MR Diffusion Tensor Imaging: Recent Advance And New Techniques ...

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MR diffusion tensor imaging: recent advance and new techniques for
diffusion tensor visualization
Yoshitaka Masutani, Shigeki Aoki, Osamu Abe, Naoto Hayashi, Kuni Otomo *
Image Computing and Analysis Laboratory, Department of Radiology, University of Tokyo (UT-RAD/ICAL), 7-3-1 Hongo Bunkyo-Ku, Tokyo 1138655, Japan
Received 12 November 2002; received in revised form 13 November 2002; accepted 14 November 2002
Recently, diffusion tensor imaging is attracting the biomedical researchers for its application in depiction of fiber tracts based on
diffusion anisotropy. In this paper, we briefly describe the basic theory of diffusion tensor MR imaging, the determination process of
diffusion tensor, and the basic concepts of diffusion tensor visualization techniques. Several results of clinical application in our
institute are also introduced. Finally, the limitations, advantages and disadvantages of the techniques are discussed for further
application of diffusion tensor visualization.
# 2002 Elsevier Science Ireland Ltd. All rights reserved.
Keywords: Diffusion tensor; White matter fiber tractography; 3D visualization
1. Introduction
In the early stage of studies for nuclear magnetic
resonance (NMR), effect of diffusion on NMR was
reported and spin diffusion measurement was initiated
by using the bipolar magnetic field gradient pulses for
encoding molecular diffusion effects in NMR signal [1/
3]. After a few decades, MR imaging techniques, known
as diffusion weighted MRI, for obtaining spatial diffusion map of free water protons were developed [4,5].
Since potential usefulness in diagnosing neurological
disorders was pointed out [6], diffusion MRI has been
widely used so far [7/12]. One of the important
advancements in the recent diffusion MRI is measurement of incoherent directional distribution of diffusivity, that is anisotropy, for application of visualizing
white matter fiber tracts [13/18], and the technique has
been developed to diffusion tensor imaging (DTI)
[19,20]. Since the output of DTI is image or volume
data in multi-channels with corresponding motion
probing gradient (MPG) vectors relatively, several
processing techniques are required for visualizing meaningful information [21,22].
The objective of this paper is to introduce and review
various techniques for visualization of DTI data. First,
we shortly describe the basic theory of diffusion tensor
MR imaging, including the determination process of
diffusion tensor and preprocessing techniques. Next, the
various visualization techniques such as neurological
fiber tractography are explained and then in vivo results
in our institute are shown. In the last section, we discuss
current limitations and further applications of the
diffusion tensor visualization based on the advantages
and the disadvantages of the techniques.
2. Basic theory for diffusion tensor determination
2.1. Diffusion weighted imaging and diffusion tensor
The relationship between the signal intensity of the
diffusion weighted images S by using diffusion sensitizing field gradient based on Stejeskal/Tanner spin echo
scheme [2] and the signal value S0 without the gradient


Dapp (1)
* Corresponding author. Fax: /81-3-5800-8935.
European Journal of Radiology 46 (2003) 53/66
0720-048X/03/$ - see front matter # 2002 Elsevier Science Ireland Ltd. All rights reserved.
where g is the gyromagnetic ratio of proton, s and G
represent the duration and the magnitude of the motion
probing (or diffusion sensitizing field) gradient, D is the
time between the centers of the pair of gradient pulses,
and Dapp is a scalar value called apparent diffusion
coefficient (ADC) which reflects molecular diffusivity
under motion restriction such as fluid viscosity.
If the directional dependency of ADC value is taken
into consideration and it is approximated by a tensor, a
part of (Eq. (1)) is replaced as;
TDg (2)
where g is the vector for MPG of which magnitude
corresponds to G , i.e. jgj/G , and D is the diffusion
tensor which is described as 3/3 symmetric matrix
(second rank tensor) as follows:
Dxx Dxy Dxz
Dxy Dyy Dyz
Dxz Dyz Dzz
A: (3)
The diffusion sensitization is represented by so-called
b -value [6] as:

d 3

: (4)
By using the b -value, the basic formula for DTI is
written in a simple form as follows.
bgTDg (5)
Fig. 1. Example of a multi-channel data set. Top row: T2-weighted image data without MPG. Bottom row: 6 channel image data with MPGs in 6
Table 1
Six motion probing vectors (MPG)
g11=2(1 0 1) g21=2(1 1 0) g31=2(0 1 1)
g41=2(1 0 1) g51=2(1 1 0) g61=2(0 1 1)
Y. Masutani et al. / European Journal of Radiology 46 (2003) 53/6654
The diffusion tensor D with six independent elements
can be uniquely determined if the number of the linearly
independent directions of the employed MPG is six. In
the case more than six, it is an approximation process to
determine D as shown in the next section. Fig. 1 shows
the series of multi-channel data for diffusion tensor
2.2. Diffusion tensor determination by solving linear
Including the case of MPG directions more than six,
elements of the diffusion tensor D can be basically
obtained by solving linear equations. By using MPG of
n directions, linear equations are obtained from (Eq. (5))
as follows.
x21 y
1 z
1 x1y1 y1z1 z1x1
n n n n n n
x2i y
i z
i xiyi yizi zixi
n n n n n n
x2n y
n z
n xnyn ynzn znxn

b ln S1
b ln Si S0
b ln Sn S0
where gi /(xi , yi , zi)
T and Si are the direction and the
signal intensity of the MPG indexed by i (i/1,. . ., n).
An example of a MPG set is shown in Table 1. One of
the computational techniques for solving this linear
equations is the singular value decomposition [23] based
on a least square method. Though it is theoretically
natural that more MPG directions provide better
approximation, a report [24] indicates that six MPG
vectors of optimized directions are enough in determining diffusion tensor for practical use.
2.3. Diffusion anisotropy by tensor parameters
The diffusion tensor representing directional anisotropy is diagonalized for obtaining the pairs of eigenvectors and eigenvalues; ei and li (i/1, 2, 3). The
eigenvalues and eigenvectors are sorted by the magnitudes of the eigenvalues (l?/l2/l3) for the convenience in subsequent processing. The diffusion tensor is an
ellipsoidal approximation of directional anisotropy of
diffusion, which shows distance covered in 3D space by
molecules in a certain diffusion time [21,25]. In the x ?/
y ?/z ? coordinate system in the frame of the principle
diffusion directions e1, e2, and e3, ellipsoid is represented


1 (7)
where T is diffusion time (Fig. 2). The ellipsoid is often
used for symbolic visualization of diffusion tensor.
Several diffusion anisotropy measures were defined by
using the eigenvalues, which are fractional anisotropy
(FA), relative anisotropy, volume ratio and so on [26].
The FA value shown as following formula is used most
frequently for anisotropy measure.
s ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
(l1  lM)
2  (l2  lM)
2  (l3  lM)
q ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi
l21  l
2  l
q (8)
where lM shows the mean eigenvalue; (l?/l2?/l3)/3.
The images by those anisotropy measures are the most
primitive visualization of the fiber tracts in the white
matter. In the sense that a single anisotropy measure is
insufficient for distinction of anisotropy types, linear,
planar, and spherical anisotropy measures were also
proposed recently [27].
2.4. Preprocessing of diffusion MRI data
Before computing diffusion tensor, preprocessing is
required depending on quality of original data. In the
cases of original data with low signal-to-noise ratio
(SNR), smoothing filters, such as gaussian filter help
restoration of the data and stable estimation of tensor
field [27]. One of the most considerable issues in
analyzing diffusion tensor data is image distortion. In
the echo planar imaging which is highly sensitive to eddy
current, each direction of MPG yields its own pattern of
global distortion in phase-encoding direction [28/31]
such as shear, scale and so on. Without correction of
those distortion patterns, visualization result of diffusion tensor data may not be reliable. Hence, analysis
and visualization of diffusion tensor data attract not
Fig. 2. Ellipsoidal approximation of directional anisotropy. The
ellipsoid surface represents the distance of molecule motion from the
origin in a certain diffusion time.
Y. Masutani et al. / European Journal of Radiology 46 (2003) 53/66 55
only biomedical researchers but also computer scientists
[32]. In the research of image science or computer vision,
this problem is categorized in non-rigid image registration and several techniques were reported so far [33,34].
Such registration process is geometric transformation
(or warping) of an image-based on maximization of
similarity measure between the image and the reference
image. In diffusion tensor imaging, multi-channel image
data by using MPG are transformed and registered to
the reference data of T2 weighted image without MPG.
For the difference of characteristics between those two
types of images with/without MPG, several similarity
measures such as mutual information [33] based on joint
intensity histogram are employed for the registration.
Fig. 3 shows the example of registration based on
mutual information.
3. Visualization techniques for diffusion tensor data
Various techniques for visualizing diffusion tensor
data were reported so far and can be categorized in the
two groups. One is the series of image-based methods in
which each voxel value represents local anisotropy
measure or principle direction of diffusion, and the 3D
rendering of those images by volume rendering or
surface rendering of the isosurface. The other is the
group of symbolic (or geometric) display methods by
using various types of glyph such as ellipsoid. In the
recent researches for the diffusion tensor visualization,
tractography based on diffusion tensor tracking is the
most attracting tools for visualizing and analyzing white
matter fiber tracts [35/37]. In this section, these
visualization methods are described.
Fig. 3. Distortion correction example based on mutual information. Top row: T2-weighted image for reference. Middle row: Before distortion
correction (from left: transformed image, mis-registration by distortion, and joint intensity histogram). Bottom row: After distortion correction (same
as middle row).
Y. Masutani et al. / European Journal of Radiology 46 (2003) 53/6656
Fig. 4. Image-based visualization of diffusion tensor data. Top: Sphere representing directional color encoding. Middle row: 2D images of imagebased visualization (from left: FA image, mean diffusivity image, and color-encoded image). Bottom row: Stereo pair image of volume rendering of
color-encoded data (frontal half was removed).
Y. Masutani et al. / European Journal of Radiology 46 (2003) 53/66 57
3.1. Image-based display of diffusion tensor data
In this category, the voxel values are determined on
the basis of eigenvectors and eigenvalues of diffusion
tensor at the location. The voxel value represents the
value of maximum diffusion coefficient l?, anisotropy
measure such as FA, orientation of the maximum
diffusion coefficient e1 and so on. The color-encoded
image of diffusion MRI was developed to visualize fiber
orientation [38]. By using DTI data, color-encoding of
the principle vector of the tensor e1 shows the fiber
tracts more distinctively than the simple FA images [39].
The simplest way to encode the orientation of e1 is to
determine the color components of the voxel by using
the FA value and the components of the normalized
eigenvector e1/(X1, Y1, Z1); (je1j/1) as follows;
(r; g; b; a)FA(jX1j; jY1j; jZ1j; 1) (9)
where r , g , b , and a represents red, blue, green and
alpha components of the voxel color, and FA is the
scalar value of the fractional anisotropy. The alpha
component is required only for the case of 3D volume
rendering. Fig. 4 shows the examples of image-based
visualization of diffusion tensor.
3.2. Symbolic display of diffusion tensor data
Varieties of display methods based on the use of
symbolic objects have been proposed. Those symbols
are; arrow, ellipsoid, and other combined objects
[20,27,40/43] and are aimed at displaying spatial
distribution of the anisotropy and the principle directions of the diffusion tensor. The ellipsoid display is the
most basic method for visualization of tensor including
stress and strain tensors in materials mechanics [44]. As
the formula (Eq. (7)) shows, an ellipsoid of diffusion
tensor represents distance covered in 3D space by
molecules in a certain diffusion time. A problem of
ellipsoid display is that apparent shape of ellipsoid
depends on view direction and it is difficult to recognize
local anisotropy. Coloring is effective for visualization
of such local properties. For example, a color-encoding
of local anisotropy mapping in our institute is described
as follows.
Fig. 5. Ellipsoidal visualization of diffusion tensor data. Top row: Superimposed on axial image (left: whole view, right: zoomed at splenium of
corpus callosum). Bottom row: Stereo pair of 3D ellipsoidal display.
Y. Masutani et al. / European Journal of Radiology 46 (2003) 53/6658
(r; g; b)

l2 l1 ;
l3 l1 
where r , g , and b are red, green and blue components of
local color. Fig. 5 shows an example of ellipsoidal
display with this color-encoding.
3.3. Fiber tractography by tracking diffusion tensor
Fiber tractography technique, initiated by Mori et al.
[35], based on tracking fibers in principle direction of
diffusion tensor provides further visualization beyond
other techniques. Tractography is basically based on the
line propagation technique, in which a tracking line is
propagated from a start point called ‘seed’. For a given
Fig. 6. White matter fiber tractography. Left: Seed ROI was set at corpus callosum on central sagittal image. Right: Target ROI (sphere) was set
around at pyramidal area.
Fig. 7. Left: Voxelized tractography data (top: axial image, bottom: sagittal image). Right: Volume rendering of voxelized tractography.
Table 2
MR imaging parameters of EPI for DTI
TR (ms) 5000
TE (ms) 78
b per axis (s/mm2) 500
FOV (mm) 240
Original matrix size (before interpolation) 128/128/30/32
Matrix size (after interpolation) 256/256/150/170
MPG axes 6 (13)
Imaging time (min) 5/7
Y. Masutani et al. / European Journal of Radiology 46 (2003) 53/66 59
Fig. 8. Well-demarcated tumor. Left: 3D rendering of the pyramidal tracts, tumor, and brain surface extracted from T2 weighted data. Right:
Coronal section of tractography.
Fig. 9. Mildly-invasive tumor. Top: Stereo pair of tractography by 3D rendering. Bottom: Axial images at the tumor level (CW from left top: T1weighted, T2-weighted, isotropic DWI and, FA).
Y. Masutani et al. / European Journal of Radiology 46 (2003) 53/6660
seed point P0, series of node coordinates Pi (i/1, 2,. . .)
on the trajectory are determined iteratively as follows.
Pi1Piddi(D(Pi)) (11)
where d is a scalar value of the propagation step
distance, di is the unit vector of propagation direction
depending diffusion tensor D at the location Pi . The
simplest propagation is based on the principle eigenvector e1 of the tensor.
diei(D(Pi)) (12)
Several techniques for determination of propagation
direction are proposed [27]. Practically, several seed
points are generated within a region (or volume) of
interest (ROI or VOI) set interactively for visualization
of a tract. Several criteria for propagation termination
are given as thresholds for several parameters such as
number of propagation steps, local anisotropy measures, angle between adjacent propagation direction
vectors, S0 value in T2 weighted data and so on. For
depiction of only tracts running through two ROIs, an
additional target ROI/VOI is utilized. Among all the
trajectories from seed ROI/VOI, only tracts reached to
the target are displayed for the purpose. Recently, a few
alternative approaches were also proposed for improvement of the depiction performance of tractography [45].
A tracking result, that is series of coordinates data of
trajectory nodes, is displayed by using line or tubular
object with supporting objects such as surface of brain,
slice image in 3D space of computer graphics. As
ellipsoidal display is aimed at visualization of local
anisotropy, color mapping of trajectory line, tube, or
surface, is effective for visualization of local property of
the tract object. Fig. 6 shows the result of tractography
with a ROI and two ROIs based on line representation
of trajectories and anisotropy color-encoding of the
formula (Eq. (10)). For displaying the section of
depicted tracts on arbitrary slice image, voxelization of
tract objects is applied, which is simply realized by
marking voxels that fiber trajectories penetrate in
volume data to display. Voxelization enables other
visualization techniques such as volume rendering and
Fig. 10. Acute infarction, Top: Stereo pair of tractography by 3D rendering including infarction volume. Bottom: Spatial relationship of the
pyramidal tracts and the infarction volume (left: arrow shows infarctioned area on DWI, right: frontal view of the pyramidal tracts and the
infarctioned area.
Y. Masutani et al. / European Journal of Radiology 46 (2003) 53/66 61
isosurface display. Fig. 7 shows an example of 3D
rendering of voxelized tractography.
4. Clinical applications
Since diffusion anisotropy of skeletal muscle was
reported [46], various types of biological fibrous structures in human and animals has been observed by DTI
[47/51]. Then, a lot of clinical applications were broadly
performed for analysis of brain development [52,53] or
change due to aging [54] and for diagnosing various
types of brain disorders [55/71]. In our institute, the
number of routine examination for neurological disorders by using DTI is over 200 cases including over 100
cases of analysis with tractography [Aoki et al., Presented in RSNA2002]. In this section, we show our
clinical application results of DTI visualization. The
DTI data sets were collected by using a MRI scanner
(Signa Horizon LX 1.5 T, GE Yokogawa Medical
Systems, Japan) and EPI imaging method with parameters shown in Table 2 was used in these studies.
Display and computing diffusion tensor were performed
with a PC workstation (Precision 330, DELL, USA) and
by using our original software developed in our institute
[Masutani et al., Exhibited in InfoRAD , RSNA2002].
The typical computation time per analysis was 5/10 s
for tractography or ellipsoid display. We would like to
show representative cases;
(1) Well-demarcated tumor: Fig. 8 shows a case of the
left medial temporal, well demarcated tumor without
any perifocal edema. By using DTI data set, the
pyramidal tract was visualized with our software. Seeds
were placed at the high signal area on T2 weighted
image in the posterior limb of internal capsule. Target is
placed at the precentral sulcas recognized by precentral
knob sign and other signs. The tract shows marked
deviation without significant change of diffusion anisotropy. The patient shows only mild weakness of the arm.
(2) Mildly-invasive tumor: A case of the left superior
frontal tumor without significant perifocal edema is
shown in Fig. 9. Some infiltration can be seen at the
medial aspect on T2 weighted image (arrow). The
pyramidal tract visualized by the similar method described above, which shows strong, rounded deviation
and minimal change of anisotropy.
Fig. 11. Agenesis of corpus callosum, Top: Posterior view of tractography. Bottom: Stereo pair in top view.
Y. Masutani et al. / European Journal of Radiology 46 (2003) 53/6662
(3) Acute Infarction: In Fig. 10, a case of 15 h deep
white matter infarction very close to the pyramidal tract
is shown. No significant difference in color-encoded
anisotropy is seen between the sides. The patient
recovered completely.
(4) Agenesis of corpus callosum: Tractography of a
patient with complete agenesis of the corpus callosum is
shown in Fig. 11. There is no commissure fibers of
corpus callosum. When we start tractography from the
portion where commissure fibers are located in normal
subjects, thick fibers which run anteroposterior direction can be tracked. This is the Probst bundle which run
(5) Fiber Crossing: Fig. 12 shows an example of
limitations in tractography at fiber crossing of superior
longitudinal fasciculus and pyramidal tract. Tracking
lines tend to be attracted to the thicker tracts at the
crossing. This issue is discussed in the next section.
5. Current limitations, further applications and the future
Diffusion tensor visualization is increasingly used and
is expected as a promising technology for improvement
of diagnosing neurological diseases. Among the diffusion tensor visualization techniques, neuronal fiber
tractography is most attractive due to several advantages. First of all, fiber tractography utilizes relationship
among voxels and holds local information of tracking
lines while other visualization techniques by imagebased or symbolic display are based on independent
analysis and visualization for each voxel. Such information along trajectory shows potentials for connectivity
assessment between two regions [72]. On the other hand,
several limitations of tractography are often pointed
out, which are due to the characteristics or property of
DTI data. The limitation of spatial resolution is well
known as the reason of partial volume effect [73].
Fig. 12. Fiber crossing, Top: Fiber crossing point is shown by an arrow. Bottom: Local anisotropy is visualized by ellipsoids and coronal image (left:
with T2-weighted image, right: with color-encoded image).
Y. Masutani et al. / European Journal of Radiology 46 (2003) 53/66 63
Especially in tractography, fiber crossing [74] is a critical
issue in determining tracking direction. At fiber crossing, low anisotropy is observed and directions of
eigenvectors do not correspond to directions of both
tracts crossing. It is also a limitation due to tensor
representation, i.e. ellipsoid, for directional distribution
of diffusion coefficient. Spectrum representation [75,76]
based on data acquisition by more MPG directions may
help the determination of tracking direction. Next, SNR
[77/80] is another factor that affects the quality of fiber
tracking which is more sensitive to noise than other
techniques. It is a practical issue, that is, trade off
between data quality and data acquisition time in
clinical use. It is necessary to employ imaging techniques
with motion compensation such as navigator echo
technique [81/85] for reduction of patient motion
artifact caused in longer acquisition time. In addition,
it is more eligible to use imaging techniques such as line
scan [86/88] or PROPELLER [89] with less distortion
than to apply image distortion correction. For all these
limitations, development of imaging technique and
imaging hardware is essential. Another important issue
of tractography is validation. Unlike other visualization
techniques, tractography is accompanied by segmentation process for fiber tracts. Therefore, the issue is same
as other segmentation algorithms in the sense that no
gold standard can be defined. Generally in segmentation
validation, the ‘silver’ standard by manual segmentation
result by radiologists is often employed instead. From
the standpoint of size and complexity of segmentation
target, fiber tract segmentation is more difficult than
that of vascular structures. In these senses, segmentation-free visualization techniques of image-based or
symbolic display method slightly have advantages.
Establishment of validation scheme for tractography is
the highest priority for broader acceptance in clinical
The application domain of diffusion tensor visualization is expanding out of neurological diagnosis. One is
surgical navigation in which specific fiber structures
such as pyramidal tract should be avoided from invasive
operation as well as eloquent area and vascular structures. Combination with information based on matching
with other imaging modalities [90] helps broadening
fields of studies. For example, combined study with
functional MRI provides brain science with more
consistent approaches for analyzing brain functions
and anatomy [43]. For the educational purpose of
biological anatomy, computerized atlas [91] is a good
application field for diffusion tensor analysis and
visualization. In addition to other brain structures
such as blood vessels, information of white matter fiber
tracts helps further understanding of brain structures
and functions.
The authors are grateful to Dr Satoshi Kunimatsu, Dr
Harushi Mori, Dr Tomohiko Masumoto, Dr Makoto
Watanabe, and Dr Takeharu Yoshikawa, in the Department of Radiology, the University of Tokyo Hospital,
Japan, and to Mr Hiroyuki Kabasawa of GE Yokogawa
Medical Systems, Japan for data analysis, assisting in
DTI study, and fruitful discussion.
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