Assignment of the Water Slow-Diffusing Component in the Central Nervous System Using q-space Diffusion MRS: Implications for Fiber Tract Imaging

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1 FULL PAPERS Magnetic Resonance in Medicine 43: (2000) Assignment of the Water Slow-Diffusing Component in the Central Nervous System Using q-space Diffusion MRS: Implications for Fiber Tract Imaging Yaniv Assaf and Yoram Cohen* Diffusion-weighted NMR spectroscopy (MRS) was performed on isolated bovine optic nerve and rat brain (in vitro) to characterize the multiexponential water signal decay in diffusion experiments. q-space analysis of the diffusion data was used to obtain structural information about the investigated neuronal tissues. This analysis provided displacement distribution profiles of the water in the sample. Two diffusing components were identified from these profiles, thus enabling us to obtain the following information about the slow decaying component: 1) displacement of this component is restricted to a diffusing distance of approximately 2 m; 2) it has a longer T 2 than the rapidly diffusing component; and 3) the population fraction of this component depends on the orientation of the nerve fiber. When the diffusion was measured perpendicular to the long axis of the bovine optic nerve, the weighting of this population was 41 2%, whereas parallel to the long axis of the nerve it was found to be 14 2%. In the randomly oriented brain tissue, the population of this component was only 7 3%. These observations led to the conclusion that the slow-decaying component originates mainly from restricted water diffusion in the neuronal fibers. In view of these findings, in vitro and in situ diffusion-weighted images with high b values (with long ) were acquired to obtain highly detailed images of white matter fiber tracts in the central nervous system. These images provide detailed information on white matter fiber tract location and allow spinal cord maturation to be followed with high accuracy. Magn Reson Med 43: , Wiley-Liss, Inc. Key words: q-space; diffusion; MRS; white matter; diffusionweighted MRI (DWI) School of Chemistry, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, Israel. Grant sponsor: United States Israel Binational Science Foundation; Grant number: /1. *Correspondence to: Dr. Yoram Cohen, School of Chemistry, Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel. ycohen@ccsg.tau.ac.il Received 21 June 1999; revised 28 September 1999; accepted 30 September Wiley-Liss, Inc. 191 Biological tissues in general and brain tissue in particular are heterogeneous systems containing micron-scale compartments separated by impermeable and semipermeable membranes. Neuronal systems include several compartments that differ in size and shape (i.e., glial cells, neurons, neuronal fibers (axons and dendrites), myelin sheaths, and extracellular space). It is difficult to distinguish between the water signals of these compartments by NMR. However, if such separation is achieved, it may allow noninvasive detection of early and fine neuronal disorders and degenerative processes. Among the NMR techniques, diffusion seems to be very promising for differentiating between different tissue compartments (1,2). However, diffusion of water in biological systems, as computed from signal attenuation in NMRdiffusion experiments, is complex and difficult to interpret. The multiple exchanges of water between the compartments within the experimental diffusion time results in signal averaging and blurs the borders between the different compartments (1,3 5). Despite these difficulties, water-diffusion measurements are very important for revealing and characterizing several brain pathologies (i.e., ischemia (6,7), trauma (8), and brain tumors (9)) and disorders (i.e., spreading depression (10)). Diffusion-weighted MRI (DWI) is not limited to the detection of brain diseases but also enables the study of brain morphology by the anisotropic diffusion of water in the central nervous system. This phenomenon is pronounced in nerve fibers in which molecular diffusion is fast parallel to the long axis of the fibers and strongly perturbed perpendicular to it (11 12). Recently, the concept of diffusion tensor imaging (DTI) has shown that by measuring diffusion in several directions and using a mathematical procedure, one can obtain anisotropy maps. These anisotropy maps enhance the contrast between the isotropic areas (gray matter) and the macroscopically ordered areas of neuronal fibers (white matter) (13 15). Signal attenuation in NMR diffusion experiments depends on the mean displacement of the observed molecules. Therefore, the extracted apparent diffusion coefficient (ADC) in biological tissues may be affected by several experimental parameters such as the pulse gradients strength (g), their duration ( ), their separation (diffusion time, ), and direction. These experimental parameters determine the magnitude of the b factor, which controls the amount of diffusion weighting according to Eq. [1] (1,2,16): I g I o exp [ 2 g 2 2 ( /3)D] I 0 exp [ bd] [1] In Eq. [1], I g and I 0 represent the echo intensities in the presence and absence of diffusion gradients, respectively, is the magnetogyric ratio, D is the diffusion coefficient, and b,, and are defined above. In this formula, the relationship between signal decay and the diffusion coefficient is monoexponential. This equation describes the signal decay for a single population exhibiting free and unrestricted diffusion. In biological tissues, free and unrestricted diffusion cannot be assumed a priori, and, as mentioned above, the observed signal is generally a superposition of signals from several compartments. This complexity appears to be the cause of the multiexponential signal decay in NMR diffu-

2 192 Assaf and Cohen sion experiments on neuronal tissue obtained at high b values (17 19). Because processing of such data can no longer be carried out using Eq. [1], a mathematical model should be used to incorporate the effect of compartmentalization and exchange. An adequate mathematical model for diffusion in neuronal tissue has to include at least six parameters (at least three compartments, two fit parameters [size and decay rate] for each compartment) (20). The addition of exchange (21) and restricted diffusion effects would produce a model with many independent parameters that could fit almost any function. Thus, the information retrieved from such a model might be limited and would have to be interpreted with caution. An alternative approach to analyze diffusion experiments in which signal attenuation is multiexponential is to use q-space analysis (2,22). The q-space theory (2,22,23) describes NMR diffusion measurements in terms of displacement probabilities, using the reciprocal spatial vector, q, which is defined as ( g)/2 in units of cm 1. The magnitude of the q vector controls the echo intensity decay for displacements as indicated in Eq. [2] (2,22) E (q) P s(r, ) exp (i2 q R)dR [2] where E (q) is the echo decay as a function of q, R is the average displacement and P s (R, ) is the displacement probability. The importance of q-space analysis is the Fourier relationship between the echo intensity decay and the displacement probability given by Eq. [2]. This means that one can obtain displacement probability profiles even within a complex system only by performing Fourier transformation of the echo decay with respect to q, without making any assumptions or using complicated mathematical models. Such an analysis was performed on normal and ischemic brain (24,25), although no separation between the compartments was achieved, despite the changes observed as a result of ischemia. In the present study, we investigated the diffusion of water in bovine optic nerve and brain tissue. Because isolated nerve is a neuronal tissue that is more ordered than brain, the diffusion experiments should be easier to interpret. Although water diffusion in nerve is known to be multiexponential and anisotropic (20), the assignment of the different components observed in the diffusion experiments is still not clear. To clarify the assignment of the components of the multiexponential decay to physiological compartments, we used q- space analysis to obtain the mean displacement of the different components of the water signal in brain and nerve. We demonstrate how this approach assists in the assignment of the slow diffusing component to a physiological compartment. We also show that this assignment enables visualization of tissues rich in white matter and that diffusion weighting at high b values and long diffusion times can be used to follow spinal cord maturation. MATERIALS AND METHODS Tissue and Animal Preparation In vitro experiments were performed on freshly excised bovine optic nerves (N 3), rat brains (N 3), and rat spinal cords at different ages (3, 7, 17, 28, 42, and 77 days postnatally, N 4 for each age). The samples were immersed in Flourinert (FC-77, Sigma, USA) because it has no protons and because its susceptibility is similar to that of water. Orientation-dependent diffusion experiments were performed by placing the long axis of the nerve parallel to the diffusion gradient direction in one NMR tube and perpendicular to the diffusion gradient direction in another tube. The total experimental time (for sample preparation and the experiment itself) was no longer than 6 hr after excision. The temperature was maintened at 25( 1) C for brain and nerve experiments and at 37( 2) C for the spinal cord experiments. In situ experiments were performed on Sprague-Dawley rat brains (N 3) and spinal cords (N 3). The rats were sacrificed by an overdose bolus of 2 g/kg urethane (ethyl carbamate, Sigma, USA). To avoid cooling, the animal s body was warmed to approximately 37 C with a waterheating blanket. The total experimental time was no longer than 4 hr in each case. In Vitro MRS Experiments Experiments on bovine optic nerve and rat brain tissue were performed using an 11.7-T narrow-bore, ARX spectrometer (Bruker, Germany). Diffusion measurements were performed with a commercial 5-mm inverse probe equipped with self-shielded z-gradient coils producing pulsed gradients of up to 50 G cm 1, using a BGU/B- AFPA 10 system (Bruker, Germany). The diffusion of water in the nerve was investigated as a function of diffusion time (at a constant TE) and as a function of echo time (at a constant diffusion time). All experiments were collected using the stimulated echo diffusion sequence (26). In the diffusion time-dependent experiments, the following parameters were used: TR 3 sec, TE 70 msec, 15 msec. Pulsed-gradient strength was incremented from 0 to 27 G cm 1 (in 14 steps). T M was changed from 5 msec to 275 msec, resulting in diffusion times in the range of msec. The maximal b values in these experiments were sec cm 2 and sec cm 2 for the diffusion times of 35 msec and 305 msec, respectively. The maximal q value of these experiments was 1727 cm 1. In the TE-dependent experiments the following parameters were used: TR 3 sec, 15 msec, 130 msec. TE was changed from 70 msec to 550 msec as described previously (27). The pulsed gradient strength was incremented as above. The maximal b value in these experiments was sec cm 2 and the maximal q value 1727 cm 1. All diffusion experiments were repeated on a sample of oil and t-butanol to verify the accuracy of the measurements and to evaluate pulse-gradient stability throughout the entire gradient strength ranges using the specific experimental parameters used in the present study. These data were also used to verify the algorithm used to obtain the probability displacement functions (see below). In Vitro MRI Experiments In vitro MRI experiments on rat spinal cords at different ages (3, 7, 17, 28, 42, and 77 days postnatally, N 4 for each age) were performed using an 8.4 T spectrometer (Bruker, Germany). Diffusion-weighted images were acquired with a micro5 imaging probe (Bruker, Germany)

3 Water q-space Diffusion MRS in CNS 193 capable of producing pulse gradients of up to 190 G cm 1 in each of the three directions. Spinal cord imaging was performed on coronal slices of the cervical cord (C3 C5). Diffusion-weighted images were obtained using a stimulated echo diffusion weighted imaging sequence with the following parameters: TR/TE/ / 1000/30/150/2 msec. In these experiments, the diffusion gradients were 0 and 70 G cm 1. The direction of the diffusion gradient was perpendicular to the long axis of the spinal cord. The maximal b value in these experiments was sec cm 2. In Situ MRI Experiments In situ MRI experiments on rat brain (N 3) and excised rat spinal cords (N 3) were performed using an 8.4 T spectrometer (Bruker) equipped with a miniimaging accessory capable of producing pulse gradients of up to 20 G cm 1 in each of the three directions. Images were produced with a home-built surface coil (12 12 mm) having a 90 pulse of 40 sec for a 10-mm water sphere placed below the coil. Brain imaging was performed on a sagittal image placed at the level of the hippocampus. We chose this slice, because it contains highly ordered neuronal fiber areas (i.e., corpus collusom, corpus striatum) in addition to less ordered neuronal tissue (i.e., cortex). Spinal cord imaging was performed on coronal slices of the cervical cord (C3 C5). Diffusion-weighted MR images were obtained using a stimulated echo diffusion-weighted imaging sequence with the following parameters: TR/TE/ / 3000/40/130/12 msec. In the spinal cord imaging experiments, the pulsed gradients were incremented from 0 to 13 G cm 1 in 14 steps. The direction of the diffusion gradients was perpendicular to the long axis of the spinal cord. The maximal b value in these experiments was sec cm 2. In the DWI of brain, the diffusion gradients were applied in each of the three directions to assess diffusional anisotropy. The diffusion pulse gradient strength was adjusted in these experiments so that the calculated b value (including cross-terms) was sec cm 2 in one set and sec cm 2 in another set of experiments. Displacement Distribution Calculations Displacement distribution profiles were obtained by Fourier transformation of the echo attenuation with respect to the q value at fixed diffusion time according to Eq. [2]. The 14 data points were zero-filled to 64 points to obtain a higher resolution of the distribution probability profile (P S (R, )). The Fourier transform analysis was tested on the NMR diffusion experimental data collected for t-butanol and oil samples. Using the mathematical procedure of Cory and Garroway (28), the analysis provided the literature self-diffusion coefficients ( and cm 2 sec 1 for the t-butanol and the oil, respectively). The displacement distribution profile was fitted to a bi-gaussian function according to Eq. [3]: n P s i 1 A i w i /2 exp 2 x2 2 w i [3] where P s is the probability, A i is the area under the peak, w I is approximately of the width of the gaussian peak at half height and n 2. RESULTS The Effect of Diffusion Time on Signal Attenuation and on the Mean Displacement Water signal decay due to diffusion in rat brain and bovine optic nerve is multiexponential, as shown in Fig. 1, for a wide range of diffusion times. The data in Fig. 1 show that for both nerve and brain tissues (17) the decay is monoexponential up to a b value of approximately sec cm 2. At higher b values, multiexponential decay is evident. Figure 1 also shows that the dependency on diffusion time of the water signal decay in nerve is oppo- FIG. 1. Normalized attenuation of water signal (I/I 0 ) as a function of the diffusion time for (a) brain (N 3) and (b) nerve (N 3). Full and open symbols represent nerve data in which the diffusion gradient direction was parallel and perpendicular to the long axis of the nerve, respectively. Error bars were omitted for clarity. Errors were less than 3% for b values up to sec cm 2 and between 10 to 15% for higher b values.

4 194 Assaf and Cohen FIG. 2. Displacement distribution profiles as a function of diffusion time for (a) brain, (b) nerve in the parallel orientation, and (c) nerve in the perpendicular orientation with respect to the diffusion gradient direction. The profiles were obtained by Fourier transformation of the signal decay shown in Fig. 1 with respect to the q values. site to that in brain. As can be seen in Fig. 1a, when the diffusion time is increased, the signal decay becomes larger for brain tissue at a particular b value, whereas in nerve (Fig. 1b) the reverse is observed. The corresponding displacement distribution profiles, as obtained from q- space analysis of the data given in Fig. 1 are shown in Fig. 2. The displacement distribution profiles of the nerve show a clear separation into two diffusing components that are not apparent in the brain (Fig. 2b and c vs. Fig. 2a). Moreover, the fraction of the narrow displacement component is larger when the diffusion is measured perpendicular to the long axis of the nerve. Note that in this case, the displacement distribution profile has wiggles that result from truncation of the data due to insufficient signal decay. Interestingly, the narrow displacement component in nerve hardly changes with the increase in diffusion time (Fig. 2c). In brain we obtain a free-diffusion -like behavior (i.e., displacement becomes larger with the increase in diffusion time). This may indicate a higher degree of restricted diffusion in the nerve as compared with that in brain tissue. In the nerve experiments, in which diffusion was measured parallel to the long axis of the nerve, mixed behavior was detected: whereas the narrow component was not influenced by diffusion time, the displacement of the broad (fast) component became larger as diffusion time increased. The mean displacements extracted from the bi-gaussian fit of the displacement distribution profiles are given for several diffusion times in Table 1. It should be noted that although the displacement profile appears to be mono-gaussian in the brain, a better fit was obtained when a bi-gaussian function was used. This fitting revealed a small, but significant, brain water population that has a narrow displacement with relative weighting of several Table 1 Mean Displacement Obtained From the Half Height Width of the Fitted Gaussian Function for the Narrow Displacement Distribution Component of Brain Tissue and Nerve in Both Orientations a (msec) Brain Nerve // Nerve m 2.3 m 2.1 m m 2.1 m 1.9 m m 2.0 m 1.9 m a Calculated according to Ref. 28. percents. In brain tissues and in optic nerve in both orientations the probability for zero displacement decreases as the diffusion time increases. This decrease is more likely to result from the effect of exchange rather than from relaxation effect. At the long diffusion time (i.e., 305 msec) the exchange between the compartments is more pronounced. The Effect of Echo Time (TE) on the Water Signal Attenuation In principle, a multiexponential decay may originate from restricted water diffusion in a single compartment. This means that the above results do not necessarily indicate the existence of two distinct compartments. If there is only a single compartment, it is more likely that the different diffusing components will have a similar T 2, and any change in TE should not affect the signal decay. Therefore, we conducted a series of diffusion experiments (Fig. 3) in which the TE was changed from 70 msec to 550 msec. The corresponding graphical representation of these experiments is depicted in Fig. 4a. These experiments show that the multiexponential decay does depend on echo time, suggesting that each diffusing component have a different T 2 value. Moreover, it was found that the slow diffusing component has a longer T 2 than the other components. This conclusion can also be drawn from the q-space analysis (Fig. 4b) in which it is clear that the weighting of the narrow displacement component increases when TE is augmented. Fiber Tract Imaging Using High b Value DWI at Long Diffusion Time From the spectroscopic results, using q-space analysis, it is possible to obtain two components with different displacement profiles. This separation is much more pronounced in macroscopically ordered neuronal tissue such as optic nerve. Therefore, to further investigate the physiological origin of this diffusing component, we acquired a series of diffusion-weighted MR images of rat spinal cord, taken with different b values (Fig. 5). It is obvious that in the high b value range ( sec cm 2 ) the remaining signal originates mainly in the white matter of the spinal

5 Water q-space Diffusion MRS in CNS 195 FIG. 3. The attenuation of water signal in bovine optic nerve as a function of the gradient strength (g) when the diffusion is measured parallel to the long axis of the nerve for different echo time (TE). (a) TE 70 msec, (b) TE 200 msec, (c) TE 300 msec, and (d) TE 550 msec. In these experiments, the diffusion gradients were incremented from 0 (first row) to 27 G cm 1 (last row) in 14 equal steps and the diffusion time was 125 msec. cord. Signal decay as a function of b value and the displacement distribution profiles obtained from regions of interest (ROIs) containing the white matter and the gray matter of the spinal cord, are shown in Fig. 6a and b, respectively. The results clearly show the high weighting of the narrow displacement component in the white matter as compared with that in gray matter. In addition, the mean displacement of the narrow component in the spinal cord (2.6 m) is very similar to that found in brain and in optic nerve (Table 1). In brain tissue, neuronal tracts are usually less ordered and it is difficult to obtain large areas of white matter in the rat brain. Therefore, for diffusion-weighted brain imaging at high b value, we chose a sagittal slice in which the structure of the corpus callosum, corpus striatum, and cerebellum are clearly defined. In this slice T 2 -weighted image shows only little contrast (Fig. 7a), although the heavily diffusion-weighted images reveal good gray/white matter contrast (Fig. 7b d). From these images it is clear that at such a high b value ( sec cm 2 ) the remaining signal originates almost exclusively in the white matter-rich areas and only where the fiber tracts are perpendicular to the diffusion gradients (see Figs. 7b, c, and d). Also, the effect of anisotropy is evident. For example, the corpus callosum that is seen as a hyperintense area in Fig. 7b, is at the noise level in Fig. 7c. The only difference between these images is the direction of the diffusion gradients: in Fig. 7b the diffusion gradients are perpendicular to the long axis of the fibers, and in Fig. 7c they are parallel to it. DISCUSSION The goal of the present work was to further our understanding of the factors contributing to the decay of the water signal in NMR diffusion experiments in neuronal tissue. We also sought to assign the slow diffusing component to a physiological compartment, using q-space analysis and to demonstrate the value of q-space analysis in providing structural information on the sample on a micron scale. The detection of the multiexponential decay of the water signal in NMR diffusion experiments suggests that proper analysis may make it possible to distinguish between physiological compartments, based on their NMR diffusion characteristics. q-space analysis of the multiexponential decay of water signal allows information to be extracted on the system without resorting to a mathematical model to represent the system. Such an analysis may also afford a displacement map of the water molecules in the sample for a particular diffusion time. This is the main advantage of q-space analysis, as it provides information about the mean displacement, the physical parameter actually measured in NMR diffusion experiments. In neuronal tissue, where compartmentalization, exchange and restricted diffusion dominate the signal decay, structural information deduced from q-space analysis is very valuable. Diffusion Characteristics of the Slow-Diffusing Water Component The very slow diffusing component of the water signal in neuronal tissue prompted us to further explore its phys-

6 196 Assaf and Cohen FIG. 4. (a) Normalized signal attenuation (I/I 0 ) of the water signal in nerve when diffusion is measured in parallel to the long axis of the nerve as a function of echo time (TE). (b) Displacement distribution profiles for the signal decay shown in Fig. 3, reflecting the effect of TE on the displacement distribution profiles. FIG. 6. (a) Normalized signal attenuation of water as a function of q, and (b) displacement distribution profiles extracted from the signal decay of water in spinal cord white matter ROI (circles) and in spinal cord gray matter ROI (squares). FIG. 5. Diffusion-weighted images of rat spinal cord (in vitro) taken with a b value of (a) 0, (b) sec cm 2,(c) sec cm 2, and (d) sec cm 2. The following parameters were used: diffusion time 130 msec, TE 40 msec, maximal gradient strength 13 G cm 1. The diffusion gradient direction was perpendicular to the long axis of the spinal cord, in this case the x (read) direction.

7 Water q-space Diffusion MRS in CNS 197 FIG. 7. MR images of in situ rat brain at the hippocampal level taken with a b value of (a) 0,(b) sec cm 2, diffusion gradient applied in the y direction, (c) sec cm 2, diffusion gradient applied in the x direction, and (d) sec cm 2, diffusion gradient applied in the z direction. (e) Histological diagram of horizontal rat brain section showing areas of macroscopically ordered white matter fiber tracts. Abbreviations used: st, striatum; cc, corpus callosum; ce, cerebelum; sc, superior colliculus; hc, hippocampus. Reprinted with permission from Academic Press, Inc., Orlando, Florida (38). iological origin. The ADC of this component, detected at very high b values only ( sec cm 2 ), is in the order of 10 8 cm 2 sec 1. Interestingly, using q-space analysis, it has been found that this component is characterized by a very narrow displacement profile. The difference between the decay rates of the slow and fast diffusing components enables their separation using a bi-gaussian fit of the q-space analyzed displacement profiles. This procedure provides the population fraction of a particular component and its mean displacement. The following characteristics of the slow-diffusing component indicate that it apparently originates from water diffusion in the axonal milieu: 1) The weighting of the slow-diffusing component is much higher in optic nerve than in brain. The population of this component reaches 41 2% when diffusion is measured perpendicular to the long axis of the neuronal fibers, and only 7 3% when measured in the randomly oriented brain tissue. 2) The population of the slow-diffusing component is highly influenced by anisotropy. When measuring the diffusion parallel to the long axis of the neuronal fibers, the population fraction of the slow diffusing component is only 14 2% compared to 41 2% when measuring the diffusion perpendicular to the long axis of the fibers. In addition, the slow diffusion component, observed only at high b values, appears to have enhanced anisotropy (Table 2). 3) The diffusion of the slow-diffusing component is highly restricted and the measured mean displacement is influenced merely by diffusion time (Table 1). The diffusion is restricted to a diffusing distance of 2 microns, which resembles the average diameter of neuronal fibers. 4) Heavily diffusion-weighted images of brain and spinal cord acquired with large b values ( sec cm 2 ) contain a signal originating in areas of macroscopically ordered white matter tracts (see Figs. 5 and 7). At such large b values, the majority of the signal represents the slow decaying component. Thus, the origin of this component must be related to neuronal fibers. 5) The T 2 of the slow diffusing component is longer than that of the other diffusing components. 6) The above diffusional characteristics are very similar to those of brain and nerve metabolites (17,27,29). Assignment of the Slow-Diffusing Water Component Cumulatively, these observations led us to the conclusion that the slow-diffusing component originates mainly from restricted water diffusion within the neuronal fibers. However, there are two other plausible explanations that Table 2 ADCs and Anisotropy Factors Calculated From Diffusion- Weighted MR Images at Low and High b Values for an ROI Taken From White Matter of a Rat Spinal Cord b value (sec cm 2 ) (I/I 0 ) // (I/I 0 ) A 1 a ADC // b (cm 2 sec 1 ) ADC b (cm 2 sec 1 ) a Anisotropy factor calculated by dividing the signal decay in the parallel and perpendicular gradient directions. b ADC calculated based on two points (because of the multiexponential behavior). c Anisotropy factor calculated by dividing the ADC in the parallel direction and ADC in the perpendicular direction. A 2 c

8 198 Assaf and Cohen might account for the existence of the slow-diffusing component. The first refers to the diffusion of water between the myelin membrane walls. Water molecules, trapped between the myelin membranes (averaged space of less than Å (30)), strongly interact with the phospholipid myelin membrane and other proteins and, thus, are expected to have a low ADC and a very short T 2. This is in contrast to our finding that the slow-diffusing component has a long T 2. Recent studies showed that the degree of myelination controls the extent of the water signal increase caused by magnetization transfer (31,32). This supports the notion that water molecules that are trapped between the myelin walls have indeed a very short T 2 and do not contribute to the observed water signal collected at relatively long TE. The second possibility is that restricted diffusion of water molecules in a single compartment may result in a multiexponential signal decay. This premise is based on the finding that even in one compartment system with simple restriction boundaries multiexponential decay was observed (33). However, the pronounced anisotropy of the slow-diffusing component and the fact that the various components have different T 2 values, makes this explanation less plausible. In addition, diffusion-weighted imaging with large b values shows that the slow-diffusing component population is larger in white matter areas. All these observations indicate that the majority of the slow-diffusing component originates from diffusion within the neuronal fibers. High b Value DWI at Long Diffusion Time-Potential Applications The observation that diffusion-weighted images enhance the contrast between gray and white matter is not new (11 12,34 35). DTI that is based on the anisotropy of water diffusion in white matter obtained at low b values enhances the contrast between gray and white matter (13 15). However, DTI requires, in addition to calculations, the acquisition of a large number of images with a good signal to noise ratio (SNR), rendering it time consuming. Imaging at high b values provides some of these advantages much more readily. For example, the anisotropy factor increases considerably and, consequently, the gray/white matter contrast is augmented (see Table 2). This increase might be very helpful when imaging early white matter disorders. This is clearly demonstrated in Fig. 7, which shows that DWI with the above experimental parameters (high b value, long diffusion time) accentuate fiber-track rich regions as compared to other brain areas. To further emphasize this point, we simulated the population fractions of the slow and the fast components as a function of b value (Fig. 8). The simulations were performed using two sets of possible physiological conditions for the two diffusing populations. The simulations show that when a b value of approximately sec cm 2 is used, most of the signal in the image is that of the slow-diffusing component, which is believed to originate from axonal water. In contrast, when using a low b value of sec cm 2, the contribution from the two components is in the same order of magnitude. At a b value of approximately sec cm 2, as used in most DWI studies, the majority of the signal represents the fast diffusing component. If we FIG. 8. Simulation of the relative weighting of each component as a function of the b value. The following parameters were used in the simulations: (a) D cm 2 sec 1 and D cm 2 sec 1 with weighting of A 1 95% and A 2 5%, respectively; (b) D cm 2 sec and D cm 2 sec 1 with original weighting of A 1 95% and A 2 5%, respectively. assume that the slow diffusing component originates from the axonal milieu, one might anticipate that white matter disorders would cause changes in the slow-diffusing population. Therefore, an imaging protocol that uses high b values should be more helpful in tracking such abnormalities. To further underscore this point we plotted in Fig. 9 the normalized residual water signal in the white matter of the rat spinal cord at a b value of sec cm 2 as a FIG. 9. In vitro normalized signal intensity in heavily diffusionweighted MR images of white matter rat spinal cord as a function of age. Experimental parameters: TE 30 msec, 150 msec, 2 msec, g 70G cm 1, and b value sec cm 2.

9 Water q-space Diffusion MRS in CNS 199 function of rat age. The data clearly demonstrate that high b value diffusion weighted images enable a follow up of spinal cord maturation with great accuracy, demonstrating the potential importance of this type of MR images in monitoring brain maturation and/or brain degeneration. Also, these results corroborate our assignment that the slow diffusing component is related to intra-axonal water diffusion, which is less restricted at the nonmyelinated newborn spinal cord. The relative weighting of the slow diffusing component increases as myelin forms (Fig. 9). CONCLUSIONS We assigned the slow-diffusing component of the multiexponential signal decay of water in neuronal tissues to restricted diffusion of water perpendicular to the long axis of neuronal fibers. These kinds of experiments, combined with q-space analysis, gives direct structural information about the tissue and may indicate the pathophysiological state of the neuronal fibers. q-space analysis of NMR diffusion data provides structural information on a micron scale. We showed that diffusion-weighted imaging at large b values and long diffusion time could be used to better visualize areas rich in white matter thus allowing spinal cord maturation to be followed with great accuracy. The full diagnostic capacity of high b value DWI for detection of axonal pathologies and white matter disorders remains to be evaluated. ACKNOWLEDGMENTS This research was supported by Grant No /1 from the United States-Israel Binational Science Foundation (BSF), Jerusalem, Israel. REFERENCES 1. Le Bihan D. Diffusion and perfusion magnetic resonance imaging. New York: Raven Press; Callaghan PT. Principles of nuclear magnetic resonance microscopy. Oxford: Clarendon Press, Le-Bihan D. 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