Magnetic Resonance in Medicine 44:713–722 (2000)
Displacement Imaging of Spinal Cord Using q-Space
Diffusion-Weighted MRI
Yaniv Assaf,1 Adi Mayk,2 and Yoram Cohen1*
Displacement MR images of water in in vitro rat spinal cord
were computed from q-space analysis of high b value diffusionweighted 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.
Key words: white matter; spinal cord; maturation; MRI; diffusion
MRI; DWI; q-space NMR; q-space DWI
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.
ln(E g/E 0)⫽⫺␥ 2g 2␦ 2(⌬⫺␦/3)D⫽⫺bD
冕
E ⌬(q)⫽ P៮ s(R,⌬)exp(i2␲q䡠R)dR
[1]
This equation relates the normalized signal decay (Eg/E0)
with the duration, time separation, and strength of the
magnetic field pulse gradients (␦ ⌬ and g, respectively), ␥
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
1
School of Chemistry, Sackler Faculty of Exact Sciences, Tel Aviv University,
Tel Aviv, Israel.
2
Teva Pharmaceutical Industries and Sackler Faculty of Medicine, Tel Aviv
University, Tel Aviv, Israel.
Grant sponsor: United States-Israel Binational Science Foundation; Grant
number: 97-00346; Grant sponsor: Israel Science Foundation.
*Correspondence to: Dr. Yoram Cohen, School of Chemistry, Sackler Faculty
of Exact Sciences, Tel Aviv University, Ramat Aviv 69778, Tel Aviv, Israel.
E-mail: [email protected]
Received 29 November 1999; revised 2 May 2000; accepted 21 June 2000.
© 2000 Wiley-Liss, Inc.
neuronal tissues in MR diffusion experiments is not monoexponential, 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 (2␲)–1␥␦g, 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 E⌬(q) represents the echo decay as a function of q,
R is the displacement and P៮ s(R, ⌬) 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 ⌬, 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
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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
Assaf et al.
iments 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, ␦ 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.
Sample Preparation
Image Analysis
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.
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 zerofilled 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).
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, ␦ ⫽
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, ⌬ ⫽ 150 msec, ␦ ⫽ 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 exper-
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.
Displacement Imaging of Spinal Cord
FIG. 1. 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,⌬)
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).
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1c), extracted from the full width at the half height of the
mean displacement profile (⌬X0.5 (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 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 con-
FIG. 2. 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 (⌬), (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.
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Assaf et al.
FIG. 3. 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 (⌬), (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 multiexponential decay function (see text for more details).
ditions, 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.
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 ␮m. In the gray
matter, however, it is within the range of 9 –10 ␮m 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.
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
FIG. 4. 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.
Displacement Imaging of Spinal Cord
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FIG. 5. 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 ␮m and 8 –10␮m, 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.
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.
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 ␮m
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 ␮m and 9.8 ⫾ 0.2 ␮m, 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 ␮m to around
2–3 ␮m, 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.
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.
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
FIG. 6. 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.
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Assaf et al.
FIG. 7. 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.
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 ␮m at a diffusion time of 30 msec to 6.6 ⫾ 0.4 ␮m 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 ␮m and 2.2 ⫾
0.2 ␮m 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
FIG. 8. 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).
boundaries and consequently perform similar displacement at different diffusion times, as depicted in Fig. 10b.
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
Displacement Imaging of Spinal Cord
719
FIG. 9. 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.
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 some structural information in neuronal
tissue (15,30). However, all of these recent applications
dealt with diffusion-weighted MRS, and therefore could
not characterize fully heterogeneous systems, such as intact organs. We sought to overcome this obstacle by computing q-space MR images where the analysis is performed
on each pixel. By this method, the spatial distribution of
the extracted parameters is characterized and the full diagnostic capacity of this approach can be challenged and
evaluated. Indeed, Figs. 5 and 7 show that the color-coded
MR images obtained with this methodology provide very
good gray/white matter contrast and allow a distinction to
be made between tissue in which the mean displacement
differs by about 2 microns.
Maturation and q-Space MR Images
The q-space MR images obtained by this relatively simple
procedure show, as expected, very pronounced gray/
white-matter contrast in the mature spinal cord. In addition, q-space MR images were found to be very useful for
following spinal cord maturation. The data presented in
Figs. 6 and 7 show unequivocally that the gray/whitematter contrast in the mature spinal cord originates mainly
from changes in the diffusion characteristics of the spinal
cord white matter upon maturation. One can therefore
speculate that as myelination progresses with the maturation process, water diffusion in the white matter becomes
more restricted and the gray/white-matter contrast increases.
As shown in Figs. 5 and 7, the q-space analysis of the
DWI data provides displacement distribution profiles from
FIG. 10. 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.
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Assaf et al.
which two types of sub-images may be computed: a mean
displacement image and an image of the probability for
zero displacement. If one accepts the notion that the myelin can serve as obstacles for water diffusion, disturbance
in the myelin network should, in principle, be accompanied by changes in the displacement profile, and the contrast of these two sub-images should vary. Under such a
disturbance the mean displacement should increase while
the probability for zero displacement should decrease.
Therefore, instead of resorting to the apparent diffusion
coefficient (ADC), which is not a direct characteristic of
the tissue, q-space MR analysis provides two parameters
which are more direct characteristics of the tissue.
Restricted Diffusion, Exchange, Displacement and
Myelination
The data in Figs. 9 and 10, together with the results shown
in Fig. 7, suggest that as maturation and myelination
progress, water diffusion becomes more restricted and the
exchange of water molecules is slowed down. These effects seem to accentuate the gray/white-matter contrast
found in the spinal cord when the diffusion is measured
perpendicular to the long axis of the spinal cord, as performed in this study. We found that the attenuation of the
water signal in the gray matter of a 7-day-old rat’s spinal
cord shows the same dependency on diffusion time as
water does in brain tissues in which ␶ for the exchange was
estimated to be in the range of 20 –30 m (34). However, the
dependency of the signal attenuation of the water signal in
the white matter of a mature spinal cord on diffusion time
shows the opposite trend, as compared with that of water
in brain tissues. It was found that the behavior of water in
white matter of a mature spinal cord parallels that of
choline in the optic nerve, where the exchange was
claimed to be much slower (30). One can therefore suggest
that as myelin forms during maturation, the exchange between the different compartments is being slowed down,
thus resulting in enhanced restricted diffusion.
Potential Applications and Limitations
Recent studies have demonstrated that signal decay in
water diffusion experiments in CNS measured with high b
values, is not mono-exponential (10 –13). Such an observation was recently reported in humans (35). Therefore, a
procedure to extract the information hidden in such a
curve should be devised. Of the few approaches available,
q-space diffusion MRI seems to be an good choice for
analyzing such diffusion experiments for the following
reasons: First, the actual displacements in each pixel are
used to obtain the contrast in the MR image. This parameter is a tissue characteristic, as oppose to the ADC, which
is a more indirect reflection of the displacement. Second,
structural information that surpasses MRI resolution is
obtained without resorting to a complicated tissue model.
In addition, the diffusion mode is more readily identified
by simple inspection of the displacement profile evolution
as a function of the diffusion time. All of these characteristics of the q-space, and the possibility that myelination
can result in increase-restricted diffusion, imply that these
types of MRI images should be extremely sensitive to
FIG. 11. Simulations demonstrating the accuracy in determination
of the mean displacement from q-space analysis of NMR diffusion
data for different diffusion times. The simulations were performed
with the following parameters: D ⫽ 5*10⫺7 cm2 s⫺1, ⌬ ⫽ 5–300
msec, ␦ ⫽ 2 msec, and g ranging from 0 –150 gauss cm⫺1 and
assuming an isotropic unrestricted diffusion. In these simulations
the signal decay was zero-filled prior to the FT.
white matter-associated diseases. Therefore, we expect
that qs-DWI will be suitable for early detection of abnormal myelination, and for following white-matter maturation and degeneration.
There are also some intrinsic limitations that make the
application of this methodology to in vivo animal studies
and to human subjects difficult with the current technology. The main problem is that the structural information
that can be obtained from these images is determined by
the q values given by (2␲)–1␥␦g. To obtain structural information on the micron scale, relatively high q values
should be used, as shown in Fig. 11. Figure 11 shows
simulations demonstrating the accuracy in the determination of the mean displacement for different q values as a
function of diffusion time. They clearly demonstrate that
for diffusion times of about 150 msec, q values of about
1500 cm–1 should be used if mean displacements on the
order of 1–2 microns are to be quantified. For such q values
when ␦ is in the range of several msec, g should be on the
order of several hundred of gauss cm–1. However, all of
these simulations were performed with zero filling. Significantly better results are obtained when the signal decay is
extrapolated to larger q and is not zero filled. To verify the
accuracy of this approach when dealing with a spinal cord,
we performed a DWI experiment in which the signal decay
was measured as a function of much higher q values.
In this imaging experiment qmax was increased from
1277 cm–1 to 3065 cm–1 by increasing ␦ from 2 msec to 4.8
msec. The experimental signal decay of this DWI experiment, and the decay curve obtained by extrapolation of the
data obtained from an experimental decay curve in which
qmax was set to 1277 cm–1, are shown in Fig. 12a. Figure
Displacement Imaging of Spinal Cord
721
FIG. 12. a: Experimental (—) and extrapolated (●) signal decays as a function of the q
values in the white matter of a mature rat
spinal cord obtained at diffusion time of
150 msec. b: The displacement distribution
profiles obtained by Fourier transform of the
date presented in a (see text for details). c:
Simulated (—) and extrapolated (●) signal decay as a function of the q values for cylindrical
fibers distribution taken from electron microscopy of the optic nerve (37). d: The corresponding displacement distribution profiles
obtained by Fourier transform of the data in c.
The simulation was performed using the Callaghan formulation for restricted diffusion in a
cylindrical geometry, according to Ref. 36, to
which the size and volume distribution according to Ref. 37 was introduced. Note that
the curve up to qmax of 1277cm–1 was used to
obtain the extrapolated curve.
12b shows the corresponding displacement distribution
profiles obtained by Fourier transformation of the data in
Fig. 12a. Interestingly, we found that the mean displacements extracted from the experimental curve, and from the
curve obtained by extrapolation of the experimental when
qmax was only 1277 cm–1, are very similar (2.3 ⫾ 0.2␮m
and 2.4⫾0.2␮m, respectively). This comparison demonstrates that such an extrapolation is justified—at least in
the spinal cord. To further challenge this extrapolation
procedure, we simulated the signal decay using the Callaghan formulation of restricted diffusion in a cylinder
(36), to which the size distribution of axons in the optic
nerve (as given in Ref. 37) was introduced and weighted.
There again we used the simulated curve up to qmax of
1277 cm–1 and extrapolated this curve using the same
procedure we have used to obtain our q-space MR images.
The resulting decay curves are shown in Fig. 12c, and the
displacement distribution profiles obtained by Fourier
transformation of the curve in Fig. 12c are shown in Fig.
12d. Here again, no significant differences were obtained
between the mean displacement extracted from the simulated data or the extrapolated curve, although some deviation between the two curves is observed at q values of
more than 7000 cm–1.
An additional factor that should be taken into account is
the SNR, as q-space DWI implies acquiring MR images
with very high diffusion weighting. One problem we face
with MRI is the lack of specificity. It appears that by
applying strong gradients one can select different components, some of which may be more restricted than others,
and thereby achieve higher specificity. In addition, there is
a significant fraction of water molecules in white matter
which signal persist even when high diffusion weighting
is applied. Therefore, the SNR is still acceptable at high
diffusion weighting in the white matter of the spinal cord,
at least under the in vitro conditions used in the present
study.
CONCLUSIONS
Here we present the first q-space-analyzed MRI images of
the CNS. In these new types of MR images a physical
parameter of the tissues, such as the mean displacement of
the water molecules, is quantified. The displacement MR
image computed from the q-space analysis of the DWI data
provides structural information that surpasses the spatial
resolution of conventional MRI. With the current conventional technology, displacement on the order of 1–2 microns can be measured. q-Space DWI was shown to be
exquisitely sensitive to spinal cord maturation. This may
be due to the increased sensitivity of this imaging approach to the integrity of the myelin network. Therefore,
we anticipate that this methodology will be extremely
suitable for early detection of white matter-associated disorders. The evaluation of the diagnostic capability of qspace DWI and its implementation in in vivo animal models is under way.
ACKNOWLEDGMENTS
The imaging accessory was purchased by a grant from the
Israel Science Foundation, founded by the Israel Academy
of Sciences and Humanities.
722
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