosis and on the basis of these they propose that the DW-MRS findings represent the in vivo MR signature of tumor apoptosis. The Cho ADC decrease accompanying apoptosis can be partly explained by increased restriction effects, caused by the reduced average cell size. The authors propose that an increase in the intracellular viscosity also contributes to this effect. The increased diffusivity of part of the tumor water is difficult to explain with this model. Since the Cho peak is known to originate from several different choline-containing compounds, possible alterations in the composition of this heterogeneous pool of molecules might be partly responsible for the observed changes in Cho ADC with ganciclovir therapy. Additional experiments are required to enhance the understanding of the relationship between the dynamic changes in water and metabolite diffusion characteristics in tumor apoptosis.

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The pioneering experiments by Hakumaki et al.,59,60 ¨ however, offer exciting prospects for the development of objective and quantitative MR-based assays for apoptotic cell death.

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CONCLUSIONS AND FUTURE PERSPECTIVES

Despite the complexity of the interpretation of in vivo diffusion-weighted MRS data, the technique offers unprecedented opportunities for assessing the biophysical chemistry of intracellular metabolites, from which (ultra)structural details of the intracellular compartment can be non-invasively inferred. There is a great need for the design of sophisticated in vitro and ex vivo model systems that can enable us to obtain a more quantitative understanding of the factors affecting metabolite diffusion. We should also aim for the development of biomathematical procedures that allow the modeling of the intracellular (and extracellular) diffusion process, starting with relatively simple geometries and gradually moving towards more complex and more realistic systems. The mathematical modeling should both aid in the interpretation of the experimental data and provide guidelines for enhanced experimentation.

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13. 14.

15. 16. 17. 18. 19.

Acknowledgements The MR research in the authors' laboratory was financially supported by the Netherlands Organization for Scientific Research (NWO) and the European Union Program for Access to Research Infrastructure (to the SONNMR-Large Scale Facility for Biomolecular NMR at the Bijvoet Center of Utrecht University). Kees Braun is a fellow of the Catharijne Foundation. Rick Dijkhuizen was supported by the Jan Ivo Foundation. Marijn Kruiskamp received financial support from the Netherlands Foundation for the Earth and Life Sciences. The authors are indebted to Gerard van Vliet for his expert technical assistance.

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