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Displacement imaging of spinal cord using q‐space diffusion‐weighted MRI

2000; Wiley; Volume: 44; Issue: 5 Linguagem: Inglês

10.1002/1522-2594(200011)44

1522-2594

Yaniv Assaf, Adi Mayk, Yoram Cohen,

Cervical and Thoracic Myelopathy

Magnetic Resonance in MedicineVolume 44, Issue 5 p. 713-722 Full PaperFree Access Displacement imaging of spinal cord using q-space diffusion-weighted MRI Yaniv Assaf, Yaniv Assaf School of Chemistry, Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, IsraelSearch for more papers by this authorAdi Mayk, Adi Mayk Teva Pharmaceutical Industries and Sackler Faculty of Medicine, Tel Aviv University, Tel Aviv, IsraelSearch for more papers by this authorYoram Cohen, Corresponding Author Yoram Cohen ycohen@ccsg.tau.ac.il School of Chemistry, Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, IsraelSchool of Chemistry, Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv 69778, Tel Aviv, Israel===Search for more papers by this author Yaniv Assaf, Yaniv Assaf School of Chemistry, Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, IsraelSearch for more papers by this authorAdi Mayk, Adi Mayk Teva Pharmaceutical Industries and Sackler Faculty of Medicine, Tel Aviv University, Tel Aviv, IsraelSearch for more papers by this authorYoram Cohen, Corresponding Author Yoram Cohen ycohen@ccsg.tau.ac.il School of Chemistry, Sackler Faculty of Exact Sciences, Tel Aviv University, Tel Aviv, IsraelSchool of Chemistry, Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv 69778, Tel Aviv, Israel===Search for more papers by this author First published: 31 October 2000 https://doi.org/10.1002/1522-2594(200011)44:5 3.0.CO;2-6Citations: 175AboutSectionsPDF ToolsRequest permissionExport citationAdd to favoritesTrack citation ShareShare Give accessShare full text accessShare full-text accessPlease review our Terms and Conditions of Use and check box below to share full-text version of article.I have read and accept the Wiley Online Library Terms and Conditions of UseShareable LinkUse the link below to share a full-text version of this article with your friends and colleagues. Learn more.Copy URL Share a linkShare onFacebookTwitterLinkedInRedditWechat Abstract Displacement MR images of water in in vitro rat spinal cord were computed from q-space analysis of high b value diffusion-weighted MRI data. It is demonstrated that q-space analysis of heavily diffusion-weighted MRI (qs-DWI) provides MR images in which physical parameters of the tissues such as the mean displacement and the probability for zero displacement of the water molecules are used as contrasts. It is shown that these MR images provide structural information surpassing the spatial resolution of conventional MRI by several orders of magnitude. This imaging methodology was used to follow spinal cord maturation in the rat. It was found that changes in the diffusion characteristics of white matter upon maturation are responsible for the emergence of gray/white matter contrast. The mean displacement of water molecules in the white and gray matter of the mature rat spinal cord was found to be 2–3, and 8–10 microns, respectively. The potential and the limitations of this new imaging methodology for early detection of white matter disorders are discussed. Magn Reson Med 44:713–722, 2000. © 2000 Wiley-Liss, Inc. Diffusion, as obtained from diffusion-weighted MRI (DWI), is known to be a valuable contrast mechanism in MRI of the CNS (1, 2). It was found to be extremely sensitive to early ischemic events (3, 4) and useful for the characterization of several brain pathologies (5-8). Until recently, in most DWI studies the well-known Stejskal-Tanner equation (9), shown in Eq. [1], was used for analyzing the signal attenuation. (1) This equation relates the normalized signal decay (Eg/E0) with the duration, time separation, and strength of the magnetic field pulse gradients (δ Δ and g, respectively), γ the magnetogyric ratio, and the self-diffusion coefficient D. However, the Stejskal-Tanner equation, in which signal attenuation is mono-exponential, applies only to a specific situation (namely, to a single population that exhibits unrestricted isotropic diffusion). Indeed, in most DWI studies performed to date mono-exponential decay and the presence of single water population was assumed (2-9). With recent advancements in gradient technology, it became apparent that the decay of the water signal in neuronal tissues in MR diffusion experiments is not mono-exponential, revealing at least two diffusing components (10-12) differing in their relaxation characteristics and diffusion time dependency (13). However, assignment of the various diffusing components to actual physiological compartments has been difficult and required extensive modeling that called for many assumptions (12, 14). We recently demonstrated that q-space diffusion-weighted magnetic resonance spectroscopy (MRS) can assist in making such assignments (15). As diffusion measurements using the pulse gradient spin echo or stimulated echo MR methods tag the observed spins at two time points, the echo intensity in NMR diffusion experiments should depend on the mean displacement of the observed spins (16, 17). This implies that proper analysis of diffusion in restricted compartments should yield structural information on the compartment in which the diffusion occurs (18). A decade ago, two groups demonstrated that Fourier transformation of the echo intensity, E(q), with respect to the so-called “reciprocal spatial vector,” q, defined as (2π)−1γδg, can provide structural information on (pseudo)-periodic samples (19-21). According to this approach the echo attenuation in NMR diffusion measurements relates to the displacement probabilities, using the reciprocal spatial vector q, according to Eq. [2], (2) where EΔ(q) represents the echo decay as a function of q, R is the displacement and s(R, Δ) is the displacement probability (19-21). The key feature here is the Fourier relationship between the echo intensity decay and the displacement probability. This means that in principle, under the narrow pulse approximation and at sufficient long Δ, one can obtain displacement probability profiles even in a complex system by only performing a Fourier transformation of the echo decay with respect to q (19-22). In the past decade, most q-space NMR diffusion applications were performed in the field of material sciences (20-24). q-Space studies dealt with pore-size and were used to obtain structural information on porous materials. Most recently, q-space diffusion NMR studies have begun to deal with biological systems (25-29). Gadian's group (25, 26) conducted a q-space spectroscopic study on normal and ischemic brain Kuchel et al. (27) resorted to this approach to study red blood cell size and shape (28, 29), and we availed ourselves of this approach to characterize both water and metabolite diffusion in neuronal tissues (15, 30). However, all these recent q-space diffusion NMR studies of biological systems dealt with NMR spectroscopy and therefore could not provide the spatial distribution of the extracted parameters (15, 19, 25-32). Here we present the first q-space diffusion-weighted MR images of rat spinal cord in vitro. We demonstrate that these MR images provide structural information surpassing the spatial resolution of conventional MRI by several orders of magnitude. We also demonstrate the sensitivity of this imaging by using it to follow rat spinal cord maturation. The potential and the limitations of this new imaging methodology for early detection of white matter disorders are discussed. MATERIALS AND METHODS Sample Preparation q-Space NMR diffusion spectroscopy was performed on freshly excised bovine optic nerves according to Assaf and Cohen (15). Imaging was performed on the excised spinal cord of rats at different ages (3, 7, 17, 28, and 77 days after birth, N = 4 for each group). The rats were sacrificed with an overdose of pentobarbital (300 mg/kg) and the spinal cords were excised from the cervical (c3–c5) or thoracic (t1–t6) cords and immersed in Flourinert (Sigma, USA) to avoid a non-tissue hydrogen signal and tissue dehydration. The total experimental time (for sample preparation and NMR experiments) was no longer than 3 hr after spinal cord excision. The temperature was kept at 36(±1)°C throughout the NMR measurements. MRS Experiments q-Space diffusion NMR spectroscopy of tert-butanol and freshly excised bovine optic nerve were obtained on a 11.7 T narrow-bore, ARX spectrometer (Bruker, Germany) with a 5 mm inverse probe equipped with self-shielded z-gradient coils capable of producing pulse gradients of up to 50 gauss cm−1, using a BGU/B-AFPA 10 system (Bruker, Germany). These experiments were performed with a diffusion weighted stimulated echo sequence (33) with the following parameters: TR = 3 sec, TE = 70 msec, δ = 15 msec. The pulse gradient strength was incremented from 0–27 gauss cm−1, and TM was incremented from 5 msec to 275 msec, resulting in diffusion time in the range of 35–305 msec. The maximal q value in these experiments was 1727 cm−1. In Vitro MRI Experiments MRI experiments were performed using an 8.4T spectrometer (Bruker, Germany) equipped with a micro5 imaging probe (Bruker, Germany) capable of producing pulse gradients of up to 190 gauss cm−1 in each of the three directions. Diffusion-weighted images were obtained, using a stimulated echo diffusion-weighted imaging sequence (33) with the following parameters: TR = 500 msec, TE = 30 msec, Δ = 150 msec, δ = 2 msec. The diffusion gradients were incremented between 0 and 150 gauss cm−1 in 16 equal steps. To qualitatively evaluate the effect of the diffusion time on the displacement distribution profiles in white and gray matter, diffusion imaging was performed on spinal cords of mature rats with diffusion times of 30 msec and 150 msec. The maximal b values in these experiments were 1.9 × 106 sec cm−2 and 9.6 × 106 sec cm−2 for a diffusion time of 30 and 150 msec, respectively. The maximal q value (qmax) in these MRI experiments was set to 1277 cm−1. To evaluate the effect of the maximal q value on the mean displacement extracted, diffusion experiments were repeated for mature spinal cords keeping all parameters constant and increasing the pulse gradient length, δ from 2 msec to 4.8 msec. In these experiments the maximal q value was 3065 cm−1. In this experiment, however, adequate signal-to-noise ratio (SNR) was obtained only up to a q value of 2265 cm−1. In all of the diffusion experiments the diffusing sensitizing gradients were perpendicular to the long axis of the spinal cord. Image Analysis The set of diffusion-weighted images was analyzed according to the q-space theory (19-21). Briefly, the 16 images were arranged in a (256 × 256 × 16) 3D array in which the x and the y coordinates are the image axes and the z direction is that of the q values. First, the noise level was calculated for ROIs outside the sample and then all pixels whose signal intensity was equal to or less than twice the noise level, were zeroed. The z direction was either zero-filled or extrapolated, using a multi-exponential decay function, to 128 data points to increase FT resolution. The effect of zero filling and extrapolation using a multiexponential function on the extracted displacement was explored. Since the extrapolation procedure was found to generate the experimental data (vide the infra) better, this procedure was used to generate the q-space MRI images. Then the signal decay in each pixel of the 256 × 256 matrix was transformed into displacement distribution profiles using Eq. [2]. The analysis was performed by a Fourier transform of the signal decay with respect to q according to Eq. [2], using an in-house Matlab® program. The Fourier transformation of the signal decay with respect to q produced a non-mono Gaussian displacement distribution profile for each of the pixel in the image. Two parameters of the displacement distribution profile, the mean displacement (calculated from the full width at half height using the mathematical procedure of Cory and Garroway (19)) and the probability for zero displacement (given by the height of the Gaussian profile at zero displacement) were then extracted by the Matlab® program for each pixel in the image. Finally, the Matlab® program was used to construct two sub-images based on these two parameters on a pixel by pixel basis (see Fig. 1). Figure 1Open in figure viewerPowerPoint A cartoon depicting the steps involved in obtaining the displacement and probability maps from a 2D DWI data set. Briefly, the 2D DWI data set is organized in a 3D array. An in-house Matlab program is then used to calculate the normalized signal decay (Eq,Δ) as a function of q for each pixel. The signal decay is then extrapolated and used to calculate the displacement distribution profiles by FT of the entire data set. Then the two parameters characterizing the displacement distribution profile of each pixel are computed and collected into two sub-images (for more details, see Materials and Methods). RESULTS Figures 2 and 3 show a q-space diffusion NMR spectroscopy of an isotropic solution of tert-butanol and of water in bovine optic nerve, respectively. The different behavior seen in these two figures exemplifies the potential of the q-space approach for characterizing diffusion in restricted compartments, as one would expect to find in the white matter of the central nervous system (CNS). Figure 2 shows that for an isotropic solution, where diffusion is unrestricted, the mean displacement obtained from a Fourier transformation (FT) of E(q) with respect to q increases with diffusion time (Fig 2b). Here the mean displacement (Fig. 1c), extracted from the full width at the half height of the mean displacement profile (ΔX0.5 (19)), follows the Einstein equation and therefore enables computation of the self-diffusion coefficient, D, as shown in Fig. 2c. Figure 3 shows the same analysis for water diffusion in bovine optic nerve when the diffusion was measured perpendicular to the long axis of the nerve fibers (15). Clearly, in this case the mean displacement did not grow with the increase in diffusion time and, hence, a deviation from the Einstein equation was observed (Fig. 3c). The data in Fig. 3 also imply that there is a large component of water molecules in optic nerve whose diffusion is restricted to about 1–2 microns at the range of diffusion time used in this study (Fig. 3b). In previous spectroscopic studies of water diffusion in brain tissue (13) and in optic nerve (15) we found that the slow diffusing population, which is restricted to about 1–2 microns, is much larger in white matter than in gray matter (15). This component is hardly changed when the diffusion time is increased by a factor of about 10. We also found that in optic nerve the relative fraction of the slow diffusing component strongly depends on the relative orientation of the diffusing sensitizing gradients and the fiber orientation (15). Based on these findings, we suggested that axonal water contributes significantly to this slow-diffusing component. Figure 2Open in figure viewerPowerPoint Characteristics of unrestricted diffusion exemplified by the diffusion behavior of a t-butanol solution showing (a) the normalized echo attenuation (Eq) as a function of the q values for different diffusion times (Δ), (b) the mean displacement obtained by Fourier transformation of the data shown in a, and (c) the root mean square (rms) displacement of t-butanol molecules as a function of (td)1/2. These values were computed from the data in b according to Ref. 19. From the slope of this graph the known self-diffusion coefficient, D, of 0.3*10−5 cm2 s−1 is calculated for t-butanol. Figure 3Open in figure viewerPowerPoint Diffusion characteristics of the water signal in bovine optic nerve when diffusion is measured perpendicular to the long axis of the nerve, showing (a) the normalized echo attenuation (Eq) as a function of the q values for different diffusion times (Δ), (b) the mean displacement obtained by Fourier transformation of the data shown in a, and (c) the rms displacement of the water molecules as a function of (td)1/2. These rms displacements were computed from the data in b according to Ref. 19. The rms displacement does not change with the increase in the diffusion time because of restriction. In this case the self-diffusion coefficient can not be calculated from the slope of this graph. Since the signals decayed only to 7.5–20% of their original values, their decay function was extrapolated using a multi-exponential decay function (see text for more details). Figure 4a shows the ROIs in the white and the gray matters of the spinal cord that were used to obtain the data presented in Fig. 4b. Figure 4b depicts the decay of the water signal in the white matter and gray matters of a mature rat spinal cord in vitro as a function of q when the diffusion was measured perpendicular to the long axis of the spinal cord and with a diffusion time of 150 msec. Figure 4c shows the displacement distribution profiles obtained by Fourier transformation of the data presented in Fig. 4b. Figure 4c shows that the ROIs in the gray and white matters are characterized by different displacement distribution profiles. In the white matter region the most prominent component is the one having a narrow displacement distribution profile while in the gray matter one observes a component with a much wider displacement distribution profile. In fact, under our measurement conditions, the broad component and the narrow component in the white and gray matters, respectively, are barely detectable. It should be noted that when the diffusion was measured parallel to the long axis on the spinal cords signal intensity was very low already in relatively low q-values, reflecting the high anisotropy of water diffusion in mature spinal cord. Therefore, the DWI data in Fig. 4 were obtained when the diffusing sensitizing gradients were perpendicular to the long axis on the spinal cord, as were all the data presented in this study. Figure 4Open in figure viewerPowerPoint a: A cartoon showing the ROIs selected for the analysis of signal decay in gray and white matter, b: normalized attenuation of the water signal as a function of q at a diffusion time of 150 msec for ROIs taken from the white and gray matter of a mature rat spinal cord, and c: the respective displacement distribution profiles obtained by FT of the data shown in b. Solid lines represent the experimental data and the dots show the extrapolation of the data. The difference in the displacement distribution profiles, as obtained from qs-DWI, can be used to differentiate between the gray and the white matter. As we wish to characterize heterogeneous samples, it is advisable to perform the q-space analysis for each pixel in the DWI images since this procedure should, in principle, afford new types of MR images. In these new MR images the physical mean displacement of the water molecules and their probability for zero displacement are used to create the contrast. Such mean displacement and probability q-space analyzed MR images of a mature rat spinal cord are presented in Fig. 5a and b, respectively. These images were obtained with a diffusion time of 150 msec. Both images show a very pronounced gray/white contrast. The extracted parameters (mean displacement and probability for zero displacement) of the gray and white matter differ by a factor of 2–3. The displacement MR image reveals that the mean displacement of water molecules in the white matter of a mature spinal cord is in the range of 2–3 μm. In the gray matter, however, it is within the range of 9–10 μm when the diffusion time is around 150 msec. In addition, according to Fig. 5b the probability for zero displacement is much higher in white matter-rich areas than in the gray matter of the mature spinal cord. Figure 5Open in figure viewerPowerPoint MR displacement (a) and probability (b) images of an excised spinal cord of a mature rat (see Methods). The contrast between the gray and white matter is very pronounced. The average displacement in the white and gray matter is about 2–3 μm and 8–10μm, respectively. The probability of zero displacement is much higher in the white matter than in the gray matter. Images were obtained with a diffusion time of 150 msec. The direction of the diffusion sensitizing gradients was perpendicular to the long axis of the cord. As we conjectured that the myelin network is a major contributor to the above difference between the gray and the white matter, we measured and analyzed the decay of the white matter water signal as a function of q for spinal cords of rats of different ages. Figure 6a shows the signal decay and Fig. 6b shows the displacement distribution profiles obtained from the Fourier transform of the data in Fig. 6a for spinal cords of rats of different ages. All these data were computed for the white matter region shown in Fig. 4a and at a diffusion time of 150 msec. These data show that maturation has a large effect on the diffusion characteristics of the water in the spinal cord. Interestingly, the data in Fig. 6b demonstrate that the diffusing component with the narrow displacement profile becomes larger as maturation progresses. Since myelination progresses with maturation it seems plausible that myelin formation is a major contributor to the large gray/white matter contrast in the mature spinal cord. This can be due to myelination that may either restrict inter-axonal water and increase the tortuosity of the extra-cellular space. Probably it is the summation of both effects that contribute to the above observation. Figure 6Open in figure viewerPowerPoint Effect of spinal cord maturation on a: the normalized decay of the white matter water signal in rat spinal cords as a function of q, and on b: the respective displacement distribution profiles obtained by FT of the data shown in a. The data was obtained when diffusion was measured perpendicular to the long axis on the cord, with a diffusion time of 150 msec. To demonstrate the ability of these new types of MR images to follow spinal cord maturation such images were computed for the spinal cord of rats at different ages. Figure 7 shows the displacement and probability MR images of spinal cord maturation in rats aged from 3 days to 10 weeks taken at a diffusion time of 150 msec. The mean displacement of the water molecules in the white matter decreased with age, reaching a value of about 2.2 ± 0.3 μm at the age of 10 weeks. At 3 days, the displacement in the white matter was similar to that in the gray matter (9.6 ± 0.2 μm and 9.8 ± 0.2 μm, respectively at a diffusion time of 150 msec). Significant changes were also observed in the probability images, in which the probability for zero displacement increased with age. Analysis of the pixels in the white and gray matter of newborn and mature rat spinal cord revealed that the contrast is formed due to a change in the diffusion characteristics of the white matter with maturation. As can be seen in Fig. 7, the mean displacement in the gray matter barely changed between day 3 (Fig. 7c) and day 77 (Fig. 7d). It is the dramatic decrease in the mean displacement in the white matter, from 9–10 μm to around 2–3 μm, that is responsible for the formation of the gray/white matter contrast in the mature spinal cord (compare Fig. 7e and f). These changes are probably due to the formation of myelin that causes an increase in restricted diffusion. Figure 7Open in figure viewerPowerPoint a: MR displacement images of excised rat spinal cords as a function of time after birth. b: MR probability images as a function of time after birth and the displacement distribution profiles of representative pixels taken from the gray (c) and the white (d) matter of a 3-day-old rat, respectively, and of the gray (e) and the white (f) matter of a 77-day-old rat, respectively. Note the dramatic change in the displacement and the probability characteristics of the white matter upon maturation. All images were collected with a diffusion time of 150 msec. Numerical values for displacement and probability for zero displacement taken from ROIs in the white matter of these spinal cords are graphically depicted in Fig. 8. It was found that the mean displacement and the probability for zero displacement reach their asymptotic values at around day 28. Figure 8Open in figure viewerPowerPoint Effect of maturation on the computed average displacement (a) and the probability for zero displacement of the water molecules in the white matter of the excised rat spinal cords (b). The formation of myelin, which seems to restrict water diffusion, may also influence the exchange rate of water between the different compartments. In the absence of myelin, water molecules may be able to diffuse more freely across these different compartments. Consequently, under these conditions water molecules might travel longer distances and should have wider displacement profiles. The effect of the exchange rate on the water signal decay can be assessed qualitatively from Fig. 9 that depicts water signal decay for several systems characterized by different exchange rates. Figure 9a and b shows the normalized signal decay as a function of the b values for different diffusion times for water in brain tissue and for choline in bovine optic nerve, respectively (13, 30). It is agreed that water exchange in brain tissue (Fig. 9a) is significantly faster than the exchange of metabolites such as N-acetyl aspartate (NAA) and choline in optic nerve, for example (Fig. 9b) (30). It is evident from these two graphs that the dependency of signal decay on diffusion time in these systems show opposite trends: while water signal decay increases with diffusion time, choline signal decay decreases. Interestingly, if one performs the same analysis on the water signal of a 7-day-old rat spinal cord and on a mature rat spinal cord, one finds the two types of behaviors (Fig. 9c and d, respectively). At the age of 7 days, this dependency is similar to that of water in brain tissues where the exchange is assumed to be fast (13) (compare Fig. 9a and c). However, in the white matter of a mature rat spinal cord this dependency was found to be similar to that observed for choline in bovine optic nerve (30), where the exchange is believed to be significantly slower compared to water (compare Fig. 9b and d). This can also be gathered from the q-space analysis of the data shown in Fig. 10. This figure shows that the mean displacement of water in the white matter of the spinal cord of a 7-day-old rat increases significantly with diffusion time. There the mean displacement increases from 2.3 ± 0.2 μm at a diffusion time of 30 msec to 6.6 ± 0.4 μm at a diffusion time of 150 msec. This increase in the displacement is similar to the expectation from the Einstein equation for free diffusion. However, in the white matter of a mature rat spinal cord the mean displacement remains the same with the increase in the diffusion time. In these cases, the mean displacements extracted are 1.9 ± 0.2 μm and 2.2 ± 0.2 μm at diffusion time of 30 and 150 msec, respectively. These results show that at 7 days, spinal cord water can diffuse more freely, attaining greater displacement as diffusion time increases as shown in Fig. 10a. However, with the formation of the myelin, water molecules reach the boundaries and consequently perform similar displacement at different diffusion times, as depicted in Fig. 10b. Figure 9Open in figure viewerPowerPoint Normalized signal decay as a function of b values at different diffusion times for the water signal in rat brain tissues (a), the choline signal in bovine optic nerve (b), the water signal originating in the white matter of the spinal cord of a 7-day-old rat (c), and for the water signal originating in the white matter of a mature rat spinal cord (d). In b–d the diffusion-sensitizing gradient direction was perpendicular to the long axis of the optic nerve and the spinal cord. Figure 10Open in figure viewerPowerPoint Displacement distribution profile of the water signal obtained from q-space DWI as a function of diffusion time for the white matter of the spinal cord of a 7-day-old rat (a) and the white matter in a mature rat spinal cord (b). The displacement profiles of water in the white matter of the mature rat spinal cord are barely affected by the fivefold increase in diffusion time. DISCUSSION The present work provides, to the best of our knowledge, the first q-space-analyzed MRI images of the CNS. In these new types of MR images, physical parameters of the tissues are quantified and used for creating the contrast in the images. Interestingly, the displacement MR image computed from q-space analysis of the DWI data provides structural information surpassing the spatial resolution of conventional MRI by several orders of magnitude. With the current technology displacement on the order of few microns can be measured. From q-Space Diffusion MRS to q-Space Diffusion MRI q-Space analysis of NMR diffusion experiments has been considered to be a valuable approach for analyzing the diffusion characteristics of complex systems (19-22). The main advantages of this analysis is that different diffusion processes can be readily identified by simply inspecting the temporal evolution of the displacement profiles with the diffusion time, and that some structural information can be obtained from this dependency without resorting to complicated models. q-Space NMR diffusion applications have been applied mainly in the field of material sciences and only infrequently to biologically oriented systems such as apple parenchyma (31), cellulose fibers (32), and red blood cells (27-29). Very recently, we demonstrated its use in obtaining