High b-value q-space analyzed diffusion

Magnetic Resonance in Medicine 47:115–126 (2002)
High b-Value q-Space Analyzed Diffusion-Weighted MRI:
Application to Multiple Sclerosis
Y. Assaf,1 D. Ben-Bashat,2 J. Chapman,3,4 S. Peled,2 I.E. Biton,1 M. Kafri,3 Y. Segev,2
T. Hendler,2,3 A.D. Korczyn,3,4 M. Graif,2,3 and Y. Cohen1*
Multiple sclerosis (MS) is an inflammatory disease of the central
nervous system (CNS) which affects nearly one million people
worldwide, leading to a progressive decline of motor and sensory functions, and permanent disability. High b-value diffusion-weighted MR images (b of up to 14000 s/mm2) were acquired from the brains of controls and MS patients. These
diffusion MR images, in which signal decay is not monoexponential, were analyzed using the q-space approach that emphasizes the diffusion characteristics of the slow-diffusing component. From this analysis, displacement and probability maps
were constructed. The computed q-space analyzed MR images
that were compared with conventional T1, T2 (fluid attenuated
inversion recovery (FLAIR)), and diffusion tensor imaging (DTI)
images were found to be sensitive to the pathophysiological
state of white matter. The indices used to construct this qspace analyzed MR maps, provided a pronounced differentiation between normal tissue and tissues classified as MS
plaques by the FLAIR images. More importantly, a pronounced
differentiation was also observed between tissues classified by
the FLAIR MR images as normal-appearing white matter
(NAWM) in the MS brains, which are known to be abnormal, and
the respective control tissues. The potential diagnostic capacity of high b-value diffusion q-space analyzed MR images is
discussed, and experimental data that explains the consequences of using the q-space approach once the short pulse
gradient approximation is violated are presented. Magn Reson Med 47:115–126, 2002. © 2002 Wiley-Liss, Inc.
Key words: high b-value DWI; diffusion MRI; white matter; multiple sclerosis (MS); q-space diffusion MRI
DIFFUSION-WEIGHTED IMAGING (DWI) IN BRAIN
TISSUE
DWI measures the motion and hence the net displacement
of water molecules in the sample. In recent years DWI has
been used to characterize different brain pathologies (1–7).
Special emphasis was directed to the use of DWI in the
early detection of stroke (1,2,8 –11). In addition, diffusion
tensor imaging (DTI) (12,13) was recently used extensively
to study white matter anisotropy in the normal and diseased brain (14,15). However, until recently, DWI and DTI
1
School of Chemistry, Raymond and Beverly Sackler Faculty of Exact Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv, Israel.
2
Wohl Institute for Advanced Imaging, Department of Radiology, Tel Aviv
Sourasky Medical Center, Tel Aviv, Israel.
3
Sackler Faculty of Medicine, Tel Aviv University, Tel Aviv, Israel.
4
Department of Neurology, Sackler Faculty of Medicine, Tel Aviv University,
Tel Aviv, Israel.
Grant sponsor: United States–Israel Binational Science Foundation; Grant
number: 97-00346; Grant sponsor: German Federal Ministry of Education and
Research.
*Correspondence to: Dr. Yoram, Cohen School of Chemistry, Sackler Faculty
of Exact Sciences, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel.
E-mail: [email protected]
Received 9 January 2001; revised 9 May 2001; accepted 28 August 2001.
© 2002 Wiley-Liss, Inc.
DOI 10.1002/mrm.10040
studies in neuronal tissues were limited to the measurement of a single apparent diffusion coefficient (ADC). In
those studies the signal decay was fitted to the well-known
Stejskal-Tanner equation (16):
I/I0 ⫽ exp关⫺␥2g2␦2 共⌬ ⫺ ␦/3兲D兴 ⫽ exp共⫺bD兲
[1]
where I/I0 is the normalized signal attenuation, ␥ is the
gyromagnetic ratio, g is the pulsed gradient amplitude, ␦ is
the pulsed gradient duration, ⌬ is the time separation
between the leading edges of these gradients, and D is the
diffusion coefficient. In this equation the term ⌬-␦/3 represents the effective diffusion time, and the b-value represents the overall diffusion weighting in the experiment
(17). As most of the DWI and DTI studies to date have used
relatively low b-values (b ⬍ 1500 s/mm–2), only a single
ADC was detected for water in neuronal tissues.
Recently, several groups showed that at high b-values
water signal decay in neuronal tissues of animals and
humans is non-monoexponential (18 –23). At least two
diffusing components could be identified from the water
signal decay in those tissues. We have shown, for example,
that the slow-diffusing component of water is mainly related to the intra-axonal water, and that its relative weighting increases with neuronal maturation (24). As Eq. [1]
cannot be used to fit non-monoexponential signal decay,
the analysis of DWI at high b-values requires a new approach. The simplest approach appears to be that of Eq.
[2]. However this equation implies the existence of two
water populations that are in the slow-exchange regime.
冘
2
I/I0 ⫽
冘
2
Aiexp关⫺␥2g2␦2 共⌬ ⫺ ␦/3兲Di兴 ⫽
i⫽1
Aiexp共⫺bDi兲
i⫽1
[2]
In Eq. [2], Ai is the relative fraction of molecules with
diffusion coefficient Di, and all other parameters are the
same as in Eq. [1].
q-Space Analysis of Diffusion Data
Cory and Garroway (25) and Callaghan et al. (26) suggested
the q-space analysis as an alternative approach to analyze
NMR diffusion experiments of complex systems, and demonstrated that it provides a means to extract structural
information on the sample without resorting to complicated models. In addition, this approach is also considered
to be extremely useful for detecting restricted diffusion
(27). These facts served as the main motivations for us to
115
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Assaf et al.
use this approach in studying the complicated diffusion of
water and metabolite in neuronal tissue (24,28,29).
In principle, q-space analysis produces (under the long
diffusion time scale limit and the short gradient pulse (␦)
approximation) the displacement distribution function
共PS 共R,⌬), where R is the displacement) of water molecules
for a certain diffusion time. The assumed form of PS 共R,⌬) is
a sum of Gaussians. The displacement distribution function, 共PS 共R,⌬)), is derived from the experimental data by
Fourier transformation (FT) of the signal decay E⌬(q)
(where q is defined as q ⫽ ␥␦g/2␲) according to Eq. [3]
(25,26).
E ⌬共q兲 ⫽
冕
fusing component, provide a pronounced differentiation
between NAWM in controls and in MS patients. The high
b-value q-space analyzed DWI maps were compared with
conventional, T1, FLAIR, and DTI. The high sensitivity of
the q-space analyzed MR images acquired while violating
the short pulse gradient approximation is discussed, and
its origin is demonstrated by evaluating experimentally
the effect of ␦ on the q-space-extracted parameters on a
demyelinating model of experimental allergic neuritis
(EAN).
METHODS
MRI on Healthy and MS-Diseased Human Brains
Ps共R, ⌬兲exp共i2␲q䡠R兲dR
[3]
In these experiments, E⌬(q) is measured by acquiring data
varying either the diffusion gradient strength, g, or the
gradient duration, ␦. The displacement distribution function can be characterized by two parameters: 1) the mean
displacement, extracted from the width at half-height, and
2) the probability for zero displacement (the peak intensity
of the displacement distribution probability function)
given in ␮m and arbitrary units, respectively (25). Recently
we reported q-space high b-value diffusion-weighted MR
images on rat spinal cord (24).
MRI in Multiple Sclerosis (MS)
MS is an autoimmune-mediated disease of the central
nervous system (CNS) characterized by demyelination of
axons and focal inflammatory reactions in the MS lesions
(30,31). MRI is the major imaging technique that supports
the clinical diagnosis of MS (32,33). T2-weighted MRI and
fluid-attenuated inversion recovery (FLAIR) are the conventional MR techniques that identify MS lesions and
measure the disease load (32,33), while gadolinium enhancement in T1-weighted images delineates acute inflammatory lesions. As the disease progresses, increasing clinical disability does not correlate well with any of these
indices. This lack of correlation, known as the “clinicoradiological paradox” (33) may suggest that the existing imaging methods do not identify key abnormalities in MS
brains. Indeed, MR spectroscopy (MRS) of MS brains
shows that normal-appearing white matter (NAWM) areas
on the T2 and FLAIR images display abnormal metabolite
distributions on many occasions (34,35). DTI and magnetization transfer imaging (MTI) have also been used recently to characterize the NAWM in MS patients (36 –39).
Since MTI and DTI show relatively small differences in the
NAWM of MS brains, and MRS suffers from low spatial
and temporal resolution, new imaging techniques with
higher sensitivity for the disease load are needed—particularly in the NAWM.
Here we report high b-value (b-value of up to
14000 s/mm2) diffusion-weighted MR images acquired on
brains of neurologically healthy subjects (control group)
and MS patients. From this high b-value DWI data we
computed q-space analyzed MR images of healthy and
MS-patient brains. These images, whose contrast is based
on the diffusion characteristics of the slow restricted dif-
Subjects
MRI scans were acquired from 13 MS patients (six clinically defined at the relapsing-remitting stage and seven at
the secondary progressive stage) and six normal healthy
subjects who served as a control group. The average age in
the MS and control groups was 44 ⫾ 10 and 38 ⫾ 11 years,
respectively. The normal subjects had no history of neuronal disease. The local Helsinki committee approved the
MRI protocol, and informed consent was obtained from
each subject (MS patients and controls).
MRI Protocol
MRI was performed on a 1.5T GE Signa horizon echo
speed LX MRI scanner (GE, Milwaukee, WI). Efforts were
made to fix the subject head with a series of foam pads to
reduce possible motion during the MRI protocol. To ensure relatively similar slice positioning for all subjects,
oblique-axial slices were selected parallel to the connection line of the anterior-posterior commisures (AC-PC).
Three slices were selected— one at the the midbody level
of the corpus callosum (identified from a midsagittal
view), one below it, and one above it, with a slice thickness of 4.5 mm. The MRI protocol included the following
clinical imaging procedures: FLAIR images (TR/TE/TI ⫽
8000/120/2000 ms), and inversion recovery T1-weighted
images (T1-IR) (TR/TE/TI ⫽ 1500/9/700 ms). The MRI protocol also included two sets of EPI diffusion experiments.
The first included the acquisition of diffusion-weighted
spin-echo EPI images with b-values of 0 and 1000 s/mm2
(TR/TE ⫽ 1500/90 ms, ⌬/␦ ⫽ 31/25 ms, gmax ⫽
2.2 gauss/cm) and gradients applied along six directions
(xy, xz, yz, –xy, –xz, and y–z) to assess the diffusion tensor
at conventional b-values according to Basser et al. (12,13).
The second diffusion experiment included the acquisition
of a set of 16 diffusion-weighted spin-echo EPI images in
which the diffusion gradient was incremented linearly
from 0 to 2.2 gauss/cm to reach a maximal b-value of
14000 s/mm2 and a maximal q-value of 850 cm–1. This set
of diffusion images was also acquired for the six aforementioned gradient directions. Other parameters of these experiments were: TR/TE ⫽ 1500/167 ms, ⌬/␦ ⫽ 71/65 ms,
and number of averages ⫽ 8. A whole set of 96 diffusion
images per slice was needed for the q-space analysis (described in the Image Analysis section). The entire diffusion protocol (q-space and DTI data) lasted 28 min, and the
entire MRI examination was concluded in 70 min.
High b-Value q-Space DWI of MS
117
FIG. 1. ROIs chosen for the analysis of the white matter indices in the three slices that were acquired in this study. (The numerical values
of the different indices appear in Fig. 6 and Table 1).
Image analysis
The q-space analysis (25,26) of the high b-value DWI data
was performed on a pixel-by-pixel basis as described previously (24). It should be noted that in q-space analysis the
resolution of the displacement distribution profile is determined by the maximal q-value used in the experiment.
In the present work the maximal q-value was 850 cm–1,
implying a digital resolution of about 4 ␮m. Therefore, the
data was zero-filled prior to FT in order to increase the FT
resolution (24). From the q-space analysis the displacement distribution function was obtained for each pixel in
each direction. These displacement distributions were
characterized by two parameters (the apparent mean displacement and the apparent probability for zero displacement) which were used to obtain the so-called q-spaceanalyzed MR images. The apparent mean displacement
image was calculated from the full width at half height of
the displacement distribution profile, 共PS 共R,⌬)), using the
method described in Ref 25. The apparent probability for
zero displacement was calculated from the peak height of
the displacement distribution profile, 共PS 共R,⌬)). It should
be noted that no fitting of any kind was applied to the
displacement distribution profile obtained from the FT of
the experimental decays. After calculating the displacement and probability images for each of the six directions,
a tensor analysis was performed for the displacement and
probability indices similarly to the DTI analysis described
in the appendix. From the displacement tensor analysis
the smallest eigenvalue was chosen to show the displacement that is perpendicular to the long axis of the neuronal
fibers at each specific pixel. For the probability, however,
the largest eigenvalue of the probability tensor analysis
was taken. To minimize noise effects, a noise filter was
applied which was determined after a series of trials to be
2.5 the average noise level. Typical SNR values for white
matter were ⬃55 and ⬃13 for b-values of 3 and
14000 s/mm2, respectively. For gray matter, typical SNR
values were ⬃60 and ⬃7 at b-values of 4 and 4000 s/mm2,
respectively. Using this noise filter, all pixels outside the
brain were zeroed in all diffusion images. Using our inhouse Matlab programs we obtained the q-space-analyzed
images in ⬍ 2 min/slice, while the computation of slow-
and fast-diffusion images following a biexponential fit
took 70 – 80 min/slice on the same computer.
DTI fractional anisotropy (FA) images were produced
from the diffusion data acquired at TE ⫽ 90 ms, and from
the q-space diffusion data acquired with TE ⫽ 167 ms,
both with a b-value of 1000 s/mm2.
Region of interest (ROI) analysis
ROI analysis was performed on the white matter areas
depicted in Fig. 1. The ROIs in the white matter of the MS
brains were classified into two groups by visual inspection: 1) ROIs from areas that appeared abnormal on the
FLAIR images of MS patients, referred to as MS lesion
ROIs; and 2) ROIs from the white matter of MS patients,
which were not classified as MS plaques on the FLAIR
images by the visual inspection, and hence were classified
as NAWM ROIs.
The control DTI and q-space values were obtained from
the respective ROIs in the white matter of control subjects.
For each ROI the FAs at TE ⫽ 90 ms and 167 ms, the
probability for zero displacement, and the displacement
values were evaluated.
Diffusion MRS on Rat Sciatic Nerves
Induction of EAN and nerve preparation
EAN was induced in two 2-month-old female Lewis rats,
weighing 175–210 g. EAN was induced by an injection
into both hind footpads of 200 ␮l of inoculums containing
10 mg of bovine peripheral myelin (BPM) and 4 mg mycobacterium tuberculosis (strain H37RA; Difco) emulsified
in 100 ␮l saline and 100 ␮l complete Freund’s adjuvant
(CFA). Two rats that served as controls were immunized
with inoculums containing the mycobacterium tuberculosis emulsified in saline and CFA. The rats were killed by
an overdose injection of pentobarbital, and their sciatic
nerve was excised at day 14 postimmunization. The excised sciatic nerves were inserted immediately after excision into a capillary filled with Flourinert (FC-77, Sigma)
to avoid nerve dehydration and nontissue signal. The diffusion experiments were performed within 4 h after nerve
excision at 36 ⫾ 1°C.
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Assaf et al.
FIG. 2. FLAIR images of (a) a control subject, and (b) and (c) MS patients. A specific ROI is superimposed on each of the images at the
frontal-temporal white matter, which represents (a) a control ROI, (b) a NAWM ROI, and (c) an MS-lesion ROI. d: The signal decay as a
function of the b-values for the ROIs shown on the FLAIR images. e: The respective q-space profiles of the data shown in d after data
extrapolation. The diffusion gradient direction in these cases was perpendicular to the fibers in this specific white matter region.
Diffusion MRS experiments
Diffusion experiments were performed on an 8.4 T NMR
spectrometer (Bruker, Karlsruhe, Germany) equipped with
a micro5 gradient probe driven by a BGU-II system producing pulse gradients of up to 190 gauss cm–1 in each of
the three directions. Diffusion experiments were performed using the PGSE pulse sequence with the following
parameters: TR/TE ⫽ 3000/206 ms and ⌬ ⫽ 100 ms. Five
sets of experiments were performed with different diffusion gradient durations and amplitudes in a way that kept
the q- and b-values constant. In these sets of diffusion
experiments the duration of the diffusion gradients were
4.5, 9, 18, 36, and 72 ms, with gradient amplitudes of 160,
80, 40, 20, and 10 gauss cm–1, respectively. We acquired
24 different q- or b-values for each combination of a diffusion pulse gradient strength and duration. Thirty-two
repetitions were sufficient to obtain adequate SNR even at
the maximal b-value (bmax ⫽ 3.7 ⫻ 105 s/mm2). In these
experiments the diffusion gradients were applied perpendicular to the long axis of the nerve. q-Space analysis of
these experiments was produced as described previously
(24) by FT of the experimental data after zero-filling up to
q-values of 16924 cm–1. The displacement distribution
profiles were fitted to a bi-Gaussian function to obtain the
displacement of the narrow and broad components and
their relative weighting according to:
冘
2
Ps ⫽
i⫽1
Ai
wi 冑␲/2
冋
exp
册
⫺2 䡠 x2
.
wi2
[4]
Where Ps is the probability function, Ai is the area under
the peak, and wi is approximately 0.849 of the width of the
Gaussian peak.
RESULTS
Findings in Normal Subjects and MS Patients
The signal decay in the white matter of control brains was
found to be non-monoexponential at high b-values. The
deviation from monoexponential decay was observed at
b-values higher than ⬃3000 s mm–2, as reported previously for both animal (19 –21) and human subjects (22,40).
Figure 2a– c shows FLAIR images of a control subject and
two MS patients, respectively, on which specific ROIs at
the right tempofrontal white matter are marked. The ROIs
shown in Fig. 2a– c represent normal white matter,
High b-Value q-Space DWI of MS
119
FIG. 3. Complete MRI data set of a control subject: (a) q-space probability (zero-filled), (b) q-space displacement (zero-filled), (c) FA (TE ⫽
90 ms), (d) FLAIR, and (e) T1-IR images.
NAWM, and MS-lesion ROIs, respectively. The diffusion
signal decays and the respective q-space profiles (after data
extrapolation) from these ROIs are depicted in Fig. 2d and
e, respectively. The signal decays were obtained from diffusion data in which the diffusion gradient direction was
perpendicular to the neuronal fibers in this particular ROI
(in this case the y–z direction). The slow-diffusing component, which is clearly detected at high b-values for the
control ROI, is less apparent in the NAWM ROI, and does
not exist in the MS-lesion ROI (Fig. 2d). The q-space profiles of these ROIs show a decrease in the amplitude and
broadening of the displacement distribution profile for the
NAWM ROI as compared that of the ROI taken from the
control subject. These changes become more significant
when the MS-lesion ROI data is analyzed.
Figure 3a and b shows representative probability and
displacement q-space analyzed MR images of a normal
subject. The contrasts in Fig. 3a and b are the probability
for zero displacement and the displacement given in arbitrary units and ␮m, respectively. The term “displacement”
used to describe the apparent displacement of water protons in a voxel, henceforth refers to the calculated displacement derived from the smallest displacement eigenvalue. From the q-space analysis it emerges that, using the
experimental parameters of the present study (when ⌬ and
␦ were 71 and 65 ms, respectively), the displacement is on
the order of 2– 4 ␮m in white matter, about 7–9 ␮m in gray
matter, and ⬎10 ␮m in CSF (Fig. 3b). In contrast, the
calculated probability for zero displacement is significantly higher in white matter as compared to gray matter
(Fig. 3a). For comparison, Fig. 3c– e shows the FA from
conventional DTI, the FLAIR images, and the inversion
recovery T1-weighted images of the same brain slice of the
normal subject presented in Fig. 3a and b.
High b-value q-space analyzed diffusion-weighted MR
images were computed for 13 clinically-defined MS patients. Figures 4 and 5 show the same MRI slice presented
in Fig. 3 for representative cases of moderate and severe
MS, respectively. Figure 4 depicts the MRI data collected
on an MS patient with several periventricular lesions.
These lesions (MS plaques) appear as hyperintense areas
in the FLAIR image (Fig. 4d). However, in the q-spaceanalyzed MR images (Fig. 4a and b), these lesions are
characterized by lower probability and larger displacement values as compared to the values obtained for similar
anatomical areas in brains of control subjects. As was
shown in Fig. 2d and e, the q-space analysis of the high
b-values diffusion MR data provides a useful means to
evaluate abnormalities in the NAWM. For example, in the
ROI depicted on the FLAIR image shown in Fig. 4d (which
is classified as NAWM for this particular patient), the
probability for zero displacement and the mean displacement are 69% and 162% of the control values, respectively. The FA computed from the conventional DTI data
for this specific ROI was 87% of the control value. A more
severe loss of white matter was found by the q-space
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Assaf et al.
FIG. 4. Complete MRI data set of a moderate MS patient (EDSS of 4.5). (a) q-space probability (zero-filled), (b) q-space displacement
(zero-filled), (c) FA (TE ⫽ 90 ms), (d) FLAIR, and (e) T1-IR images. A specific ROI in the NAWM is outlined on the FLAIR image (see text for
more details on this ROI).
analysis of patients with severe MS. Figure 5a and b shows
such q-space displacement and the probability maps obtained from a patient with a severe case of MS, in which an
extensive white matter abnormality is observed. These
abnormalities are much more apparent as compared with
conventional FLAIR and T1-weighted images (Fig. 5d and
e). For this patient, significant abnormality is also observed in the FA map presented in Fig. 5c. For this MS
patient the ROI depicted in Fig. 5d is also classified as
NAWM. Here again, the displacement, probability, and FA
in the same ROI were found to be 122%, 88%, and 96%,
respectively, of the control values. In general, the relative
changes in the FA were found to be significantly smaller
than the relative changes in the displacement and probability values extracted from the q-space MR images.
Figure 6 shows the histograms of the different indices
calculated for all ROIs depicted in Fig. 1 for the entire
population studied after their classification into the three
different groups of ROIs (control, NAWM, and MS lesion).
Tissue classification in the MS brains was performed (as
explained in the Methods section) using the FLAIR images. Table 1 depicts the numerical values of the above
analysis. Figure 6a and b shows the histograms of the ROI
analysis for the q-space probability and displacement values, respectively. The differences between the histograms
of the control (in red) and the lesion (in blue) are highly
significant (also see Table 1). For the NAWM ROIs of MS
patients, the histogram appears between the control and
MS lesion histograms, suggesting that some of these ROIs
have abnormal probability and displacement values, while
other such ROIs in the NAWM have values similar to those
of controls. Figure 6c and d show the ROI histograms for
the FA index obtained from conventional DTI analysis,
with TEs of 90 ms and 167 ms, respectively. The FA ROI
histograms show differentiation between the values of the
control ROIs and those of the lesion ROIs (MS plaques) at
both TEs. However, at TE ⫽ 90 ms there is no significant
difference between the histograms of the control ROIs and
the NAWM ROIs (Table 1). At TE ⫽ 167 ms, some difference between the two histograms can be observed (compare Fig. 6c and d; see Table 1).
Findings in Excised Rat Sciatic Nerve
Because of the relatively weak gradient pulse available on
clinical scanners, the human q-space DWI experiments
were performed with long pulse gradients that violate the
short gradient pulse condition. This resulted in deviation
of the distribution profile extracted from the q-space analysis as compared with the real displacement distribution
function. To estimate the effect of the violation of the short
gradient pulse approximation, we acquired similar data
sets on excised sciatic nerves using a much stronger gradient system. This enabled us to evaluate the effect of the
High b-Value q-Space DWI of MS
121
FIG. 5. Complete MRI data set of a severe MS patient (EDSS of 7.0): (a) q-space probability (zero-filled), (b) q-space displacement
(zero-filled), (c) FA (TE ⫽ 90 ms), (d) FLAIR, and (e) T1-IR images. A specific ROI in the NAWM is outlined on the FLAIR image (see text for
more details on this ROI).
duration of ␦ on the extracted displacement distribution
profiles. In these experiments we compared the displacement distribution profiles obtained when strong and short
diffusion gradient pulses are used (gmax ⫽ 160 gauss cm–1,
␦ ⫽ 4.5 ms) as compared to a situation in which weak and
long diffusion gradient pulses (gmax ⫽ 10 gauss cm–1, ␦ ⫽
72 ms) are used. In these experiments all the other experimental parameters were kept the same (TE, TR, ⌬, and band q-values). Figure 7 shows the effect of the diffusion
gradient duration (␦) on the signal decay and on the respective q-space profiles extracted from this data for a
normal rat sciatic nerve. As expected for diffusion in a
restricted geometry (41), the signal decay is smaller as the
diffusion gradient duration is increased and the relative
population of the slow-diffusing component became more
apparent. Consequently, the displacement distribution
profiles became narrower and more intense. The displacement decreased from a value of 3.3 ␮m at ␦ of 4.5 ms to a
value of about 1.6 ␮m at ␦ of 72 ms.
The effect of the gradient pulse duration on the diagnostic ability of these diffusion experiments is shown in Fig.
8, where the signal decays and the q-space displacement
profiles are depicted for normal and EAN-diseased rat
sciatic nerves. The signal decays (Fig. 8a) for the control
and EAN-diseased nerves are better distinguished when
using the long gradient pulse. This can be also observed
from the respective q-space profiles (Fig. 8b), where the
differences between normal and EAN diseased nerves are
more significant when using the long diffusion gradient.
The effect of changing the pulse gradient duration (␦) on
the extracted parameters from the q-space analysis is summarized in Table 2. The data clearly show that as ␦ became
longer the extracted displacement became smaller. However, the relative changes in the displacement are less
pronounced for the broad and less restricted component in
the EAN sciatic nerve.
DISCUSSION
In this work we present high b-value q-space analyzed
diffusion MR images of normal and diseased human
brains. The data presented demonstrate that the slow (restricted) diffusing component observed at high b-value
enhances the detection of demyelination and axonal loss
that occurs in MS. The q-space analysis of such data provides images displaying widespread disease load which
provide evidence of abnormalities in the NAWM of MS
patients that are not detected by FLAIR, T1, or even conventional DTI (bmax ⬃1000 s/mm–2). The data demonstrate
the relevance of the slow-diffusing component in assessing
the pathophysiological state of neuronal white matter in
white matter-associated disorders.
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FIG. 6. ROI histograms for (a) the q-space probability index, (b) q-space displacement index, (c) the FA at TE ⫽ 90 ms, and (d) the FA at
TE ⫽ 167 ms for the control, NAWM, and MS-lesion ROIs. The numerical data of this ROI analysis are summarized in Table 1.
Analysis of Diffusion Data at High b-Values
Once a non-monoexponential signal decay is observed in
an MR diffusion experiment, one faces the question of how
to analyze the data. The simplest approach is most likely
to fit the data with a biexponential function, such as Eq.
[2]. However, this implies the existence of two populations
that are in the slow-exchange regime. In addition, we
found that a biexponential fit of noisy data (such as obtained when using high b-value diffusion data of human
brains) is difficult and time-consuming, and suffers from
low reproducibility. Furthermore, when the DTI analysis
is performed on the biexponential fit, there are many pix-
els having certain directions in which the signal decay is
not biexponential. This makes the biexponential fit and
the extraction of the different parameters even more difficult. Convergence occurred 40 – 60 times more slowly
when the row data used to compute the q-space-analyzed
MR images were subjected to biexponential fit. In most
cases, the indices of the apparent slow-diffusing component were very noisy and appeared to be much less meaningful. Therefore, we decided to analyze the signal decay
using the q-space approach, and to combine it with a
tensor analysis to determine the smallest apparent displacement and the maximal apparent probability for zero
Table 1
ROI Analysis of q-Space and DTI Data for MS and Control Brains for the ROI Depicted in Figure 1*
ROI
Probability
Displacement (␮m)
FA (TE ⫽ 90 ms)
FA (TE ⫽ 167 ms)
Control
NAWM
MS lesion
8.3 ⫾ 0.7
7.5 ⫾ 1.1 (P ⬍ 1 ⫻ 10⫺6)
5.0 ⫾ 0.9 (P ⬍ 1 ⫻ 10⫺6)
3.3 ⫾ 0.8
4.0 ⫾ 1.2 (P ⬍ 1 ⫻ 10⫺6)
8.1 ⫾ 2.4 (P ⬍ 1 ⫻ 10⫺6)
0.54 ⫾ 0.15
0.52 ⫾ 0.15 (n.s.)
0.39 ⫾ 0.11 (P ⬍ 1 ⫻ 10⫺3)
0.56 ⫾ 0.12
0.51 ⫾ 0.13 (P ⬍ 1 ⫻ 10⫺6)
0.32 ⫾ 0.08 (P ⬍ 1 ⫻ 10⫺6)
*Values are averages ⫾ SD. P values are results of independent t-test compared to the control values in the first raw (n.s. is not significant
between the groups on the 0.05 level).
High b-Value q-Space DWI of MS
123
FIG. 7. The effect of the length of the diffusion
gradient pulse of water diffusion in sciatic nerve
on (a) the signal decays, and (b) the respective
q-space distribution profiles. The gradients
were applied perpendicular to the long axis of
the nerve.
displacement within each pixel. By this approach, we
could extract structural information from the sample by a
simple FT of the row data. Also, it should be noted that
q-space analysis provides a simple means for detecting
restricted diffusion by observing the effect of the diffusion
time on the displacement distribution function. Both the
probability and the displacement indices should change
once a demyelination process takes place. These changes
should be in opposite directions. Furthermore, q-space
analysis of diffusion data (at sufficiently high q- and bvalues) in neuronal tissue enables the extraction of structural information with a spatial resolution of a few microns.
According to the q-space theory, two conditions have to
be fulfilled in order to measure the real displacement
distribution profile in a system exhibiting restricted diffusion (24 –26). The first condition is the short gradient pulse
approximation, and the second is the long diffusion time
scale limit. The diffusion time used in the present study is
sufficiently long to fulfill the long diffusion time scale
condition. However, the pulsed gradient duration used in
this study had nearly the same length as the diffusion time,
thus violating the short gradient pulse approximation. As
stated above, this violation may cause deviations of the
extracted displacements and probabilities from the real
values (41). To estimate these deviations, we performed a
set of diffusion experiments in which the length of the
gradient pulse was varied. These experiments were performed on excised rat sciatic nerves (Figs. 7 and 8). Indeed,
the signal decay became slower as the duration of the
diffusion gradient pulse was increased, and the displacement distribution profile became narrower and more in-
tense, as expected theoretically for diffusion in a restricted
geometry (41). However, these experiments showed that
from the diagnostic point of view, it is better to use a long
gradient pulse compared to a short pulse since it overemphasizes the restricted compartment. However, for large ␦
one obtains less accurate displacement probability functions.
Despite the miscalculation of the actual displacements
in the human data set, q-space analysis of DWI data of MS
patients provides very informative images with a potentially better estimation of the disease load, particularly in
the NAWM. This can be gathered by comparing Fig. 4a and
b and Fig. 5a and b with Fig. 4c and d and 5c and d,
respectively, and by comparing the histograms shown in
Fig. 6a and b and Fig. 6c and d (also see data in Table 1).
Figure 8 shows the signal decays and the displacement
distribution profiles of the control and the EAN sciatic
nerves obtained from q-space analysis of diffusion data
acquired with ␦ ⫽ 4.5 ms and 72 ms. This figure provides
an explanation as to the origin of the increased sensitivity
and diagnostic capacity of this analysis in the region of
moderate q-values (500 cm–1 ⬍ q ⬍ 1000 cm–1). The data
in this figure clearly show that the difference between the
control and the EAN sciatic nerves is more significant in
the moderate q-value regions when ␦ is long. At very high
q-values (q ⬎ 2000 cm–1), and hence very high b-values
(b ⬎ 30000 s/mm2), the differences between the control
and the EAN nerves are nearly the same. However, it is
clear that such high q-value cannot be achieved with the
current technology on clinical MRI scanners. These experiments demonstrate that when high b-value diffusion data
are acquired with long gradient pulses, the restricted pop-
FIG. 8. a: Signal decay of water in control
and EAN-diseased rat sciatic nerves. The
EAN-diseased nerve was excised at day
14 postimmunization. The signal decays
were acquired with diffusion gradient pulses
of 4.5 ms with 160 gauss cm–1, and 72 ms
with 10 gauss cm–1. b: The respective qspace profiles of the data presented in a.
124
Assaf et al.
Table 2
Displacement of the Narrow and Broad Displacement
Components of EAN and Control Sciatic Nerves
␦ (ms)
4.5
9.0
18
36
72
Displacement,
narrow (␮m)a
Displacement,
broad (␮m)a
Control
EAN
Control
EAN
3.2
2.7
2.2
1.8
1.6
4.6
3.9
3.4
2.9
2.6
16.1
13.5
11.1
9.8
9.4
27.1
26.2
25.3
23.6
23.4
a
Displacement values were calculated from the full width at halfheight obtained by bi-Gaussian fit of the displacement distribution
profile.
ulation is more apparent. The data in Figs. 7 and 8 suggest
that there is no need to achieve very high q- and b-values
to differentiate between the different apparent diffusing
components.
Clinical Significance of High b-Value DWI in MS
When high b-value DWI is performed, at least two diffusing components can be identified: a fast and a slow components (Fig. 2). Until now, the diagnostic value of the
slow-diffusing component has been neglected. We suggest
that the slow-diffusing component, as measured perpendicular to the long axis of the fibers, is a relevant component when studying white matter-associated disorders.
This claim is based on the assumption that this component
should be sensitive to the integrity of myelin in white
matter (24). Our results suggest that q-space analysis of
high b-value DWI data provides MR images that appear to
characterize the disease load in MS better than other conventional methods such as T1 and FLAIR. The changes in
the NAWM of controls and MS patients when the slowdiffusing component is analyzed are even more prominent
and pronounced than in conventional DTI. This is evident
from the images shown in Figs. 3–5 and from the data
presented in Fig. 6 and Table 1.
The q-space-analyzed MR images suggest that the abnormalities in MS brain are not concentrated only in the
hyperintense areas seen on the T2 images, but are of a more
global nature, which is compatible with the known occurrence of diffuse axonal loss in advanced MS. The main
contribution of high b-values diffusion MR images appears
to be in the evaluation of diffused pathology in white
matter and the probable axonal pathology in MS. The
q-space-analyzed MR images may provide a more accurate
picture of the severity of the disease, as it is known that at
the later stages of the disease conventional MR changes
correlate poorly with the progression of the patient’s disability.
High b-Value q-Space DWI vs. Conventional DTI
Conventional MR methods are known to have a limited
diagnostic capacity for MS (33). Recently, MT and DWI
were suggested as better methods for the evaluation of MS
(36 –39). In this study we compared the DTI method measured at low b-values (1000 s/mm2) with DWI at very high
b-values, bearing in mind that information about the axonal integrity might be more available from high b-value
DWI. Furthermore, areas that appeared significantly abnormal in the q-space-analyzed MR images proved to be abnormal in DTI, but with lower statistical significance. This
suggests that the high b-value q-space MR images could
possibly identify areas of abnormal NAWM in a single
subject while DTI may fail to do so. It should be noted,
however, that low probability for zero displacement as
extracted from the q-space may also result from an incoherent arrangement of normal fibers, as found for the FA
extracted from DTI (42). Therefore, the different fiber architecture of different subjects may increase the variability
of these parameters, and may result in the erroneous classification of normal incoherent fiber arrangement as abnormal pathology.
An interesting point is the difference between the values
of the DTI collected at TE of 90 ms vs. those collected at
167 ms. It appears that the significance of the differences
between the ROI groups increases with the increase in the
TE of the DTI experiment (see Fig. 6c and d). Our results
show also that in the high b-value q-space MR images the
differences in the extracted indices for NAWM and MS
plaques in MS brain and the control values are larger than
with conventional DTI at both TEs (Table 1). The large
difference between the q-space indices of abnormal
NAWM in MS patients compared to white matter of controls may suggest that these abnormalities can be detected
in a single patient, whereas in low b-value conventional
DTI data the differences between the groups are apparent
only for large numbers of patients. However, a clear statement about the diagnostic capacity of the slow-diffusing
component as compared to conventional DTI must await
further analysis. One such analysis is a comparison between the high b-value q-space and conventional DTI indices and the NAA distribution as obtained from MRS.
Such studies are currently in progress in our laboratory.
ACKNOWLEDGMENTS
Financial support for this research was provided by the
United States–Israel Binational Science Foundation, grant
97-00346 (to Y.C.), and by the German Federal Ministry of
Education and Research within the framework of the German–Israeli Project Cooperation (DIP) (to Y.C.). The authors thank General Electric Medical Systems Europe for
supplying a flexible pulse sequence for DWI.
APPENDIX A: DISPLACEMENT AND PROBABILITY
TENSOR IMAGE CALCULATION
For the general case, we can perform a tensor analysis if we
find a set of parameters that are characterized by the following relation: A ⫽ ␣ 䡠 B, where A is a column vector
including a physical parameter that we measure, ␣ is a
constant, and B is a column vector containing tensor elements. In the case of DTI we use the following relation:
A ⫽ ln共Ii /I0 兲.
[5]
In this case, ␣ is the b-value and B is a vector containing
the diffusion tensor elements (B ⫽ Dii). In this case it is
High b-Value q-Space DWI of MS
125
possible to extract the tensor elements B from a linear
combination of the measured parameter (A) as shown in
the following equations according to Basser et al. (13):
冤冥 冤冥
冤
A1
A2
A3
A4
A5
A6
⫽k䡠I䡠
B1
B2
B3
B4
B5
B6
I⫽
;
1
1
0
0
1
1
0
0
1
1
1
1
1
1
1
1
0
0
0
2
0 ⫺2
0
0
0
0
2
0
⫺2 0
0
0
2
⫺2
0
0
冥
[6]
where I is the gradient scheme matrix and k is a constant
that depends on the experimental parameters. This set of
linear equations is then solved to give the following relations:
冤冥 冤冥
冤
B1
B2
B3
B4
B5
B6
⫽ k⬘ 䡠 O 䡠
O⫽
A1
A2
A3
A4
A5
A6
1
⫺1
1
0
1
0
;
冋
1 ⫺1
⫺1 1
1
1
0
0
⫺1 0
0
1
册
冕
␳共r 0兲P共r 0兩共r 0 ⫹ x兲, t d兲dr 0
[9]
where ␳(r0) is the density at point r0, and P(r0|(r0 ⫹ x),td)
is the probability that spin initially positioned at point r0
will move to r within a time tD. Intuitively, P(r0|(r0 ⫹ x),td)
depends on the diffusion gradient direction in the same
way D is. Therefore, one can use the displacement distribution profile in the six aforementioned directions to find
the probability function tensor elements in the same way
one uses ln(Ii/I0) to find the diffusion tensor elements.
Using the formalism given above and in Ref. 13, in the
linear relation A ⫽ ␣ 䡠 B we use the FT of the signal decay
as A and the displacement distribution profile tensor elements as B. In our analysis, instead of taking the whole
displacement distribution profile, I(x), in each of the six
directions, we took two parameters that characterize this
profile: the full width at half height and the profile peak
intensity. These two parameters were used to replace Ai in
Eq. [5]. Two tensors, one of the full width at half height
and one of the profile peak intensity, were calculated.
Since we used the same gradient directions as proposed by
Basser et al. (13), both the I and O matrices are the same,
and can be used to calculate the probability function tensor elements.
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⫺1 1
1
1
1 ⫺1
0
1
0
0
⫺1 0
1
1
⫺1
⫺1
0
0
冥
[7]
where the O matrix represents the linear combinations of
Ai and will give the desired B matrix element. Once the
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finding the rotation matrix that will give the three eigenvectors of the tensor according to the following equation:
B1 B4 B5
B4 B2 B6
B5 B6 B3
I共x兲 ⫽
䡠T⫽T䡠
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␭1
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