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diffusion, tensor, imaging, with, Reson, visualization, Magn, data, fiber, anisotropy, Radiology, using, Fig., brain, human, tractography, image, matter, magnetic, imaging., based, shows, resonance, such, which, techniques, white, Journal, European, tracts

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

Abstract

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

imaging

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

is;

SS0e

g2G2d2

Dd

Dapp (1)

* Corresponding author. Fax: /81-3-5800-8935.

European Journal of Radiology 46 (2003) 53/66

www.elsevier.com/locate/ejrad

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;

G2Dappg

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

The diffusion sensitization is represented by so-called

b -value [6] as:

bg2G2d2

d

By using the b -value, the basic formula for DTI is

written in a simple form as follows.

SS0e

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

directions.

Table 1

Six motion probing vectors (MPG)

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

analysis.

2.2. Diffusion tensor determination by solving linear

equations

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

Dxx

Dyy

Dzz

Dxy

Dyz

Dzx

b ln

n

b ln Si

n

b ln Sn

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

as;

x?2

2l1T

y?2

2l2T

z?2

2l3T

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.

ffiffiffi

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

anteroposteriorly.

(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

use.

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.

Acknowledgements

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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