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Multicomponent water proton transverse relaxation and T2-discriminated water diffusion in myelinated and nonmyelinated nerve
Magnetic Resonance Imaging, Vol. 16, No. 10, pp. 1201–1210, 1998 © 1998 Elsevier Science Inc. All rights reserved. Printed in the USA. 0730-725X/98 $19.00 1 .00
PII S0730-725X(98)00151-9
● Original Contribution
MULTICOMPONENT WATER PROTON TRANSVERSE RELAXATION AND T2-DISCRIMINATED WATER DIFFUSION IN MYELINATED AND NONMYELINATED NERVE CHRISTIAN BEAULIEU, FRANCES R. FENRICH,
AND
PETER S. ALLEN
Department of Biomedical Engineering, University of Alberta, Edmonton, Alberta, Canada The influence of compartmental boundaries on water proton transverse relaxation and diffusion measurements was investigated in three distinct excised nerves, namely, the non-myelinated olfactory nerve, the Schwann cell myelinated trigeminal nerve, and the oligodendrocyte myelinated optic nerve of the garfish. The transverse relaxation decay curves were multiexponential and their decomposition yielded three primary components with T2 values ;30 –50, 150, and 500 ms, which were subsequently assigned to water protons in the myelin, axoplasm, and interaxonal compartments. The short T2 component was absent in the non-myelinated olfactory nerve, but present in both myelinated nerves and thus provides supporting evidence for the use of quantitative T2 measurements to measure the degree of myelination. The signal contribution of each T2 component to the apparent diffusion coefficient measurements was varied by incrementing the spin-echo time with a preparatory CPMG train of radiofrequency pulses. The apparent diffusion coefficient and its anisotropy were shown to be independent of the spin-echo time over the range of 70 to 450 ms. © 1998 Elsevier Science Inc. Keywords: Diffusion; Nerve; Nuclear magnetic resonance; Transverse relaxation.
consistent with several exponential components, both in vitro and in vivo.1–11 The individual T2 components have been interpreted in terms of different water compartments, such as inter-axonal, axonal, and myelin domains, within the heterogeneous tissue. There is considerable evidence from several laboratories to support this hypothesis. First, T2-weighted microimages of the crayfish abdominal nerve cord clearly differentiate axonal water from that in the surrounding inter-axonal spaces.4 Further support of compartmentalization and in particular the assignment of myelin to the short T2 component can be found in the reduced amplitude of the short T2 component as demyelination takes place in the white matter and spinal cord of guinea pigs induced with experimental allergic encephalomyelitis,5 and in the association of a disappearing short T2 component in frog sciatic nerve, in vivo, when progressive nerve degeneration and concomitant myelin loss takes place.10 Moreover, the correspon-
INTRODUCTION Although the spatial resolution of magnetic resonance imaging (MRI) as practiced clinically is sufficient to resolve individual organ sub-structures, e.g., the basal ganglia or white matter tracts in brain, it is insufficient to resolve structures on a cellular level. However, even though they cannot be resolved spatially, it may well be possible to distinguish between distinct microstructures through their nuclear magnetic resonance (NMR)-governing water characteristics because these characteristics can vary between the different cellular structures while remaining quite uniform within each type of cellular structure. For example, the transverse decay of the water proton magnetization in heterogeneous tissue such as nerve, white matter, or spinal cord can only rarely be described by a single exponential. Instead, the relaxation curves obtained from these tissues are generally found to be RECEIVED 2/2/98; ACCEPTED 7/3/98. Address correspondence to Peter S. Allen, c/o Department of Biomedical Engineering, 10 –102 Clinical Sciences Bldg., University of Alberta, Edmonton, Alberta, T6G 2G3. Email: [email protected]
Present address of C. Beaulieu c/o: Department of Radiology, Stanford University, Palo Alto, CA, 94305-5488. Present address of F. R. Fenrich c/o: Space Sciences Lab, University of California, Berkeley, CA, 94720. 1201
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dence of known distributions of myelin with short T2 component maps in human brain7,11 also reinforces the hypothesis. However, a direct comparison of the transverse relaxation time distributions between structurally intact myelinated and non-myelinated nerve, which would test the association of the short T2 component with myelin water is lacking. If T2 component assignments could be established definitively, then changes in their proportions, when experimentally quantifiable in vivo, may provide a measure of compartmental degradation in white matter with multiple sclerosis7 and in nerve with wallerian degeneration.10 In addition to the transverse relaxation behaviour of water protons, their apparent diffusion coefficient (ADC) and its potential anisotropy might also be expected to vary with their microstructural environments. Certainly at a macroscopic level, the anisotropy of ADC reflects the substructural arrangement of the ordered axons in the white matter of cat12 and human brain,13 and in excised garfish nerve.14 However, the overall ADC is a function of the individual compartmental ADCs, T2s, and proton populations in heterogeneous tissue such as nerve. A better characterization of water diffusion in nerve could result if the ADC were measured in the individual compartments. If, for example, one could determine compartmental differences (or similarities) in ADC (i.e., intraversus inter-axonal), the proposed mechanisms for the reduction of ADC in acute stroke might be better established.15 The overall goal of the work presented here was to provide more definitive evidence of compartmentalization in nerve water T2 and ADC by utilizing the garfish model with its three markedly different cranial nerves, one non-myelinated (the olfactory), one from the peripheral nervous system myelinated by Schwann cells (the trigeminal), and the other from the central nervous system myelinated by oligodendrocytes (the optic). In order to test the correspondence of myelin with the short T2 component observed in nerve and in white matter, the T2 distribution of normal non-myelinated nerve was compared to normal myelinated nerve. In addition, the assignment of a compartmental structure based on T2 components was a prerequisite to the exploration of the compartmental ADC in the present work. The ADC measurements presented here preferentially discriminated against water in faster relaxing compartments by utilizing a train of p radiofrequency (RF) pulses to increase the echo time, in a manner similar to van Dusschoten et al.16 In contrast, previous work has isolated compartment ADC characteristics by choosing a model in which a single compartment overwhelmingly dominates, namely, the giant axon of the squid.17
MATERIALS AND METHODS Sample Preparation The olfactory, the trigeminal, and the optic nerves of 18 garfish were excised and immediately stored in appropriate Ringer’s solution.18 The outer connective tissue sheath of each optic nerve was also removed. Twelve of the garfish were used for the T2 analysis and six were used in the evaluation of diffusion characteristics. For the T2 measurements, the nerve samples were placed in 5-mm diameter NMR tubes (one tube for each nerve) and bathed with buffer. For the diffusion measurements, the freshly excised nerves were quickly dried and transferred to paraffin oil (to prevent them from dehydrating during the measurements) and individually aligned in capillary tubes in order to facilitate the determination of diffusional anisotropy relative to the long axis of the nerve. In contrast to the preparation for T2 analysis, buffer was not used as the bathing medium during the diffusion measurements. This was because the buffer water signal, which in T2 measurements can be readily separated from nerve water, seriously contaminates the nerve water signal in diffusion measurements. Previous diffusion experiments on the garfish nerves have shown that immersion of the nerves in paraffin oil does not affect the nerve water diffusional characteristics.14 Others have also used light oils to prevent dehydration of tissue samples.19,20 The viability and structural integrity of the nerves throughout the duration of the NMR experiment was confirmed with electron microscopy (EM) and action potential measurements. Furthermore, direct comparison of in vitro and in vivo measurements made in this laboratory of T2 in frog sciatic nerve show that they correspond quite well.8 Representative EM sections of the olfactory, trigeminal, and optic nerve are shown in Fig. 1 and the relevant physical characteristics of the garfish nerves have been described previously.14 NMR Measurements and Analysis All NMR measurements were carried out at room temperature (;20°C) in a 40-cm bore Bruker CXP spectrometer (Bruker Instruments, Billerica, MA, USA) operating at a proton frequency of 100.19 MHz. The sample tube containing a given nerve type was located centrally in a small solenoidal RF coil. The transverse relaxation decay curves were acquired using a 4096 echo Carr-Purcell-Meiboom-Gill (CPMG) add/subtract sequence21,22 with an inter-echo spacing, t, of 1.6 ms. The p pulses were 10 ms in duration and the sequence repetition time was 20 s. In order to reduce baseline errors caused by inaccurate p pulses and receiver DC offsets, the pulse sequence was phase cycled over 16 add/subtract sequences.23 Typical proton line widths were 30 Hz. The signal-to-noise ratio (SNR), given by the ratio of the
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Fig. 1. Electron micrographs of transverse sections from the olfactory (A, B), trigeminal (C), and optic (D) nerves of the garfish. (A) Schwann cell domains (SD), which consist of many nonmyelinated axons (see B) enveloped together by a Schwann cell wrapping, are seen in the olfactory nerve. Connective tissue channels (CT) separate the Schwann cell domains. (B) This high magnification EM shows the individual axons (AX) bounded by their axonal membrane (x) in the olfactory nerve. The axons are very homogeneous in size (;0.2 mm diameter) and are packed together tightly. Microtubules (arrowhead), neurofilaments (arrow), and mitochondria (M) can be distinguished within the axoplasm. (C) Intact myelin sheaths (MY) are seen surrounding the axons (AX) in the trigeminal nerve. Axons are myelinated by Schwann cells (SC) in peripheral nerves. (D) The multilamellar nature of the myelin sheath (MY) is evident in these myelinated axons of the optic nerve. The axonal membrane (x), neurofilaments (arrow), and microtubules (arrowhead) are also visible.
signal at an echo time of 1.6 ms and the standard deviation of the noise, was typically 3000. The demands of a short echo spacing (1.6 ms) to minimize losses of transverse magnetization due to diffusion in local field inhomogeneities, and the long acquisition range (1.6 ms to 6.6 s) required to sample the relaxation decay curve adequately, together gave rise to a large number of echoes (4096). However, in order to limit computational demands, it was found necessary to use only 230 of the 4096 echoes for the T2 algorithm. Specifically, the 4096 point decay data set was reduced to a 230 point decay data set by sampling every point from 1.6 ms to 40 ms, every 4th point from 40 ms to 200
ms, every 8th point from 200 ms to 500 ms, and finally every 24th point from 500 ms to 6.5 s.4 This procedure was adopted to approximate logarithmic sampling and thereby maintain equitability for each of the component relaxation times. The inversion of the reduced multiexponential decay data set into a continuous distribution of relaxation times was accomplished using the non-negative least squares algorithm of Lawson and Hanson,24 as modified by Whittall and MacKay.25 This algorithm is a linear inverse technique that is stable, has the significant advantage of requiring no a priori guess of the number of components, and produces a continuous distribution of the relaxation times which is a realistic description for
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Fig. 2. CPMG-diffusion pulse sequence in which the rectangular gradient strength, Gi, is incremented, the timings d and D represent constant time intervals, and TE is increased by incrementing the number of intervening hard p RF pulses (n) spaced by t. The train of hard p pulses was closely spaced to minimize losses in transverse magnetization due to diffusion in the presence of susceptibility gradients. The acquisition time (AQ) for the echo peak is 10 ms.
biologic tissue.26 The different T2 components were identified as distinct peaks in the continuous distribution. Each component population was determined by summing the grid point amplitudes comprising that component while the T2 value was determined by a weighted average of the component T2 grid points. To prevent spurious T2 components arising due to the fitting of noise, all solutions maintained a chi-squared misfit corresponding to the 99% confidence level. Simulation tests of resolution indicate that with an SNR of 3000, we can expect to resolve components with a minimum factor of ;2 between peak relaxation times.27 For the diffusion coefficient measurements, a homemade gradient coil (3 cm bore) provided the diffusionsensitizing rectangular gradient pulses {available strengths: Gz, max ; 1.61 T m21, Gx, max ; 0.64 T m21} employed in a Stejskal-Tanner spin-echo diffusion sequence.28 However, the sequence was modified (Fig. 2) with a preparatory CPMG subsequence21,22 in order to select the T2 range of the water proton magnetization entering the diffusion measuring sequence. The train of hard p pulses was closely spaced to minimize losses in transverse magnetization due to diffusion in the presence of susceptibility gradients. Moreover, to excite the nerve water protons selectively from the protons of the bathing paraffin oil, 1331 (p/2) and 2662 (p) binomial RF pulses29 were employed, whose component lengths were multiples of 1.25 ms and whose separations were 1.316 ms. The gradient pulse timings (d 5 6 ms, D 5 30.128 ms) were kept constant while the gradient strength, Gi, was incremented to a maximum of ;0.12 T m21 thereby yielding a maximum gradient factor, bmax, of ;1 3 105 s cm22 where b 5 g2Gi2d2(D 2 d/3)30 and g is the magnetogyric ratio of the protons. The remaining symbols are defined in Fig. 2. The spacing between successive hard p pulses of the preparatory CPMG sequence, t,
was 5 ms, and the number (n) of such pulses was either 2, 18, 38, 58, or 78 giving rise to overall spin-echo times (TE) of 70, 150, 250, 350, or 450 ms, respectively. The minimum (70 ms) and maximum (450 ms) spin-echo times arose respectively from limitations of the gradient hardware and from the available SNR. Echoes were averaged over 4, 8, or 16 scans depending on SNR with a repetition interval of 5 s (20 s for the comparative distilled water sample). At each TE, ADC values were obtained from single component fits (5 data points per ADC) of the diffusion decay curves {ln[(echo amplitude, Gi Þ 0)/(echo amplitude, Gi 5 0)] versus b} measured both parallel and perpendicular to the axis of the nerve. Comparisons within the various groups were made with the Student’s t test and the level of significance was defined as p # 0.05. To verify the accuracy and isotropy of the ADC over a range of spin-echo times, self-diffusion measurements were performed on distilled water. Doing so demonstrated the isotropy of diffusion {i.e., ADC(//) 5 ADC(')} and a mean ADC value that was within 5% of the accepted self-diffusion coefficient of pure water at 20°C.31 The decay of spin-echo amplitudes resulting from the CPMG-diffusion composite sequence when Gi 5 0, conformed to the T2 when measured with the CPMG sequence alone for both nerve water and tap water. In particular, a T2 of 2140 ms was measured for tap water using the former sequence versus a T2 of 2150 ms for the latter sequence. RESULTS Typical transverse relaxation time distributions for the non-myelinated olfactory, myelinated trigeminal, and myelinated optic nerves are presented in Fig. 3. A summary of the component populations and relaxation times are given in Table 1. All three types of nerve have a long T2 component ;500 ms and a medium T2 component ;150 ms. However, a substantial component with a T2 between 30 ms and 50 ms is only seen in the myelinated trigeminal and optic nerves. The relaxation component due to the buffer (T2 ; 2.2 s) is not shown in either Fig. 3 or Table 1. The effect of the CPMG preparation phase of the composite CPMG-diffusion sequence is presented in Fig. 4. These curves illustrate the reduction of nerve water proton transverse magnetization as the preparation phase, and therefore the effective TE, was incremented with Gi set to zero. Approximately 50 to 65% of the initial proton magnetization of nerve water persisted at TE 5 70 ms whereas only ;5–10% of the original signal survived at TE 5 450 ms. The residual signal from nerve water following CPMG preparation is in agreement with that expected from the component T2 values and their respec-
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Table 1. Summary of transverse relaxation times and component populations in the nonmyelinated olfactory nerve, and the myelinated trigeminal and optic nerves*† Nerve Olfactory Trigeminal
Optic
T2 Component‡
T2 (ms)
Population (%)
A B D A B C D A B C D
510 6 90 170 6 20 17 6 10 460 6 50 140 6 20 34 6 5 863 480 6 40 140 6 20 49 6 8 11 6 3
21 6 6 76 6 7 362 41 6 6 40 6 4 14 6 3 565 25 6 2 53 6 4 16 6 5 661
* The mean 6 standard deviation is presented. † The number of samples were 10, 12, and 6 for the olfactory, trigeminal, and optic nerves, respectively. Two olfactory and six optic nerves were not studied due to surgical complications. ‡ the representative components are shown in Fig. 3.
tive populations listed in Table 1. The TE dependence of the ADC measured both parallel and perpendicular to the long axis of each nerve (sample tube in the case of water) is shown in Fig. 5. Neither ADC(//) nor ADC(') varies as a function of echo time (range of 70 to 450 ms) for any of the three garfish nerves. The Student’s t test showed that ADCs at TE 5 70 ms and 450 ms were not significantly different (all p values . 0.05) irrespective of nerve or direction. The TE-independent ADCs and their anisotropy ratios are summarized in Table 2.
Fig. 3. Typical T2 spectra for the non-myelinated olfactory nerve (A), the myelinated trigeminal nerve (B), and the myelinated optic nerve (C). Individual T2 components are labeled A, B, C, and D. The short T2 component, C, is present in both of the myelinated nerves, yet is absent in the non-myelinated olfactory nerve.
Fig. 4. An example of the decay of water proton transverse magnetization in excised garfish nerves as the spin-echo time of the preparation phase in the CPMG-diffusion pulse sequence was incremented. The echoes were obtained at the various TE with no applied diffusion-sensitizing gradients. The amplitudes are normalized to an extrapolated signal amplitude of 100 at TE 5 0 ms.
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Fig. 5. Mean diffusion coefficients, ADC, of water measured parallel and perpendicular to the long axis of a distilled water sample (A), and freshly excised olfactory (B), trigeminal (C), and optic (D) nerves from six garfish as the spin-echo time was incremented (70, 150, 250, 350, 450 ms). The vertical error bars correspond to the 95% confidence intervals. The horizontal lines represent the ADC values averaged over all of the spin-echo times (70 – 450 ms). The ADC values and their anisotropy are independent over the 70 – 450 ms range of spin-echo times in all three garfish nerves. The ADCs at TE 5 70 ms and 450 ms are not significantly different for any of the nerves (p . 0.05).
DISCUSSION The first important finding of the experiments described in the previous section is the multiple component Table 2. Apparent diffusion coefficients (ADC) in distilled water, and in the olfactory, trigeminal, and optic nerves of the garfish averaged over spin-echo times ranging from 70 to 450 ms*†‡ Sample Distilled water Garfish nerves (N 5 6) Olfactory Trigeminal Optic
ADC(//) ADC(') (1025 cm2 s21) (1025 cm2 s21)
ADC(//) ADC(')
2.08 6 0.05
2.08 6 0.05
1.0 6 0.1
1.00 6 0.04 1.37 6 0.09 0.81 6 0.05
0.27 6 0.05 0.41 6 0.04 0.27 6 0.04
3.7 6 0.5 3.4 6 0.3 3.1 6 0.3
* Measurements were made at room temperature (20 6 1°C). † Diffusion coefficients were obtained from echoes with 0 # b # 1 3 105 s cm22. ‡ The mean 6 95% confidence interval are given for the results over all of the spin-echo times (70, 150, 250, 350, and 450 ms) used in the CPMG-diffusion pulse sequence.
nature of the transverse relaxation of water in garfish nerve, illustrated in Fig. 3. This finding supersedes an earlier publication of relaxation in garfish nerve in which a single component was reported, probably because only 20 echoes were acquired over a limited TE range and any multiexponentiality in the decay curves was not extractable.32 Our results are very much in accord with data obtained from the crayfish abdominal nerve cord,4 cat brain,3 bovine optic nerve,6 frog sciatic nerve,8 and human brain.11 Seeking to evaluate such multicomponent relaxation in terms of compartmental water pools, the garfish model was chosen because three significantly different cranial nerves could be obtained from each fish. As shown in Fig. 1A and B, the non-myelinated olfactory nerve provides the simplest of the nerve structures, in which closely packed, homogeneous axonal fields of several hundred small axons (diameter ;0.24 mm) are enclosed within a single Schwann cell domain, adjacent domains being separated by connective tissue channels. On the basis of experiments using suspended and layered preparations of red blood cell ghosts,33 it is reasonable to postulate that while transmembrane ex-
T2 and diffusion of water in nerve ● C. BEAULIEU
change across a single membrane will be sufficiently rapid to give rise to a single relaxation component from within the Schwann cell domains, the large number of closely spaced axons together with the enfolding Schwann cell will lengthen the lifetime of water within the domain sufficiently to separate the T2 of water in the Schwann cell domains from the T2 of water in the connective tissue channels. Such a postulate is entirely consistent with the presence of two T2 components for the olfactory nerve listed in Table 1. In addition, the Schwann cell domains comprise a larger volume of the nerve, and hence, would be consistent with component B (Table 1, Fig. 3). The other two nerves, namely, the trigeminal and the optic, are both myelinated. They are shown by Fig. 1C and D to be similar in compartmental composition, each having individual axons enclosed in myelin sheaths ;20 to 50 wrappings thick, and connective tissue spaces (i.e., extracellular) and glial cells comprising the inter-axonal space. We assume that water in the connective tissue spaces and in the glial cells are in rapid exchange. Because of the limited permeability of myelin, we postulate that the average rate of passage of water out of a myelinic water pool and into either the axoplasm on the one hand, or inter-axonal spaces on the other, will be sufficiently slow as to make these compartments well separated from each other on the time scale of a transverse relaxation experiment. This hypothesis is largely borne out by the similarity of the three more intense components in the T2 distributions of trigeminal and optic nerves shown in Fig. 3B and C, to which we give the broad assignments of inter-axonal water (A), axonal water (B), and myelin water (C). Assuming that myelin is 40% water,34 estimates of the cross-sectional areas of myelin in the electron micrographs of the trigeminal and optic nerves would suggest that the contribution of water in myelin to the total nerve water signal is 15 to 20%. This EM-based estimate of the proportion of myelin water is in agreement with the component populations of the short T2 component (C) (Table 1). Confidence in the assignments is further strengthened, first by the striking absence of a substantial short T2 component (myelin water compartment) in the non-myelinated olfactory nerve, and secondly by the agreement between the T2 (;170 ms) measured unambiguously in the axoplasm of the squid giant axon17 and that observed in the component assigned to axonal water in the garfish nerves (Table 1). The assignment hypotheses for the nerve water T2 components is still being established as more experimental evidence becomes available. However, the present work clearly provides further support for the use of quantitative transverse relaxation as an in vivo measure of myelination in the brain7 or nerve.10
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A very short T2 component (T2 ; 10 –15 ms), denoted by “D” in the T2 spectra, is seen in all three of the garfish nerves and represents a very small percentage of the entire nerve signal (3– 6%). At such a short T2 the possibility exists that it may arise from lipid protons and as a result no attempt has been made to assign it to any particular anatomical compartment. Following the T2 component analysis in the garfish nerves, exploration of compartmental variations in ADC could be undertaken. Based on the hypothesis that the components of the T2 distribution in nerve correspond to different water compartments and that the long T2 component corresponds to the inter-axonal space, the component T2 values and their respective populations (Table 1) predict that the inter-axonal space provides ;(35 6 5) % and ;(85 6 5) % of the total nerve water signal at TE 5 70 ms and 450 ms, respectively. In spite of this gross change in signal composition, the measured diffusion coefficients (Fig. 5) are not altered. The magnitude and anisotropy of the ADC in all three of the garfish nerves remains independent of the preparation spin-echo time over the range 70 ms to 450 ms in the CPMGdiffusion pulse sequence. This experimental finding is consistent with anisotropic diffusion seen in long spinecho time diffusion-weighted images of human white matter in vivo.35 The insensitivity of the ADC and its anisotropy to the preparatory spin-echo time does not necessarily invalidate the compartmental (and therefore slow intercompartmental exchange) hypothesis upon which the multicomponent T2 distributions have been interpreted. Unlike relaxation, which carries with it the history of previous compartmental migrations, short diffusion measurements do not reflect diffusion history prior to the measurement time. Because the diffusion measurement itself takes place in less than 30 ms, it also precludes (see ADC values) significant intercompartmental exchange (and therefore diffusional averaging) during that measurement. However, both the difference in the T2s of the two longer-lived components and the difference between the two extremes of the preparatory CPMG sequence are each an order of magnitude greater than this diffusion measurement time. We are confident therefore that the ADC measured at the long effective spin-echo time of 450 ms predominantly reflects the anisotropic motion of the long T2 component and our results indicate that water diffusion perpendicular to the nerve is hindered in this component. Because the mechanism of molecular hindrance is likely related to the dense packing of membranes,36 it is not particularly surprising that the ADC of inter-axonal space water may exhibit anisotropy. The structural anisotropy of each of the nerves studied (and this is also true for human white matter) is dominated by the packed
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and parallel orientation of numerous axonal membranes, whether or not those axons are myelinated or non-myelinated. The multiplicity of encounters of diffusing water molecules with that anisotropic distribution of membranes results in the diffusional anisotropy.17 Averaged over all of the garfish nerves, the one-dimensional rootmean-square displacements, lRMS, (where lRMS 5 {2(ADC)td}1/2 and td 5 D-d/3) are 7.3 6 1.3 mm parallel and 4.4 6 0.6 mm perpendicular to the long axis of the nerves for a diffusion time, td, of 28 ms (for pure water lRMS would be ;11 mm). Over this experimental diffusion time the inter-axonal water molecules moving perpendicular to the long axis of the fibers would encounter many membrane barriers because the observed lRMS(') is larger than typical separations between individual barriers (;1 mm between adjacent myelin sheaths in the myelinated nerves and ;0.5–2 mm between Schwann cell domains of axons in the non-myelinated nerve). In nerve therefore, both the intra-axonal and inter-axonal microenvironments of water are likely to exhibit similar tortuosities, as was proposed for the brain,36 and it is not surprising that they each give rise to similar water diffusion parameters. Measurements of diffusion using iontophoresis of tetramethylammonium (TMA1) combined with ion-selective microelectrodes have shown anisotropic diffusion in the extracellular space of turtle cerebellum.37 However, it should be borne in mind that diffusion measurements using TMA1 ions probe a longer length (;100 mm) than the NMR measurements and thus will emphasize anisotropy to a greater extent. A similar finding of anisotropic diffusion might be expected for the extracellular space of adult white matter in which the limited amount of extracellular water (;15–20%)38 would be distributed thinly between numerous packed axons (including their myelin sheaths if present). These results, as well as our own, suggest that it might be presumptuous to assume a priori that extracellular water is freely and rapidly diffusing. Using substantially higher values of the gradient factor, b, than is normal for diffusion measurements on clinical MRI systems, a non-exponentiality was previously demonstrated by us in the echo decay from garfish nerves using the Stejskal-Tanner sequence.14 In the light of the present results, this non-exponentiality seems much more likely to be due to restricted diffusion39 than to multiple water compartments with differing diffusional characteristics. However, because of our need to maintain good SNR out to long echo times, the full diffusion curves to b values higher than the typical clinical range were not measured in this study and our hypothesis remains speculative at this point. Nevertheless, other data do not support a primary role of multicomponent ADCs in the multiexponential nature of dif-
fusion curves in nervous tissue. Bi-exponential fits to diffusion decay curves from rat brain have yielded fractions of fast and slow decaying components which are not equivalent to the fractions of the intracellular and extracellular compartments.40 Moreover, Stanisz et al. have modeled the non-exponential decay of the diffusion curves in bovine optic nerve with a multicompartment (3 pool) model that incorporates partially permeable membranes that result in restricted diffusion and have shown that the non-linearity of the diffusion decay curves is not simply due to components with different ADCs.41 A corollary of this discussion is that one cannot assume a much smaller intrinsic D value for water in the axonal space than in the inter-axonal (or extracellular) space of nerve (and presumably white matter). Moreover, measurements of water diffusion in squid giant axons have shown that water diffusion in large axoplasmic regions, with little interference from the axonal membrane, is only ;20% less than in pure water and is nearly isotropic.17 This is consistent with the simulations of Latour et al. that showed that the ADC reduction in stroke could be explained primarily by alterations in restriction rather than by marked differences between the intra- and extracellular ADCs since their simulations used an intracellular diffusion coefficient of water that was only 25% less than the extracellular diffusion coefficient.42 Other simulations have also demonstrated the marked impact of membranes on the ADC.43 CONCLUSION The decomposition of the multiexponential water proton transverse relaxation decay curves in three normal cranial nerves of the garfish has demonstrated individual components which can be assigned to water in the myelin, in the axoplasm, and in the inter-axonal space. The short T2 component assigned to myelin is present in both myelinated nerves (trigeminal and optic), but is conspicuously absent in the non-myelinated olfactory nerve. Therefore, this data lend support to the use of quantitative measurements of transverse relaxation to provide a method for monitoring demyelination. By preparing the transverse magnetization to progressively exclude shorter T2 components (expected to be the myelin water and the axonal water) but to preserve longer T2 components (expected to be inter-axonal water) the measured ADC and its anisotropy were found to be independent of the T2 component of origin. It therefore appears that the microenvironments provided by the packed, parallel membrane structures of the axonal system give rise to similar diffusional properties (magnitude and anisotropy) in both the axonal and the inter-axonal spaces in normal nerve and likely also in white matter.
T2 and diffusion of water in nerve ● C. BEAULIEU Acknowledgments—Both an operating grant and a postgraduate scholarship (C.B.) from the Medical Research Council of Canada are gratefully acknowledged, as is an equipment grant and postgraduate scholarship (C.B., F.F.) from the Alberta Heritage Foundation for Medical Research. F.F. also received financial support from the Natural Sciences and Engineering Research Council of Canada. The authors are also grateful to Dan Doran and Karim Damji for technical assistance.
16.
17.
REFERENCES 1. Swift, T.J.; Fritz, O.G. A proton spin-echo study of the state of water in frog nerves. Biophys. J. 9:54 –59; 1969. 2. Vasilescu, V.; Katona, E.; Simplaceanu, V.; Demco, D. Water compartments in the myelinated nerve. III. Pulsed NMR results. Experientia 34:1443–1444; 1978. 3. Menon, R.S.; Allen, P.S. Application of continuous relaxation time distributions to the fitting of data from model systems and excised tissue. Magn. Reson. Med. 20:214 – 227; 1991. 4. Menon, R.S.; Rusinko, M.; Allen, P.S. Proton relaxation studies of water compartmentalization in a model neurological system. Magn. Reson. Med. 28:264 –274; 1992. 5. Stewart, W.A.; MacKay, A.L.; Whittall, K.P.; Moore, G.R.W.; Paty, W.D. Spin-spin relaxation in experimental allergic encephalomyelitis. Analysis of CPMG data using a non-linear least squares method and linear inverse theory. Magn. Reson. Med. 29:767–775; 1993. 6. Henkelman, R.M.; Stanisz, G.J.; Kim, J.K.; Bronskill, M.J. Anisotropy of NMR properties of tissues. Magn. Reson. Med. 32:592– 601; 1994. 7. MacKay, A.; Whittall, K.; Adler, J.; Li, D.K.B.; Paty, D.; Graeb, D. In vivo visualization of myelin water by magnetic resonance. Magn. Reson. Med. 31:673– 677; 1994. 8. Does, M.D.; Snyder, R.E. T2 relaxation of peripheral nerve measured in vivo. Magn Reson Imaging 13:575–580; 1995. 9. Harrison, R.; Bronskill, M.J.; Henkelman, R.M. Magnetization transfer and T2 relaxation components in tissue. Magn. Reson. Med. 33:490 – 496; 1995. 10. Does, M.D.; Snyder, R.E. Multi-exponential T2 relaxation in degenerating peripheral nerve. Magn. Reson. Med. 35: 207–213; 1996. 11. Whittall, K.P.; MacKay, A.L.; Graeb, D.A.; Nugent, R.A.; Li, D.K.B.; Paty, D.W. In vivo measurement of T2 distributions and water contents in normal human brain. Magn. Reson. Med. 37:34 – 43; 1997. 12. Moseley, M.E.; Cohen, Y.C.; Kucharczyk, J.; Asgari, H.S.; Wendland, M.F.; Tsuruda, J.; Norman, D. Diffusionweighted MR imaging of anisotropic water diffusion in cat central nervous system. Radiology 176:439 – 445; 1990. 13. Chenevert, T.L.; Brunberg, J.A.; Pipe, J.G. Anisotropic diffusion in human white matter: Demonstration with MR techniques in vivo. Radiology 177:401– 405; 1990. 14. Beaulieu, C.; Allen, P.S. Determinants of anisotropic water diffusion in nerves. Magn. Reson. Med. 31:394 – 400; 1994. 15. Moseley, M.E.; Cohen, Y.; Mintorovitch, J.; Chileuitt, L.; Shimizu, H.; Kucharczyk, J.; Wendland, M.F.; Weinstein, P.R. Early detection of regional cerebral ischemia in cats:
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Comparison of diffusion- and T2-weighted MRI and spectroscopy. Magn. Reson. Med. 14:330 –346; 1990. van Dusschoten, D.; de Jager, P.A.; van As, H. Extracting diffusion constants from echo-time dependent PFG NMR data using relaxation-time information. J. Magn. Reson. 116:22–28; 1995. Beaulieu, C.; Allen, P.S. Water diffusion in the giant axon of the squid: Implications for diffusion-weighted MRI of the nervous system. Magn. Reson. Med. 32:579–583; 1994. Easton, D.M. Garfish olfactory nerve: easily accessible source of numerous, long, homogeneous nonmyelinated axons. Science 172:952–955; 1971. Bunch, W.H.; Kallsen, G. Rate of intracellular diffusion as measured in barnacle muscle. Science 164:1178–1179; 1969. Hodgkin, A.L.; Keynes, R.D. Experiments on the injection of substances into the squid giant axon by means of a microsyringe. J. Physiol. 131:592; 1956. Carr, H.Y.; Purcell, E.M. Effects of diffusion on free precession in nuclear magnetic resonance experiments. Phys. Rev. 94:630 – 638; 1954. Meiboom, S.; Gill, D. Modified spin-echo method for measuring nuclear relaxation times. Rev. Sci. Instrum. 29:688 – 691; 1958. Hughes, D.G.; Lindblom, L. Baseline drift in the CarrPurcell-Meiboom-Gill pulsed NMR experiment. J. Magn. Reson. 26:469; 1977. Lawson, C.L.; Hanson, R.J. Solving least squares problems. Englewood Cliffs, NJ: Prentice Hall, Inc., 1974. Whittall, K.P.; MacKay, A.L. Quantitative interpretation of NMR relaxation data. J. Magn. Reson. 84:134–152; 1989. Kroeker, R.M.; Henkelman, R.M. Analysis of biologic NMR relaxation data with continuous distributions of relaxation times. J. Magn. Reson. 69:218 –235; 1986. Fenrich, F.R.E.; Allen, P.S. A simulation evaluation of a linear inverse technique for determining continuous relaxation time distributions. In: Book of abstracts: Eleventh Annual Meeting of the Society of Magnetic Resonance Medicine, Vol. 1, Berlin, Germany: 1992: p. 1309. Stejskal, E.O.; Tanner, J.E. Spin diffusion measurements: spin echoes in the presence of a time-dependent field gradient. J. Chem. Phys. 42:288 –292; 1965. Hore, P.J. Solvent suppression in Fourier transform nuclear magnetic resonance. J. Magn. Reson. 55:283–300; 1983. Le Bihan, D.; Breton, E.; Lallemand, D.; Grenier, P.; Cabanis, E.; Laval-Jeantet, M. MR imaging of intravoxel incoherent motions: application to diffusion and perfusion in neurologic disorders. Radiology 161:401– 407; 1986. Mills, R. Self-diffusion in normal and heavy water in the range 1– 45°C. J. Phys. Chem. 77:685– 688; 1973. Jolesz, F.A.; Polak, J.F.; Adams, D.F.; Ruenzel, P.W. Myelinated and non-myelinated nerves: comparison of proton MR properties. Radiology 164:89 –91; 1987. Menon, R.S.; Rusinko, M.S.; Allen, P.S. Multiexponential proton relaxation in model cellular systems. Magn. Reson. Med. 20:196 –213; 1991. Koenig, S.H.; Brown III, R.D.; Spiller, M.; Lundbom, N. Relaxometry of brain: why white matter appears bright in MRI. Magn. Reson. Med. 14:482– 495; 1990.
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35. Oatridge, A.; Hajnal, J.V.; Cowan, F.M.; Baudouin, C.J.; Young, I.R.; Bydder, G.M. MRI diffusion-weighted imaging of the brain: Contributions to image contrast from CSF signal reduction, use of a long echo time and diffusion effects. Clin. Radiol. 47:82–90; 1993. 36. Nicholson, C. Functional MRI of the Brain Syllabus, Workshop Presented by the Society of Magnetic Resonance in Medicine and the Society for Magnetic Resonance Imaging, 1–7 (1993). 37. Rice, M.E.; Okada, Y.C.; Nicholson, C. Anisotropic and heterogeneous diffusion in the turtle cerebellum: Implications for volume transmission. J. Neurophysiol. 70:2035– 2044; 1993. 38. Nicholson, C.A. Quantitative analysis of extracellular space using the method of TMA1 iontophoresis and the issue of TMA1 uptake. Can. J. Physiol. Pharmacol. 70: S314 –S322; 1992.
39. Hu¨rlimann, M.D.; Helmer, K.G.; de Swiet, T.M.; Sen, P.N.; Sotak, C.H. Spin echoes in a constant gradient and in the presence of simple restriction. J. Magn. Reson. A 113:260 –264; 1995. 40. Niendorf, T.; Dijkhuizen, R.M.;Norris, D.G.; van Lookeren Campagne, M.; Nicolay, K. Biexponential diffusion attenuation in various states of brain tissue: implications for diffusion-weighted imaging. Magn. Reson. Med. 36: 847– 857; 1996. 41. Stanisz, G.J.; Szafer, A.; Wright, G.A.; Henkelman, R.M. An analytical model of restricted diffusion in bovine optic nerve. Magn. Reson. Med. 37:103–111; 1997. 42. Latour, L.L.; Svoboda, K.; Mitra, P.M.; Sotak, C.H. Timedependent diffusion of water in a biologic model system. Proc. Natl. Acad. Sci. USA 91:1229 –1233; 1994. 43. Szafer, A.; Zhong, J.; Gore, J.C. Theoretical model for water diffusion in tissues. Magn. Reson. Med. 33:697–712; 1995.
PII S0730-725X(98)00151-9
● Original Contribution
MULTICOMPONENT WATER PROTON TRANSVERSE RELAXATION AND T2-DISCRIMINATED WATER DIFFUSION IN MYELINATED AND NONMYELINATED NERVE CHRISTIAN BEAULIEU, FRANCES R. FENRICH,
AND
PETER S. ALLEN
Department of Biomedical Engineering, University of Alberta, Edmonton, Alberta, Canada The influence of compartmental boundaries on water proton transverse relaxation and diffusion measurements was investigated in three distinct excised nerves, namely, the non-myelinated olfactory nerve, the Schwann cell myelinated trigeminal nerve, and the oligodendrocyte myelinated optic nerve of the garfish. The transverse relaxation decay curves were multiexponential and their decomposition yielded three primary components with T2 values ;30 –50, 150, and 500 ms, which were subsequently assigned to water protons in the myelin, axoplasm, and interaxonal compartments. The short T2 component was absent in the non-myelinated olfactory nerve, but present in both myelinated nerves and thus provides supporting evidence for the use of quantitative T2 measurements to measure the degree of myelination. The signal contribution of each T2 component to the apparent diffusion coefficient measurements was varied by incrementing the spin-echo time with a preparatory CPMG train of radiofrequency pulses. The apparent diffusion coefficient and its anisotropy were shown to be independent of the spin-echo time over the range of 70 to 450 ms. © 1998 Elsevier Science Inc. Keywords: Diffusion; Nerve; Nuclear magnetic resonance; Transverse relaxation.
consistent with several exponential components, both in vitro and in vivo.1–11 The individual T2 components have been interpreted in terms of different water compartments, such as inter-axonal, axonal, and myelin domains, within the heterogeneous tissue. There is considerable evidence from several laboratories to support this hypothesis. First, T2-weighted microimages of the crayfish abdominal nerve cord clearly differentiate axonal water from that in the surrounding inter-axonal spaces.4 Further support of compartmentalization and in particular the assignment of myelin to the short T2 component can be found in the reduced amplitude of the short T2 component as demyelination takes place in the white matter and spinal cord of guinea pigs induced with experimental allergic encephalomyelitis,5 and in the association of a disappearing short T2 component in frog sciatic nerve, in vivo, when progressive nerve degeneration and concomitant myelin loss takes place.10 Moreover, the correspon-
INTRODUCTION Although the spatial resolution of magnetic resonance imaging (MRI) as practiced clinically is sufficient to resolve individual organ sub-structures, e.g., the basal ganglia or white matter tracts in brain, it is insufficient to resolve structures on a cellular level. However, even though they cannot be resolved spatially, it may well be possible to distinguish between distinct microstructures through their nuclear magnetic resonance (NMR)-governing water characteristics because these characteristics can vary between the different cellular structures while remaining quite uniform within each type of cellular structure. For example, the transverse decay of the water proton magnetization in heterogeneous tissue such as nerve, white matter, or spinal cord can only rarely be described by a single exponential. Instead, the relaxation curves obtained from these tissues are generally found to be RECEIVED 2/2/98; ACCEPTED 7/3/98. Address correspondence to Peter S. Allen, c/o Department of Biomedical Engineering, 10 –102 Clinical Sciences Bldg., University of Alberta, Edmonton, Alberta, T6G 2G3. Email: [email protected]
Present address of C. Beaulieu c/o: Department of Radiology, Stanford University, Palo Alto, CA, 94305-5488. Present address of F. R. Fenrich c/o: Space Sciences Lab, University of California, Berkeley, CA, 94720. 1201
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dence of known distributions of myelin with short T2 component maps in human brain7,11 also reinforces the hypothesis. However, a direct comparison of the transverse relaxation time distributions between structurally intact myelinated and non-myelinated nerve, which would test the association of the short T2 component with myelin water is lacking. If T2 component assignments could be established definitively, then changes in their proportions, when experimentally quantifiable in vivo, may provide a measure of compartmental degradation in white matter with multiple sclerosis7 and in nerve with wallerian degeneration.10 In addition to the transverse relaxation behaviour of water protons, their apparent diffusion coefficient (ADC) and its potential anisotropy might also be expected to vary with their microstructural environments. Certainly at a macroscopic level, the anisotropy of ADC reflects the substructural arrangement of the ordered axons in the white matter of cat12 and human brain,13 and in excised garfish nerve.14 However, the overall ADC is a function of the individual compartmental ADCs, T2s, and proton populations in heterogeneous tissue such as nerve. A better characterization of water diffusion in nerve could result if the ADC were measured in the individual compartments. If, for example, one could determine compartmental differences (or similarities) in ADC (i.e., intraversus inter-axonal), the proposed mechanisms for the reduction of ADC in acute stroke might be better established.15 The overall goal of the work presented here was to provide more definitive evidence of compartmentalization in nerve water T2 and ADC by utilizing the garfish model with its three markedly different cranial nerves, one non-myelinated (the olfactory), one from the peripheral nervous system myelinated by Schwann cells (the trigeminal), and the other from the central nervous system myelinated by oligodendrocytes (the optic). In order to test the correspondence of myelin with the short T2 component observed in nerve and in white matter, the T2 distribution of normal non-myelinated nerve was compared to normal myelinated nerve. In addition, the assignment of a compartmental structure based on T2 components was a prerequisite to the exploration of the compartmental ADC in the present work. The ADC measurements presented here preferentially discriminated against water in faster relaxing compartments by utilizing a train of p radiofrequency (RF) pulses to increase the echo time, in a manner similar to van Dusschoten et al.16 In contrast, previous work has isolated compartment ADC characteristics by choosing a model in which a single compartment overwhelmingly dominates, namely, the giant axon of the squid.17
MATERIALS AND METHODS Sample Preparation The olfactory, the trigeminal, and the optic nerves of 18 garfish were excised and immediately stored in appropriate Ringer’s solution.18 The outer connective tissue sheath of each optic nerve was also removed. Twelve of the garfish were used for the T2 analysis and six were used in the evaluation of diffusion characteristics. For the T2 measurements, the nerve samples were placed in 5-mm diameter NMR tubes (one tube for each nerve) and bathed with buffer. For the diffusion measurements, the freshly excised nerves were quickly dried and transferred to paraffin oil (to prevent them from dehydrating during the measurements) and individually aligned in capillary tubes in order to facilitate the determination of diffusional anisotropy relative to the long axis of the nerve. In contrast to the preparation for T2 analysis, buffer was not used as the bathing medium during the diffusion measurements. This was because the buffer water signal, which in T2 measurements can be readily separated from nerve water, seriously contaminates the nerve water signal in diffusion measurements. Previous diffusion experiments on the garfish nerves have shown that immersion of the nerves in paraffin oil does not affect the nerve water diffusional characteristics.14 Others have also used light oils to prevent dehydration of tissue samples.19,20 The viability and structural integrity of the nerves throughout the duration of the NMR experiment was confirmed with electron microscopy (EM) and action potential measurements. Furthermore, direct comparison of in vitro and in vivo measurements made in this laboratory of T2 in frog sciatic nerve show that they correspond quite well.8 Representative EM sections of the olfactory, trigeminal, and optic nerve are shown in Fig. 1 and the relevant physical characteristics of the garfish nerves have been described previously.14 NMR Measurements and Analysis All NMR measurements were carried out at room temperature (;20°C) in a 40-cm bore Bruker CXP spectrometer (Bruker Instruments, Billerica, MA, USA) operating at a proton frequency of 100.19 MHz. The sample tube containing a given nerve type was located centrally in a small solenoidal RF coil. The transverse relaxation decay curves were acquired using a 4096 echo Carr-Purcell-Meiboom-Gill (CPMG) add/subtract sequence21,22 with an inter-echo spacing, t, of 1.6 ms. The p pulses were 10 ms in duration and the sequence repetition time was 20 s. In order to reduce baseline errors caused by inaccurate p pulses and receiver DC offsets, the pulse sequence was phase cycled over 16 add/subtract sequences.23 Typical proton line widths were 30 Hz. The signal-to-noise ratio (SNR), given by the ratio of the
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Fig. 1. Electron micrographs of transverse sections from the olfactory (A, B), trigeminal (C), and optic (D) nerves of the garfish. (A) Schwann cell domains (SD), which consist of many nonmyelinated axons (see B) enveloped together by a Schwann cell wrapping, are seen in the olfactory nerve. Connective tissue channels (CT) separate the Schwann cell domains. (B) This high magnification EM shows the individual axons (AX) bounded by their axonal membrane (x) in the olfactory nerve. The axons are very homogeneous in size (;0.2 mm diameter) and are packed together tightly. Microtubules (arrowhead), neurofilaments (arrow), and mitochondria (M) can be distinguished within the axoplasm. (C) Intact myelin sheaths (MY) are seen surrounding the axons (AX) in the trigeminal nerve. Axons are myelinated by Schwann cells (SC) in peripheral nerves. (D) The multilamellar nature of the myelin sheath (MY) is evident in these myelinated axons of the optic nerve. The axonal membrane (x), neurofilaments (arrow), and microtubules (arrowhead) are also visible.
signal at an echo time of 1.6 ms and the standard deviation of the noise, was typically 3000. The demands of a short echo spacing (1.6 ms) to minimize losses of transverse magnetization due to diffusion in local field inhomogeneities, and the long acquisition range (1.6 ms to 6.6 s) required to sample the relaxation decay curve adequately, together gave rise to a large number of echoes (4096). However, in order to limit computational demands, it was found necessary to use only 230 of the 4096 echoes for the T2 algorithm. Specifically, the 4096 point decay data set was reduced to a 230 point decay data set by sampling every point from 1.6 ms to 40 ms, every 4th point from 40 ms to 200
ms, every 8th point from 200 ms to 500 ms, and finally every 24th point from 500 ms to 6.5 s.4 This procedure was adopted to approximate logarithmic sampling and thereby maintain equitability for each of the component relaxation times. The inversion of the reduced multiexponential decay data set into a continuous distribution of relaxation times was accomplished using the non-negative least squares algorithm of Lawson and Hanson,24 as modified by Whittall and MacKay.25 This algorithm is a linear inverse technique that is stable, has the significant advantage of requiring no a priori guess of the number of components, and produces a continuous distribution of the relaxation times which is a realistic description for
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Fig. 2. CPMG-diffusion pulse sequence in which the rectangular gradient strength, Gi, is incremented, the timings d and D represent constant time intervals, and TE is increased by incrementing the number of intervening hard p RF pulses (n) spaced by t. The train of hard p pulses was closely spaced to minimize losses in transverse magnetization due to diffusion in the presence of susceptibility gradients. The acquisition time (AQ) for the echo peak is 10 ms.
biologic tissue.26 The different T2 components were identified as distinct peaks in the continuous distribution. Each component population was determined by summing the grid point amplitudes comprising that component while the T2 value was determined by a weighted average of the component T2 grid points. To prevent spurious T2 components arising due to the fitting of noise, all solutions maintained a chi-squared misfit corresponding to the 99% confidence level. Simulation tests of resolution indicate that with an SNR of 3000, we can expect to resolve components with a minimum factor of ;2 between peak relaxation times.27 For the diffusion coefficient measurements, a homemade gradient coil (3 cm bore) provided the diffusionsensitizing rectangular gradient pulses {available strengths: Gz, max ; 1.61 T m21, Gx, max ; 0.64 T m21} employed in a Stejskal-Tanner spin-echo diffusion sequence.28 However, the sequence was modified (Fig. 2) with a preparatory CPMG subsequence21,22 in order to select the T2 range of the water proton magnetization entering the diffusion measuring sequence. The train of hard p pulses was closely spaced to minimize losses in transverse magnetization due to diffusion in the presence of susceptibility gradients. Moreover, to excite the nerve water protons selectively from the protons of the bathing paraffin oil, 1331 (p/2) and 2662 (p) binomial RF pulses29 were employed, whose component lengths were multiples of 1.25 ms and whose separations were 1.316 ms. The gradient pulse timings (d 5 6 ms, D 5 30.128 ms) were kept constant while the gradient strength, Gi, was incremented to a maximum of ;0.12 T m21 thereby yielding a maximum gradient factor, bmax, of ;1 3 105 s cm22 where b 5 g2Gi2d2(D 2 d/3)30 and g is the magnetogyric ratio of the protons. The remaining symbols are defined in Fig. 2. The spacing between successive hard p pulses of the preparatory CPMG sequence, t,
was 5 ms, and the number (n) of such pulses was either 2, 18, 38, 58, or 78 giving rise to overall spin-echo times (TE) of 70, 150, 250, 350, or 450 ms, respectively. The minimum (70 ms) and maximum (450 ms) spin-echo times arose respectively from limitations of the gradient hardware and from the available SNR. Echoes were averaged over 4, 8, or 16 scans depending on SNR with a repetition interval of 5 s (20 s for the comparative distilled water sample). At each TE, ADC values were obtained from single component fits (5 data points per ADC) of the diffusion decay curves {ln[(echo amplitude, Gi Þ 0)/(echo amplitude, Gi 5 0)] versus b} measured both parallel and perpendicular to the axis of the nerve. Comparisons within the various groups were made with the Student’s t test and the level of significance was defined as p # 0.05. To verify the accuracy and isotropy of the ADC over a range of spin-echo times, self-diffusion measurements were performed on distilled water. Doing so demonstrated the isotropy of diffusion {i.e., ADC(//) 5 ADC(')} and a mean ADC value that was within 5% of the accepted self-diffusion coefficient of pure water at 20°C.31 The decay of spin-echo amplitudes resulting from the CPMG-diffusion composite sequence when Gi 5 0, conformed to the T2 when measured with the CPMG sequence alone for both nerve water and tap water. In particular, a T2 of 2140 ms was measured for tap water using the former sequence versus a T2 of 2150 ms for the latter sequence. RESULTS Typical transverse relaxation time distributions for the non-myelinated olfactory, myelinated trigeminal, and myelinated optic nerves are presented in Fig. 3. A summary of the component populations and relaxation times are given in Table 1. All three types of nerve have a long T2 component ;500 ms and a medium T2 component ;150 ms. However, a substantial component with a T2 between 30 ms and 50 ms is only seen in the myelinated trigeminal and optic nerves. The relaxation component due to the buffer (T2 ; 2.2 s) is not shown in either Fig. 3 or Table 1. The effect of the CPMG preparation phase of the composite CPMG-diffusion sequence is presented in Fig. 4. These curves illustrate the reduction of nerve water proton transverse magnetization as the preparation phase, and therefore the effective TE, was incremented with Gi set to zero. Approximately 50 to 65% of the initial proton magnetization of nerve water persisted at TE 5 70 ms whereas only ;5–10% of the original signal survived at TE 5 450 ms. The residual signal from nerve water following CPMG preparation is in agreement with that expected from the component T2 values and their respec-
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Table 1. Summary of transverse relaxation times and component populations in the nonmyelinated olfactory nerve, and the myelinated trigeminal and optic nerves*† Nerve Olfactory Trigeminal
Optic
T2 Component‡
T2 (ms)
Population (%)
A B D A B C D A B C D
510 6 90 170 6 20 17 6 10 460 6 50 140 6 20 34 6 5 863 480 6 40 140 6 20 49 6 8 11 6 3
21 6 6 76 6 7 362 41 6 6 40 6 4 14 6 3 565 25 6 2 53 6 4 16 6 5 661
* The mean 6 standard deviation is presented. † The number of samples were 10, 12, and 6 for the olfactory, trigeminal, and optic nerves, respectively. Two olfactory and six optic nerves were not studied due to surgical complications. ‡ the representative components are shown in Fig. 3.
tive populations listed in Table 1. The TE dependence of the ADC measured both parallel and perpendicular to the long axis of each nerve (sample tube in the case of water) is shown in Fig. 5. Neither ADC(//) nor ADC(') varies as a function of echo time (range of 70 to 450 ms) for any of the three garfish nerves. The Student’s t test showed that ADCs at TE 5 70 ms and 450 ms were not significantly different (all p values . 0.05) irrespective of nerve or direction. The TE-independent ADCs and their anisotropy ratios are summarized in Table 2.
Fig. 3. Typical T2 spectra for the non-myelinated olfactory nerve (A), the myelinated trigeminal nerve (B), and the myelinated optic nerve (C). Individual T2 components are labeled A, B, C, and D. The short T2 component, C, is present in both of the myelinated nerves, yet is absent in the non-myelinated olfactory nerve.
Fig. 4. An example of the decay of water proton transverse magnetization in excised garfish nerves as the spin-echo time of the preparation phase in the CPMG-diffusion pulse sequence was incremented. The echoes were obtained at the various TE with no applied diffusion-sensitizing gradients. The amplitudes are normalized to an extrapolated signal amplitude of 100 at TE 5 0 ms.
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Fig. 5. Mean diffusion coefficients, ADC, of water measured parallel and perpendicular to the long axis of a distilled water sample (A), and freshly excised olfactory (B), trigeminal (C), and optic (D) nerves from six garfish as the spin-echo time was incremented (70, 150, 250, 350, 450 ms). The vertical error bars correspond to the 95% confidence intervals. The horizontal lines represent the ADC values averaged over all of the spin-echo times (70 – 450 ms). The ADC values and their anisotropy are independent over the 70 – 450 ms range of spin-echo times in all three garfish nerves. The ADCs at TE 5 70 ms and 450 ms are not significantly different for any of the nerves (p . 0.05).
DISCUSSION The first important finding of the experiments described in the previous section is the multiple component Table 2. Apparent diffusion coefficients (ADC) in distilled water, and in the olfactory, trigeminal, and optic nerves of the garfish averaged over spin-echo times ranging from 70 to 450 ms*†‡ Sample Distilled water Garfish nerves (N 5 6) Olfactory Trigeminal Optic
ADC(//) ADC(') (1025 cm2 s21) (1025 cm2 s21)
ADC(//) ADC(')
2.08 6 0.05
2.08 6 0.05
1.0 6 0.1
1.00 6 0.04 1.37 6 0.09 0.81 6 0.05
0.27 6 0.05 0.41 6 0.04 0.27 6 0.04
3.7 6 0.5 3.4 6 0.3 3.1 6 0.3
* Measurements were made at room temperature (20 6 1°C). † Diffusion coefficients were obtained from echoes with 0 # b # 1 3 105 s cm22. ‡ The mean 6 95% confidence interval are given for the results over all of the spin-echo times (70, 150, 250, 350, and 450 ms) used in the CPMG-diffusion pulse sequence.
nature of the transverse relaxation of water in garfish nerve, illustrated in Fig. 3. This finding supersedes an earlier publication of relaxation in garfish nerve in which a single component was reported, probably because only 20 echoes were acquired over a limited TE range and any multiexponentiality in the decay curves was not extractable.32 Our results are very much in accord with data obtained from the crayfish abdominal nerve cord,4 cat brain,3 bovine optic nerve,6 frog sciatic nerve,8 and human brain.11 Seeking to evaluate such multicomponent relaxation in terms of compartmental water pools, the garfish model was chosen because three significantly different cranial nerves could be obtained from each fish. As shown in Fig. 1A and B, the non-myelinated olfactory nerve provides the simplest of the nerve structures, in which closely packed, homogeneous axonal fields of several hundred small axons (diameter ;0.24 mm) are enclosed within a single Schwann cell domain, adjacent domains being separated by connective tissue channels. On the basis of experiments using suspended and layered preparations of red blood cell ghosts,33 it is reasonable to postulate that while transmembrane ex-
T2 and diffusion of water in nerve ● C. BEAULIEU
change across a single membrane will be sufficiently rapid to give rise to a single relaxation component from within the Schwann cell domains, the large number of closely spaced axons together with the enfolding Schwann cell will lengthen the lifetime of water within the domain sufficiently to separate the T2 of water in the Schwann cell domains from the T2 of water in the connective tissue channels. Such a postulate is entirely consistent with the presence of two T2 components for the olfactory nerve listed in Table 1. In addition, the Schwann cell domains comprise a larger volume of the nerve, and hence, would be consistent with component B (Table 1, Fig. 3). The other two nerves, namely, the trigeminal and the optic, are both myelinated. They are shown by Fig. 1C and D to be similar in compartmental composition, each having individual axons enclosed in myelin sheaths ;20 to 50 wrappings thick, and connective tissue spaces (i.e., extracellular) and glial cells comprising the inter-axonal space. We assume that water in the connective tissue spaces and in the glial cells are in rapid exchange. Because of the limited permeability of myelin, we postulate that the average rate of passage of water out of a myelinic water pool and into either the axoplasm on the one hand, or inter-axonal spaces on the other, will be sufficiently slow as to make these compartments well separated from each other on the time scale of a transverse relaxation experiment. This hypothesis is largely borne out by the similarity of the three more intense components in the T2 distributions of trigeminal and optic nerves shown in Fig. 3B and C, to which we give the broad assignments of inter-axonal water (A), axonal water (B), and myelin water (C). Assuming that myelin is 40% water,34 estimates of the cross-sectional areas of myelin in the electron micrographs of the trigeminal and optic nerves would suggest that the contribution of water in myelin to the total nerve water signal is 15 to 20%. This EM-based estimate of the proportion of myelin water is in agreement with the component populations of the short T2 component (C) (Table 1). Confidence in the assignments is further strengthened, first by the striking absence of a substantial short T2 component (myelin water compartment) in the non-myelinated olfactory nerve, and secondly by the agreement between the T2 (;170 ms) measured unambiguously in the axoplasm of the squid giant axon17 and that observed in the component assigned to axonal water in the garfish nerves (Table 1). The assignment hypotheses for the nerve water T2 components is still being established as more experimental evidence becomes available. However, the present work clearly provides further support for the use of quantitative transverse relaxation as an in vivo measure of myelination in the brain7 or nerve.10
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A very short T2 component (T2 ; 10 –15 ms), denoted by “D” in the T2 spectra, is seen in all three of the garfish nerves and represents a very small percentage of the entire nerve signal (3– 6%). At such a short T2 the possibility exists that it may arise from lipid protons and as a result no attempt has been made to assign it to any particular anatomical compartment. Following the T2 component analysis in the garfish nerves, exploration of compartmental variations in ADC could be undertaken. Based on the hypothesis that the components of the T2 distribution in nerve correspond to different water compartments and that the long T2 component corresponds to the inter-axonal space, the component T2 values and their respective populations (Table 1) predict that the inter-axonal space provides ;(35 6 5) % and ;(85 6 5) % of the total nerve water signal at TE 5 70 ms and 450 ms, respectively. In spite of this gross change in signal composition, the measured diffusion coefficients (Fig. 5) are not altered. The magnitude and anisotropy of the ADC in all three of the garfish nerves remains independent of the preparation spin-echo time over the range 70 ms to 450 ms in the CPMGdiffusion pulse sequence. This experimental finding is consistent with anisotropic diffusion seen in long spinecho time diffusion-weighted images of human white matter in vivo.35 The insensitivity of the ADC and its anisotropy to the preparatory spin-echo time does not necessarily invalidate the compartmental (and therefore slow intercompartmental exchange) hypothesis upon which the multicomponent T2 distributions have been interpreted. Unlike relaxation, which carries with it the history of previous compartmental migrations, short diffusion measurements do not reflect diffusion history prior to the measurement time. Because the diffusion measurement itself takes place in less than 30 ms, it also precludes (see ADC values) significant intercompartmental exchange (and therefore diffusional averaging) during that measurement. However, both the difference in the T2s of the two longer-lived components and the difference between the two extremes of the preparatory CPMG sequence are each an order of magnitude greater than this diffusion measurement time. We are confident therefore that the ADC measured at the long effective spin-echo time of 450 ms predominantly reflects the anisotropic motion of the long T2 component and our results indicate that water diffusion perpendicular to the nerve is hindered in this component. Because the mechanism of molecular hindrance is likely related to the dense packing of membranes,36 it is not particularly surprising that the ADC of inter-axonal space water may exhibit anisotropy. The structural anisotropy of each of the nerves studied (and this is also true for human white matter) is dominated by the packed
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and parallel orientation of numerous axonal membranes, whether or not those axons are myelinated or non-myelinated. The multiplicity of encounters of diffusing water molecules with that anisotropic distribution of membranes results in the diffusional anisotropy.17 Averaged over all of the garfish nerves, the one-dimensional rootmean-square displacements, lRMS, (where lRMS 5 {2(ADC)td}1/2 and td 5 D-d/3) are 7.3 6 1.3 mm parallel and 4.4 6 0.6 mm perpendicular to the long axis of the nerves for a diffusion time, td, of 28 ms (for pure water lRMS would be ;11 mm). Over this experimental diffusion time the inter-axonal water molecules moving perpendicular to the long axis of the fibers would encounter many membrane barriers because the observed lRMS(') is larger than typical separations between individual barriers (;1 mm between adjacent myelin sheaths in the myelinated nerves and ;0.5–2 mm between Schwann cell domains of axons in the non-myelinated nerve). In nerve therefore, both the intra-axonal and inter-axonal microenvironments of water are likely to exhibit similar tortuosities, as was proposed for the brain,36 and it is not surprising that they each give rise to similar water diffusion parameters. Measurements of diffusion using iontophoresis of tetramethylammonium (TMA1) combined with ion-selective microelectrodes have shown anisotropic diffusion in the extracellular space of turtle cerebellum.37 However, it should be borne in mind that diffusion measurements using TMA1 ions probe a longer length (;100 mm) than the NMR measurements and thus will emphasize anisotropy to a greater extent. A similar finding of anisotropic diffusion might be expected for the extracellular space of adult white matter in which the limited amount of extracellular water (;15–20%)38 would be distributed thinly between numerous packed axons (including their myelin sheaths if present). These results, as well as our own, suggest that it might be presumptuous to assume a priori that extracellular water is freely and rapidly diffusing. Using substantially higher values of the gradient factor, b, than is normal for diffusion measurements on clinical MRI systems, a non-exponentiality was previously demonstrated by us in the echo decay from garfish nerves using the Stejskal-Tanner sequence.14 In the light of the present results, this non-exponentiality seems much more likely to be due to restricted diffusion39 than to multiple water compartments with differing diffusional characteristics. However, because of our need to maintain good SNR out to long echo times, the full diffusion curves to b values higher than the typical clinical range were not measured in this study and our hypothesis remains speculative at this point. Nevertheless, other data do not support a primary role of multicomponent ADCs in the multiexponential nature of dif-
fusion curves in nervous tissue. Bi-exponential fits to diffusion decay curves from rat brain have yielded fractions of fast and slow decaying components which are not equivalent to the fractions of the intracellular and extracellular compartments.40 Moreover, Stanisz et al. have modeled the non-exponential decay of the diffusion curves in bovine optic nerve with a multicompartment (3 pool) model that incorporates partially permeable membranes that result in restricted diffusion and have shown that the non-linearity of the diffusion decay curves is not simply due to components with different ADCs.41 A corollary of this discussion is that one cannot assume a much smaller intrinsic D value for water in the axonal space than in the inter-axonal (or extracellular) space of nerve (and presumably white matter). Moreover, measurements of water diffusion in squid giant axons have shown that water diffusion in large axoplasmic regions, with little interference from the axonal membrane, is only ;20% less than in pure water and is nearly isotropic.17 This is consistent with the simulations of Latour et al. that showed that the ADC reduction in stroke could be explained primarily by alterations in restriction rather than by marked differences between the intra- and extracellular ADCs since their simulations used an intracellular diffusion coefficient of water that was only 25% less than the extracellular diffusion coefficient.42 Other simulations have also demonstrated the marked impact of membranes on the ADC.43 CONCLUSION The decomposition of the multiexponential water proton transverse relaxation decay curves in three normal cranial nerves of the garfish has demonstrated individual components which can be assigned to water in the myelin, in the axoplasm, and in the inter-axonal space. The short T2 component assigned to myelin is present in both myelinated nerves (trigeminal and optic), but is conspicuously absent in the non-myelinated olfactory nerve. Therefore, this data lend support to the use of quantitative measurements of transverse relaxation to provide a method for monitoring demyelination. By preparing the transverse magnetization to progressively exclude shorter T2 components (expected to be the myelin water and the axonal water) but to preserve longer T2 components (expected to be inter-axonal water) the measured ADC and its anisotropy were found to be independent of the T2 component of origin. It therefore appears that the microenvironments provided by the packed, parallel membrane structures of the axonal system give rise to similar diffusional properties (magnitude and anisotropy) in both the axonal and the inter-axonal spaces in normal nerve and likely also in white matter.
T2 and diffusion of water in nerve ● C. BEAULIEU Acknowledgments—Both an operating grant and a postgraduate scholarship (C.B.) from the Medical Research Council of Canada are gratefully acknowledged, as is an equipment grant and postgraduate scholarship (C.B., F.F.) from the Alberta Heritage Foundation for Medical Research. F.F. also received financial support from the Natural Sciences and Engineering Research Council of Canada. The authors are also grateful to Dan Doran and Karim Damji for technical assistance.
16.
17.
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35. Oatridge, A.; Hajnal, J.V.; Cowan, F.M.; Baudouin, C.J.; Young, I.R.; Bydder, G.M. MRI diffusion-weighted imaging of the brain: Contributions to image contrast from CSF signal reduction, use of a long echo time and diffusion effects. Clin. Radiol. 47:82–90; 1993. 36. Nicholson, C. Functional MRI of the Brain Syllabus, Workshop Presented by the Society of Magnetic Resonance in Medicine and the Society for Magnetic Resonance Imaging, 1–7 (1993). 37. Rice, M.E.; Okada, Y.C.; Nicholson, C. Anisotropic and heterogeneous diffusion in the turtle cerebellum: Implications for volume transmission. J. Neurophysiol. 70:2035– 2044; 1993. 38. Nicholson, C.A. Quantitative analysis of extracellular space using the method of TMA1 iontophoresis and the issue of TMA1 uptake. Can. J. Physiol. Pharmacol. 70: S314 –S322; 1992.
39. Hu¨rlimann, M.D.; Helmer, K.G.; de Swiet, T.M.; Sen, P.N.; Sotak, C.H. Spin echoes in a constant gradient and in the presence of simple restriction. J. Magn. Reson. A 113:260 –264; 1995. 40. Niendorf, T.; Dijkhuizen, R.M.;Norris, D.G.; van Lookeren Campagne, M.; Nicolay, K. Biexponential diffusion attenuation in various states of brain tissue: implications for diffusion-weighted imaging. Magn. Reson. Med. 36: 847– 857; 1996. 41. Stanisz, G.J.; Szafer, A.; Wright, G.A.; Henkelman, R.M. An analytical model of restricted diffusion in bovine optic nerve. Magn. Reson. Med. 37:103–111; 1997. 42. Latour, L.L.; Svoboda, K.; Mitra, P.M.; Sotak, C.H. Timedependent diffusion of water in a biologic model system. Proc. Natl. Acad. Sci. USA 91:1229 –1233; 1994. 43. Szafer, A.; Zhong, J.; Gore, J.C. Theoretical model for water diffusion in tissues. Magn. Reson. Med. 33:697–712; 1995.