diffusion tensor mrimaging ofthe human brain’...tensor inaclinical setting. materials and methods...

Carlo Pierpaoli, MD #{149}Peter Jezzard, PhD #{149}Peter J. Basser, PhD #{149}Alan Barnett, PhDGiovanni Di Chiro, MD

Diffusion Tensor MR Imaging ofthe Human Brain’

Index terms: Brain, MR. 13.121412, 13.121416, 13.12146 #{149}Magnetic resonance (MR), diffusion

study, 13.121412, 13.121416, 13.12146, 13.92 #{149}Magnetic resonance (MR), experimental, 13.12 1412,

13.121416, 13.12146, 13.92 #{149}Magnetic resonance (MR), tissue characterization, 13.121412, 13.121416,

13.12146, 13.92

Abbreviations: ADC = apparent diffusion coefficient, CSF = cerebnospinal fluid, DW = diffusion

weighted, ROI = region of interest, S/N = signal-to-noise ratio, TE = echo time.

Radiology 1996; 201:637-648

I From the Neuroimaging Branch, National Institute of Neurological Diseases and Stroke (C.P.,

A.B., G.D.C.); Unit of MRI Physics, National Institute of Mental Health (P.J.); and the National Cen-ten for Research Resources (P.J.B.); National Institutes of Health, Bldg 10, Room 1C227, 9000 Rock-ville Pike, Bethesda, MD 20892-1178. Received July 3, 1996; revision requested August 12; revisionreceived August 19; accepted August 26. Address reprint requests to C.P.

, RSNA, 1996

637

PURPOSE: To assess intrinsic prop-erties of water diffusion in normalhuman brain by using quantitativeparameters derived from the diffu-sion tensor, D, which are insensitiveto patient orientation.

MATERIALS AND METHODS: Mapsof the principal diffusivities of D, ofTrace(D), and of diffusion anisotropyindices were calculated in eighthealthy adults from 31 multisection,interleaved echo-planar diffusion-weighted images acquired in about25 minutes.

RESULTS: No statistically sig-nificant differences in Trace(D)(n2,100 x 10-b mm2/sec) were foundwithin normal brain parenchyma,except in the cortex, where Trace(D)was higher. Diffusion anisotropy var-ied widely among different white mat-ter regions, reflecting differences infiber-tract architecture. In the corpuscallosum and pyramidal tracts, theratio of parallel to perpendicular dif-fusivities was approximately three-fold higher than previously reported,and diffusion appeared cylindricallysymmetric. However, in other whitematter regions, particularly in thecentrum semiovale, diffusion anisot-ropy was low, and cylindrical sym-metry was not observed. Maps of pa-rameters derived from D were alsoused to segment tissues based ontheir diffusion properties.

CONCLUSION: A quantitative char-acterization of water diffusion in an-isotropic, heterogeneously orientedtissues is clinically feasible. This

should improve the neuroradiologicassessment of a variety of gray andwhite matter disorders.

r”i IFFUSION-WEIGHTED (DW) imagesL� are magnetic resonance (MR)images with signal intensities sensi-

tized to the random motion of watermolecules (1-3). This is usually achievedby including strong magnetic field

gradient pulses in the imaging Se-quence. From a series of DW images,it is possible to calculate an apparent

diffusion coefficient (ADC) of watermolecules in the direction of the dif-fusion sensitizing gradient (2).

A number of studies have suggested

that images of water diffusivity canprovide information about tissuepathophysiobogy complementary tothat contained in Ti- and T2-weightedimages (4). The most clinically impor-

tant results to date pertain to the as-

sessment of brain diseases, especially

acute cerebral ischemia (5), where asignificant reduction in the ADC of

water demarcates the ischemic re-gions before signal intensity changesare detectable in conventional T2-

weighted images (6).Although the determinants of wa-

ter diffusion in tissues are still not

completely understood, there is gen-

eral agreement that physicochemicalproperties of the tissue (eg, viscosityand temperature) as well as its struc-

tural components (macromolecules,membranes, and intracellular organ-

elles) can substantially affect water

diffusivity. Their importance in deter-

mining the behavior of water diffusiv-

ity is suggested by the observationthat in tissues that have a randommicrostructure, the measured ADC

appears to be the same in all dimec-tions (isotropic diffusion), while in

tissues that have a regularly ordered

microstructure, the measured ADCvaries with tissue orientation (aniso-

tropic diffusion). This phenomenon

has been observed in white matter

(7-9); in skeletal (10), cardiac (ii), and

uterine (12) muscles; in portions ofthe kidney (13); and in the lens (14). It

is reasonable to speculate that patho-logic conditions that alter tissue mi-crostructure could affect not only the

bulk diffusivity, but also the aniso-tropic diffusion characteristics of wa-ter or metabolites.

Assessing diffusion in anisotropic

tissues, however, requires a knowl-edge of molecular displacements inall directions, whereas the ADC onlyprovides a measure of the displace-ments of molecules in one direction.Efforts to characterize anisotropic dif-fusion by measuring ADCs in two orthree perpendicula r directions havebeen made (15-18). Implicit in theseschemes are the assumptions that the

larger ADC represents the diffusioncoefficient parallel to the longitudinalaxis of the anisotropic structure and

638 #{149}Radiology December 1996

that the smaller ADC is a measure of

water diffusivity perpendicular to it.Unfortunately, these conditions are

impossible to satisfy in clinical MR

imaging of heterogeneously orientedtissues, such as brain white matter,

because it is not possible to align the

diffusion gradients with the axes ofthe fibers in all voxels. The depen-dence of the ADC on gradient direc-tion introduces an orientation biasinto anisotropy indices which canlead to erroneous conclusions abouttissue structure and potentially to di-

agnostic errors. For example, it hasbeen recently demonstrated in mon-key brain that various measures of

diffusion anisotropy using ADCs ac-

quired with diffusion gradients ap-plied in three perpendicular direc-tions, ADC� ADC�, and ADCD generallyunderestimate the degree of diffusionanisotropy of white matter structures

(19). The error is so severe in white

matter fibers oriented obliquely withrespect to the magnet coordinates asto make these fibers appear isotropic,indistinguishable from gray matter.

Moreover, implicit in the use of theratio of ADCs as an anisotropy mea-sure is the assumption of cylindricalsymmetry of the tissue, that is, that

there are only two relevant directions,one that is parallel and the other that

is perpendicular to the fiber tract. This

view of fiber architecture, while prob-ably appropriate for some tissue struc-

tures, is generally too simplistic.The estimation of a diffusion tensor,

D, has been proposed as an effective

means to overcome these problems ofcharacterizing diffusion in anisotropic,

heterogeneously oriented tissues (20,21).The six independent scalar elements ofthe diffusion tensor contain the informa-lion required to characterize diffusion inall directions. Moreover, by using them,it is possible to calculate new quantities

that are intrinsic to the tissue, that is,that are rotationally invariant, inde-pendent of the orientation of the sub-ject in the magnet.

The most fundamental rotationallyinvariant quantities are the three princi-

pal diffusivities (eigenvalues) of D,which are the principal diffusion coef-ficients measured along the three (in-trinsic) coordinate directions that con-stitute the local fiber frame of referencein each voxel. (Each eigenvalue is as-sociated with a principal direction[eigenvector] that is also intrinsic tothe tissue. The three eigenvectors ofD are mutually perpendicular anddefine the local “fiber” frame of refer-ence in which the description of dif-fusion is the simplest and most natu-ral.) In each voxel, these eigenvalues

can be sorted in order of decreasing

magnitude (X1 = highest diffusivity,X2 intermediate diffusivity, andx3 lowest diffusivity). In anisotropictissues organized in parallel bundles,

the largest eigenvalue, X1, representsthe diffusion coefficient along the di-rection parallel to the fibers (ADC11),

while X2 and X3 represent the trans-verse diffusion coefficients (ADC1

and ADC1’).

Finally, from D one can computescalar measures that characterize spe-cific features of the diffusion process,

such as Trace(D) that is used to mea-sure the onientationally averaged dif-fusivity and quantities that are used

to measure the degree of diffusionanisotropy. More general informationabout the underpinnings of diffusiontensor MR imaging may be found inrecent review articles (22).

We performed this study to charac-terize the diffusion properties of wa-ten in the human brain by using theprincipal diffusivities or eigenvaluesof D, along with Trace(D) and diffu-

sion anisotropy indices derived fromD. These measures share the attributesof being quantitative and indepen-dent of the position and orientationof the subject within the magnet. We

also considered the technical require-

ments for measuring the diffusiontensor in a clinical setting.

MATERIALS AND METHODS

Subjects

Eight adult healthy volunteers (aged27-36 years) participated in the study un-

der a protocol approved by the Institu-tional Review Board of the National Insti-tute of Neurological Diseases and Stroke(Bethesda, Md). Written informed consentwas obtained before each study. Each sub-ject underwent MR imaging at least onceto acquire a data set of axial DW images;

four of the eight subjects also underwent

imaging to obtain sagittab, coronal, or bothsagittal and coronal data sets.

MR Imaging

Studies were performed with a 1.5-Tmagnet (Signa Advantage; GE MedicalSystems, Milwaukee, Wis) equipped witha gradient insert (Medical Advances, Mi!-

waukee, Wis) capable of producing gradi-ent pulses up to 25 mT/rn and a birdcagequadrature radio-frequency coil. Reduc-tion of subject head motion was achievedby gently inflating two custom-built pneu-matic pillows placed on either side of thesubject’s head. After positioning the sub-

ject with the help of gradient-recalled-echo sagittal and axial images, the mag-netic field was shimmed by using the

standard nonlocabized shimming routineprovided by the manufacturer.

Diffusion images were acquired with arecently developed interleaved spin-echo,echo-planar imaging sequence (23) with anavigator echo used to correct for motionartifacts (24-28). The navigator-echo cor-rection was accomplished by collecting aread-direction navigator echo as part ofthe data acquisition of each echo-planarinterleaf. An additional “ reference” imagewas used to correct for ghosting due to theodd and even echoes of the echo-planarreadout. A description of the pulse Se-quence diagram and the algorithm for im-age reconstruction is presented elsewhere(23).

Diffusion sensitization was attained byapplying identical trapezoidal diffusiongradient pulses before and after the 180#{176}radio-frequency pulse (29). These gradi-ents had a duration of 22 msec and a ramp

time of 0.2 msec and were separated by atime interval of 42.4 msec (center to cen-

ter). To attain the maximum diffusion sen-sitization for a given echo time (TE), thediffusion gradients were asymmetricallypositioned with respect to the 180#{176}radio-frequency pulse. Six different gradient di-rections were sampled sequentially by ap-plying pairs of diffusion gradients, G�, G�,

and G,, simultaneously. The following di-rectional pattern was used for the six gra-dients: {(1/G()) (G�, G�, G,) = (1,0,1), (-1,0,1),(0,1,1), (0,1,- 1), (1,1,0), (-1,1,0)], where(for the acquisition of axial images) G. isthe component of the diffusion gradient inthe phase-encoding direction (horizontal),G, is the component of the diffusion gradi-ent in the readout direction (vertical), G, isthe component of the diffusion gradient inthe section-select direction (bore), and G0is the strength of the diffusion gradient.

In each direction, we acquired five DWimages with different diffusion gradientstrengths. The maximum gradient strengthwas 23 mT/rn. A total of 31 DW imageswere obtained for each section, which in-cluded one image obtained with no diffu-sion sensitization. The values of the Trace

of the b-matrix ranged between 0.2sec/mm2 and 1,016 sec/mm2.

Imaging acquisition parameters were asfollows: 18 axial sections, 3-mm sectionthickness, 2-mm section separation, 128 x128 in-plane resolution (eight interleaves,16 echoes per interleaf), 220-mm field ofview, a repetition time of greater than 5seconds and a TE of 80 msec, and cardiacgating (two to three acquisitions per heart-beat, depending on the heart rate, startingwith a 200-msec delay after systole).

The imaging time for the acquisition ofthe entire diffusion imaging data set wasusually less than 25 minutes (24.8 minutes,assuming a heart rate of 60 beats per minute).Including positioning and shimming, thetotal time spent in the magnet by the sub-ject was about 40 minutes.

Analysis of the MR Imaging Data

The raw data were transferred to aSparc-JO workstation (Sun Microsystems,

Volume 201 #{149}Number 3 Radiology #{149}639

Mountain View, Calif) and processed forphase correction, navigator-echo correc-tion, and Fourier reconstruction. For eachreconstructed magnitude image, the b-matrix (30) was numerically calculatedfrom the imaging and gradient wave-forms. The six independent elements ofthe diffusion tensor D � � D,�, �

� Dy,) and the signal intensity withoutdiffusion sensitization, A(b = 0), were sta-tisticably estimated in each voxel according

to the method of Basser et al (20,21).Background noise levels were measured

in regions of the images that contained notissue (31). These regions were chosen in

the frequency-encoding direction to avoidcontamination by signals originating fromghosts present in the phase-encoding di-rection. A mask was then applied to ex-dude all voxebs having a non-diffusion-weighted signal intensity ofless than eighttimes the average background noise level.The square of the deviation between eachmeasured value of the logarithm of signalmagnitude and the corresponding valuepredicted by the model (which appears asa term in x2) was normalized by the squareof the ratio of the root-mean-squaredbackground noise in each image and thesignal intensity in each voxel. This prop-erly weights the observed deviation ineach measurement by the experimentalvariance corrected for the bias introducedby taking the logarithm of the signal in-tensity (32).

Once D was calculated in each voxel,its eigenvectoms and eigenvabues were ob-

tamed by using the numeric routine TQLI(33) provided in IDL (Iterative Data Lan-guage; Research Systems, Boulder, Cob).

The eigenvalues of D were then sorted inorder of decreasing magnitude in eachvoxel.

Maps of rotationally invariant param-

eters derived from D, including the Trace

of the diffusion tensor, Trace(D), and tworecently proposed anisotropy indices, theVolume Ratio index (19,34) and the Latticeanisotropy index (19,35), were also calcu-lated on a voxel-by-voxel basis directlyfrom the map of D. The Volume Ratio is

an intravoxel anisotropy index that repre-sents geometrically the ratio of the volume

of an ellipsoid whose semimajor axes arethe three eigenvalues of D and the vol-ume of a sphere whose radius is the meandiffusivity, Trace(D)/3. The Lattice anisot-ropy index is an intervoxel measure of dif-fusion anisotropy that exploits informa-tion about the orientational coherence ofthe eigenvectors of D in adjacent voxels toimprove the estimate of diffusion anisot-ropy within a reference voxel. The Lattice

anisotropy index is especially immune to

background noise in the DW images andprovides a quantitative, robust measure-

ment of diffusion anisotropy (19,35).Averages of these imaging parameters

were also obtained in different regions ofinterest (ROIs) by adding their values on a

voxel-by-voxel basis. Anatomic ROIs weredrawn by a trained neurologist (C.P.) onthe T2-weighted axial amplitude images ofA(b#{176}=O).ROIs of small anatomic structureson the in-plane images were constructed

by pooling voxels of the same structures indifferent sections.

Statistical Analysis of the Data

After estimating D in each voxel, thecorrelation coefficient (calculated in eachvoxel during the regression procedure)was used to mask or exclude voxebs inwhich the linear model poorly fit the data.Voxels with a correlation coefficient of lessthan 0.85 were excluded from further con-sideration. To assess the statistical signifi-cance of variations of Trace(D) and theanisotropy indices between different ana-

tomic regions, we used one-way analysisof variance followed by post hoc compari-sons with the Sheffe test.

In principle, if there were no noise inDW imaging, one could determine whetherwater diffusion is isotropic (X1 = X2 =

cylindrically symmetric and anisotropic

(X1 � X2 � or X� = X2 � X3), or asymmet-ric and anisotropic (X1 � X2 � X3) in eachanatomic ROl by inspecting the eigenval-ues. However, when the DW images arenoisy, sorting the eigenvabues biases theirdistributions (19), so that standard statisti-

cal tests that analyze the significance oftheir differences are not valid.

To address this problem, we have usedan empiric hypothesis-testing procedureinstead. To test the hypothesis of diffusion

isotropy in each ROl, we constructed anisotropic diffusion tensor whose Traceequaled the experimentally measuredTrace(D) in the ROI. Distributions of thethree eigenvalues of D were then gener-ated by using Monte Carlo simulations(19). In these simulations, the signal-to-noise ratio (S/N) was identical to thatmeasured in each ROl. It was obtained bydividing the mean signal intensity in the

ROl by the root-mean-squared back-ground noise (31). Moreover, the b-matri-ces were the same as those used in thepresent study. We used a one-tailed t testwith X� and X3 and a two-tailed t test withX2 to assess whether there were significantdifferences between actual (measured)and expected (simulated) distributions ofeach eigenvalue.

If significant differences were assessedin at least one of the eigenvalues, the hy-pothesis of isotropic diffusion in the ROI

was rejected. In such ROIs, the hypothesisof cylindrically symmetric and anisotropicdiffusion was then tested in turn. This wasdone by generating a set of diffusion ten-sors whose Trace equaled the ROI-aver-aged Trace(D) but for which X� � K2 =

or X� = �‘2 � 1(3. Monte Carlo simulationswere then performed (as described above)by using these cylindrically symmetrictensors. We selected tensors whose mean

values of Xi and X3 matched those measuredin the ROI. Then, by using a one-tailedtest, we were able to assess whether sig-nificant differences existed between actual

(measured) and expected (simulated) dis-tributions of X2. If such differences werenot significant, we concluded that the tis-sue was cylindrically symmetric and an-

isotropic; otherwise, we concluded thatthe tissue was asymmetric and anisotropic.

RESULTS

The head restraint was well toler-ated by all subjects, and all subjectscompleted the study. The use of headrestraint and cardiac gating did notentirely eliminate motion artifacts inDW images, so a navigator-echo-cor-

rection scheme was necessary to ob-tam usable data. Overall, about 10%of the DW images were corrupted bymotion artifacts even after navigator-echo correction. The S/N of thenon-DW images was relatively con-stant in the various studies: about

18-20 in white matter, 22 in deep graymatter, and 25 in cortical gray matter.

By means of direct computation, the

contribution of the imaging gradientsto the b-matrix was found to be negli-gible (less than 1%) for all the images.

Diagonal and Off-diagonalElements of D

For an axial section of the brain,Figure la shows images of the diago-nal elements of D � � and �

which correspond to the ADCs in thex, y, and z directions, respectively.

(We did not measure the ADCs alongthe x, y, and z coordinate directionsdirectly because we applied diffusionsensitizing gradients only along

oblique directions. When imaginggradients can be shown to have a

negligible effect on echo attenuation,ADCX, ADC�, and ADCZ are equal tothe corresponding diagonal elementsof the diffusion tensor.) Figure lbshows images of the off-diagonal ele-

ments of D � � and � Boththe diagonal and off-diagonal ele-ments of D depend on the intrinsicdiffusion properties and the orienta-tion of the tissue; however, the off-diagonal elements of D do not repre-sent ADCs along the oblique directions.Rather, they indicate how stronglyrandom displacements are correlatedin the x, y, and z directions. The graybackground of the images in Figurelb corresponds to a zero value, whichindicates no correlation; brighter vox-els indicate a positive correlation; anddarker voxels indicate a negative cor-relation. When all off-diagonal ele-ments are zero, it may indicate isot-ropy or that locally fibers lie parallelto the x, y, or z axes. In both cases, theestimation of the entire diffusion ten-son would not be necessary to prop-

erly characterize anisotropy, andADCs measured along the three mag-net axes would be sufficient.

Positive or negative values of theoff-diagonal elements of D indicateregions where the anisotropic struc-

a.

h.

Figure 1. Axial maps of diffusion tensor elements in the brain of a healthy 33-year-old woman.

(a) Images of the diagonal elements of D: � � and D,.,, which correspond to ADCX, ADC5,and ADC1, respectively. Black corresponds to 0 mm/sec and white corresponds to 2,500 x10-s mm/sec. (b) Images of the off-diagonal elements of D: � Dx,, and D�.,. Gray-scale val-

ues lie between -1,250 x 10� mm/sec and 1,250 x 10� mm2/sec. Image contrast of all ele-ments of D depends on both the intrinsic diffusion properties of the tissue and the orientation

of the subject in the magnet.

Figure 2. Maps of the three sorted eigenvalues of D (Xi, X2, and X�) computed from the maps

of the six diagonal elements of D depicted in Figure 1. Structures in which diffusion is isotro-

pic should have the same intensity in the three images, while structures that are anisotropic

should exhibit significant differences in intensity in the three different images. If the two dif-

fusion coefficients perpendicular to the fiber tracts were the same (cylindrically symmetric and

anisotropic diffusion), we would also expect the contrast in the images of X2 and X3 to be the

same. For most white matter regions, this condition is not satisfied.


tures are oblique with respect to the x,

y, or z axes. In this case, one would

underestimate the degree of anisot-ropy by using ADCx, ADC�, and ADCZ

rather than the eigenvalues of D. Aswe can see in Figure lb. a number of

regions in the corpus callosum, cen-

trum semiovale, and subcortical whitematter possess off-diagonal elementsthat are nonzero.

In Figure lb. notice that all voxels atthe periphery of the brain have non-zero off-diagonal elements. This issurprising because these regions con-

tam cerebrospinal fluid (CSF), andtherefore should exhibit no aniso-tropic diffusion. This finding is artifac-

tual. It is due to shearing and dilata-tional distortion of the DW imagescaused by eddy currents induced

when diffusion gradients are applied.The misregistration of the distortedDW images introduces an artifact inthe estimation of D. This results inblurring of maps of quantities derivedfrom D and the appearance of spuri-ous boundaries-regions of apparently

increased anisotropy-at the inter-

faces between structures having mark-

edly different diffusion properties.

Eigenvalues of D

Figure 2 comprises maps of thethree sorted eigenvalues of D (X1, X2,and X�), computed from the six im-ages depicted in Figure 1. The eigen-

values of D are the three principaldiffusion coefficients that are charac-

tenistics of the tissue, so that, unlikeADCX, ADC�, and ADC1, they do not

depend on the direction along whichthe diffusion gradients have been ap-plied. We see that, in contrast withthe images of the elements of D inFigure 1, we do not detect any onien-

tational bias in the images in Figure 2.The image of 1’.i, for example, is a map

of the highest diffusion coefficient

measurable in each voxel, while the

image of X3 is a map of the smallest

diffusion coefficient measurable in

each voxel for all possible directionsof diffusion sensitizing gradients. In

gray matter, it can be seen that the

images of Xi, X2, and X3 show similar,

but not equal, intensities. This is also

the case in regions of CSF. Aniso-

tropic structures, such as white mat-

ter, exhibit marked differences in in-tensity in the three different images.

Table 1 contains the eigenvalues ofD (X’, X2, and X�) juxtaposed with the

diagonal elements of D measured indifferent anatomic ROIs in the brain.Average values of Trace(D) and of the

Volume Ratio and the Lattice anisot-ropy indices in these ROIs are also

presented. Table 2 summarizes our

analysis of the anatomic ROIs pre-

sented in Table 1. Trace(D) is approxi-mately 2,100 x l06 mm2/sec in most

brain regions but is approximately2,400 x 10-6 mm2/sec in the cortex.

Table 2 shows that no statistically sig-nificant differences exist between

Tmace(D) in different ROIs, with theexception of in the cortex, where the

value is significantly higher than it is

in all the other regions.

The sorted eigenvalues of D suggest

that water diffusion is highly anisotropicin some white matter structures, such asin the pyramidal tract and in the con-

pus callosum, where the values of X1( � i,700 x i0-� mm2/sec) are much

larger than the values of X2 ( � 300 x

106 mm2/sec) and X3 ( � 110 x


Table 1Eigenvalues and Diagonal Elements of D, Trace (D), and Two Amsotropy Measures Obtained in Nine ROIs

Splenium Posteriorof the Limb of the

Pyramidal Corpus Optic Internal Centrum Caudate Frontal Cerebrospinal

Measure Tract Callosum Radiation Capsule U Fibers Semiovale Nucleus Cortex Fluid

Eigenvalues of D(x 106 mm2/sec)

xl 1,708 ± 131 1,685 ± 121 1,460 ± 75 1,320 ± 54 1,200 ± 79 995 ± 66 783 ± 55 1,002 ± 118 3,600 ± 235x2 303±71 287±71 496±59 447±36 545±64 602±32 655±28 810±65 3,141±144x3 114±12 109±26 213±67 139±41 208±73 349±17 558±17 666±53 2,932±212

Diagonal elements of D(x 1O� mm2/sec)

311 ± 131 841 ± 486 933 ± 507 451 ± 99 455 ± 138 606 ± 119 635 ± 69 874 ± 102 3,187 ± 165

D� 420 ± 188 942 ± 537 827 ± 490 380 ± 84 456 ± 176 603 ± 103 706 ± 91 795 ± 136 3,080 ± 178D� 1,340 ± 245 287 ± 143 405 ± 62 1,070 ± 98 1,040 ± 84 736 ± 93 656 ± 35 809 ± 36 3,206 ± 162

Trace (D)(x106mm2/sec) 2,125 ± 132 2,081 ± 141 2,169 ± 77 1,906 ± 80 1,953 ± 154 1,945 ± 73 1,996 ± 52 2,477 ± 164 9,573 ± 305

Anisotropy measures1 - volume ratio 0.93 ± 0.04 0.86 ± 0.05 0.62 ± 0.12 0.70 ± 0.08 0.55 ± 0.11 0.27 ± 0.03 0.08 ± 0.03 0.08 ± 0.05 0.02 ± 0.01Lattice index 0.73 ± 0.06 0.77 ± 0.05 0.54 ± 0.07 0.61 ± 0.04 0.46 ± 0.05 0.31 ± 0.03 0.12 ± 0.05 0.09 ± 0.04 0.05 ± 0.02

Note-Values are expressed as mean ± standard deviation.

Table 2Statistical Analysis of Diffusion Anisotropy and Trace (D) between ROIs

ROI

Frontal Caudate Centrum U Optic Internal Pyramidal CorpusROI Cortex Nucleus Semiovale Fibers Radiation Capsule Tract Callosum

Lattice anisotropy indexFrontal cortex . . . No Yes Yes Yes Yes Yes YesCaudate nucleus No . . . Yes Yes Yes Yes Yes YesCentrum semiovale Yes Yes . . . Yes Yes Yes Yes YesU fibers Yes Yes Yes . . . No Yes Yes YesOptic radiation Yes Yes Yes No . . . No Yes YesInternal capsule Yes Yes Yes Yes No . . . No YesPyramidal tract Yes Yes Yes Yes Yes No . . . NoCorpus callosum Yes Yes Yes Yes Yes Yes No ...

Trace (D)Frontal cortex . . . Yes Yes Yes Yes Yes Yes YesCaudate nucleus Yes . . . No No No No No NoCentrum semiovale Yes No . . . No No No No NoU fibers Yes No No . . . No No No NoOptic radiation Yes No No No . . . No No NoInternal capsule Yes No No No No . . . No NoPyramidal tract Yes No No No No No . . . NoCorpus callosum Yes No No No No No No ...

Note-P < .05 indicated a statistically significant difference. “Yes” indicates significance and “no’� indicates no significance at the P < .05 level by using theSheffe test.

l06 mm2/sec). The pyramidal tract

and the corpus callosum also have thehighest values of the 1 - Volume Ratioand Lattice anisotropy indices. Thedegree of anisotropy is substantiallylower in other white matter regions,with the lowest values observed inthe centrum semiovale. In contrastwith the results obtained for Trace(D),the Volume Ratio and Lattice anisot-ropy indices show significant differ-ences among many white matter re-gions (Table 2).

In all regions, the diagonal elementsof D in the x, y, and z directions (whichin this study are equivalent to ADCsin the x, y, and z directions) are sig-

nificantly different from the eigenval-ues of D. Within each ROl, the range

of values of the ADCs is always lowerthan the range of the eigenvalues ofD. These differences, however, aremore pronounced in some anatomicregions than in others and depend

primarily on the degree of misalign-ment of the fiber tract axis with re-spect to the magnet x, y, and z coordi-nates.

Moreover, in regions that containanisotropic structures, the ADCs inthe x, y, and z directions exhibit sig-nificantly higher intersubject variabil-ity (as reflected in the standard devia-

tion) than the eigenvalues ofD. Higherintersubject variability of the ADCs isdue to their dependence on the orien-tation of the anisotropic structures.This artifact is removed by comparing

the eigenvalues, which are intrinsic tothe tissue and independent of its on-entation.

Clustering and Classifying Tissueon the Basis of Diffusion Properties

Another advantage of workingwith measures of diffusion that arenot affected by fiber orientation isthat they can be used as features withwhich to cluster and classify tissues.Figure 3 is a scatter plot that displays

values of the 1 - Volume Ratio an-isotropy index and the Trace(D) ineach voxel of an axial brain section asx-y coordinate pairs. Voxels with bowvalues of anisotropy and Trace(D)correspond mainly to regions of gray

a.

b.

Figure 3. (a) Maps of the intravoxel anisotropy index, I - Volume Ratio (left) and Trace(D)(right). 0’) Scatter plot of 1 - Volume Ratio versus Trace(D) in each voxel. Units of 1 - Vol-ume Ratio are dimensionless. One can identify gray matter, white matter, and CSF regions onthe basis of their diffusion properties.


matter, voxels with high anisotropy

but low Trace(D) correspond mainlyto regions of white matter, and

voxels with low anisotropy and high

Trace(D) correspond to regions ofCSF.

Such classification is impossible

when only the ADCs are used. In the

scatter plot, however, the clusters that

correspond to gray matter, white mat-

ten, and CSF regions are not disjoint(well demarcated). This is caused inpart by partial volume contamination,because some voxels may contain a

mixture of tissue types. This artifact isespecially likely to manifest itself invoxels at the boundary between conti-cal gray matter and CSF. Another rea-

son why we do not see distinct clus-

tens is that, unlike Trace(D), the

degree of anisotnopy varies markedly

among different white matter regions.While the anisotropy in the corpus

callosum or the pyramidal tract is

cleanly higher than that in gray mat-

ten, the anisotropy in other whitematter regions may be so low thatthey could be misclassified as gray

matter. Within a large ROI that con-

tains white matter regions, one sees acontinuum in the degree of diffusionanisotnopy.

Figures 4, 5, and 6 are a series of

axial, coronal, and sagittal images,respectively. The top rows of each

figure show images of A(b=O), whichis a T2-weighted image with the same

contrast as a non-DW image but that

has less background noise because it

is derived from the entire set of 31DW images (as described above). Thesecond row of each of the figures

shows the Lattice anisotnopy index

images. Regions of highly ondened

white matter fiber tracts appear hy-penintense on these images, whereas

isotropic regions appear black. The

greatest hypenintensity is observed in

the corpus callosum and the pynami-

dab tracts, followed by the posteriorlimb of the internal capsule and theU-shaped fibers. Less hypenintensity

is seen in the centrum semiovale. The

CSF-filled and gray matter regionsappear black. Figure 4 also comprises

images of Tnace(D). A remarkable fea-

tune of these images is the absence ofcontrast variations in the brain panen-

chyma and the hyperintensity in me-

gions that contain CSF.

Figure 7 shows a diffusion ellipsoid

image (axial section) for a region of

the brain that includes the splenium

of the corpus callosum, the lateralventricles, and portions of the occipi-

tal cortex. The diffusion ellipsoid rep-resents a surface of constant mean-

squared displacement of water

molecules that would arise in a hypo-thetical experiment in which theywere released at the center of thevoxel and allowed to diffuse for atime -r. The geometric features of thediffusion ellipsoid are influenced by

the physicochemical state, the localmaterial properties, and the micro-structure of the tissue. In particular,the diffusion ellipsoid embodies local,intrinsic features of diffusion, such as

the degree of anisotropy, and themean diffusivity, which are exten-sively treated in this article. More-

over, it displays intrinsic vectorial in-formation about diffusion, in particular,the three principal directions, whichinclude the fiber-tract direction that isdepicted by the longest semimajoraxis. The striking onientational patternof prolate ellipsoids in voxels contain-ing the corpus callosum corresponds

a.


b.

c.Figure 4. Axial maps of (a) the T2-weighted amplitude, (b) the (Lattice) anisotropy index, and (c) Trace(D) in a 33-year-old healthy woman.Anisotropy index images clearly show anisotropic white matter regions as hypemintense and isotropic CSF and gray matter as hypointense.

However, the degree of anisotropy varies widely among white matter regions, with higher intensity observed in regions where the fiber pat-tern is more coherent and lower intensity where it is more incoherent. Note that iron-rich regions, such as the pallidum, the substantia nigra,

and the red nucleus, which all appear hypointense in a, appear dark in b, which permits identification of the neighboring pyramidal tract. c clearlyshows CSF regions as hypemintense and tissue (gray and white matter regions) as hypointense.

to the expected orientation of thewhite matter fiber tract in this region.

DISCUSSION

Before discussing the relevance of

measures of diffusion derived fromthe diffusion tensor, it is useful to dis-

cuss the effect of noise on their deten-

mination. Noise in the DW imagesintroduces variability in the distnibu-tion of Tnace(D) but no bias in itsmean value (19). However, for theindividual sorted eigenvalues, noisein the DW images not only increasestheir variability, but also introduces asignificant bias in their mean values(19). The severity of this bias dependson the degree of overlap in the distni-butions of the eigenvalues. If we wereto use standard statistical tests, suchas analysis of variance, to analyzetheir distributions in an ROI, wewould ernoneously conclude that sta-tistically significant differences exist

between Xi and X�, as well as betweenX2 and X�, even in isotropic media inwhich no differences are expected

between them. Moreover, bias intro-duced by sorting the eigenvalues pre-

cludes the use of standard statistical

tests to assess whether anisotropic

diffusion is cylindrically symmetric or

asymmetric within a region of inter-

est. Here, we resorted to Monte Carlo

simulations of the MR diffusion ten-

son imaging experiments to explain

the observed distribution of eigenval-ues within an ROl. Table 3 summa-

nizes the results of this analysis fordifferent anatomical ROIs.

A particularly irksome aspect of this

sonting bias is that it makes measures

of diffusion anisotropy which dependon the scheme by which eigenvaluesare ordered (eg, the ratio of the larg-est and smallest eigenvalues, X1/X3;

the eccentricity, [1 - �X3/X1}2J) sosusceptible to contamination by noise

as to preclude their clinical use (19).

The lattice anisotropy index and Vol-ume Ratio that we use here are im-mune to this sorting bias becausetheir values, as with Trace(D), are in-sensitive to the way one orders the

eigenvalues.

Trace(D)

Trace(D) is homogeneous in the nor-

mal brain parenchyma. Its value liesin a narrow range between 1,950 x10-6 mm2/sec and 2,200 x 10mm2/sec in most brain regions, which

corresponds to an average diffusivity

of about 700 x i06 mm2/sec. Only in

the cortex is the value of Trace(D)(2,477 x i0-� mm2/sec) significantly

different from that in the other ana-tomic regions we investigated. How-

ever, it is likely that this discrepancyis caused by partial volume contami-

nation of CSF in the cortical ROI.The fact that white matter and gray

matter have virtually identical valuesof Trace(D) has no obvious biologicalexplanation at the present time and isworthy of further study. It is also in-

teresting that, in comparing these val-ues of Trace(D) with previously ac-

quined values in normal cynomolgusmonkeys (19) and cats (36) undersimilar experimental conditions, wesee that its intenspecies variability is

remarkably low.

a.

M4 #{149}Radiology December 1996

b.

Figure 5. Coronal maps of (a) the T2-weighted amplitude and (b) the (Lattice) anisotropy index in a healthy 31-year-old woman.

a.

b.

Figure 6. Sagittal maps of (a) the T2-weighted amplitude and (b) the (Lattice) anisotropy index in a healthy 34-year-old man. Note the high

degree of anisotropy in the corpus callosum and the lower degree of anisotropy in many other white matter regions. Some portions of the cen-trum semiovale are almost isotropic.

Trace(D) is independent of the po-sition and orientation of the patient

within the magnet, intrinsically has a

lower background noise level than an

individual ADC, and is unbiased.

Moreover, one observes a high degree

of uniformity throughout normal

brain parenchyma within the same

subject, as well as low variability be-

tween the brains of different age-

matched normal human subjects.

These factors make Trace(D) a pan-

ticulamly desirable diagnostic panam-

eter since small deviations from itsnormal value are statistically signiui-cant. Consequently, Trace(D) may be

able to detect more subtle changes in

diffusivity (which may occur in de-

generative diseases, aging, and devel-

opment) than the gross changes ob-served in ischemia. Moreover, its low

intersubject variability can potentially

improve the quality of pooled datacollected in multicenter studies.

It should be noted that althoughTrace(D) is homogeneous in normalbrain, its changes in white and gray

matter could be different for the samenoxious stimulus. For example, the de-crease of Trace(D) was shown recently

to exhibit a different time course in

white and gray matter in hyperacute

global brain ischemia in cats (36).

Anisotropy

In contrast with Trace(D), whitematter anisotropy is highly heteroge-neous in normal brain panenchyma.We found statistically significant dif-ferences in the degree of anisotropynot only between gray matter and

white matter regions, but also between

almost all white matter regions. In some

white matter regions, such as in the

corpus callosum and the pyramidal

tract, water diffusivity in the direction

parallel to the fibers ( � 1,700 x i06

mm2/sec) is approximately seven times

larger than the average diffusivity inthe perpendicular direction ( � 250 x

10�6 rnm2/sec). This ratio is much

higher than has been reported in all

previous studies of diffusion anisot-

ropy in any region of the human brain

(15-18). Because the distributions ofxl and ([X2 + X31/2) cleanly do notoverlap in both the corpus callosumand the pyramidal tract, their meanvalues will not be biased in these

ROIs. Therefore, the high measuredanisotropy is not an artifact caused

by the sorting bias mentioned above.


. . . . . - . rectangular ROI that includes

d portions of the occipital cortex; ROl (bottom). For each diffu-in its shape (eccentricity), the

iber tract direction is given by

spherical ellipsoids contain CSF;while voxels with prolate ellip-

ion along which the apparentrection in this region.

We attribute the disparity betweenour results and those of other studiesto the fact that in previous works dif-fusion anisotnopy was calculated from

ADCs acquired in two or three per-pendiculan directions rather thanfrom quantities derived from the dif-fusion tensor. Ratios of perpendiculanADCs depend on the subject’s onien-tation in the magnet and generallyresult in underestimation of the de-gree of anisotropy. To demonstratethe severity of these artifacts, one canform the ratio of the average of thelargest and smallest ADCs in the ROI.Using the same data set, we obtained

values of ADCmax/ADCm1n of 4.3 and3.3 in the pyramidal tract and in the

corpus callosum, respectively. These

resulting anisotropy ratios are consis-tent with those in previous reportsbut are still smaller by a factor of two

than XjI([X2 + X31/2).

Nevertheless, the question must be

addressed as to how one can explain

the high variability in the measure-ments of diffusion anisotropy observedin the living brain, as well as the lowdegree of anisotropy seen in somewhite matter regions. Although thediffusion distances of water (for the

given diffusion time in these experi-ments) are on the order of microme-tens, the echo magnitude measured in

each voxel reflects an average over aparticular voxel. For our voxel size of9 p1, each voxel contains approxi-

mately 1020 hydrogen nuclei and, inwhite matter, approximately 106 fl.bers. Therefore, our diffusion mea-

surement is influenced by molecular,ultrastructural, microstructural, and

macrostructural (architectural) fea-tunes of the tissue.

White matter in icrostructu re-In par-ticular, the microscopic structure of

fibers is likely to affect the measureddiffusion anisotropy. Regional differ-

ences in fiber packing density, degreeof myelination, fiber diameter, and

packing density of neunoglial cellscould all contribute to the observed

variation in diffusion anisotropy. Un-fortunately, it is presently difficult toassess their relative effect on the mea-

sured voxel-avenaged diffusion an-isotropy. In white matter, one doesnot observe regions in which there is

a predominance of fibers with onlyone diameter; rather, one sees a broaddistribution of fiber diameters withina voxel. For example, the pyramidal

tract contains white matter fiberswhose diameter reaches 25 jim (37);however, the majority of fibers areless than I �im in diameter.

One might suppose that the pack-ing density of fibers would contributeto the measured diffusion anisotropy.Hajnal et al (8) reported that the packingdensity of fibers varies tenfold be-

tween major tracts and suggested thatwhite matter tracts with a lower pack-ing density could also have a loweranisotropy. The packing density ofthe fibers is highly variable betweendifferent white matter regions: It isreported to be 60,000-70,000/mm2in the pyramidal tract (38) and338,000/mm2 in the corpus callosum(39). Despite this disparity in the

packing density of the fibers, wefound no significant difference in thevalues of anisotropy between thesetwo structures.

One might suppose that diffusionanisotropy is influenced by the pack-ing density of neunoglial cells. How-ever, this quantity is reported to befairly uniform throughout the brain inboth white matter and gray matter(40), so it does not seem to be respon-sible for the high variability of anisot-ropy. Moreover, Friede (41) reportsthat the density distribution of neuro-glial cells is slightly lower in the inter-nal capsule and in the pyramidal tractat the level of the cerebral peduncles(37,000-48,000 cells/mm2) than in thecorpus calbosum and the optic nadia-tion (85,000 and 96,000 cells/mm2).Our data in the pyramidal tract andcorpus callosum show a similar de-


gree of anisotropy, which is higherthan that of the internal capsule andthe optic radiation.

One can also speculate that myelindensity and distribution are impor-

tant in determining diffusion anisot-ropy. Findings of classical ultrastruc-tural studies on myelin in brain whitematter suggest that many white mat-ten structures contain a mix of myelin-ated and nonmyelinated fibers. How-ever, the average amount of myelin inwhite matter is relatively constantthroughout the brain (42). Therefore,it seems that the differences in diffu-sion anisotnopy that we observed in

white matter could not be explainedby a diffenent degree of myelination

in the different structures.In summary, we were unable to

identify a single micnostnuctural factoror a combination of them to accountfor the observed differences in diffu-sion anisotropy in all regions of whitematter in the normal human brain.

White matter fiber architecti� ral para-digrns.-On a grosser length scale,

groups of fibers are arranged to formfasciculi on laminae that lie in differ-ent planes, nun in different directions,and intersect each other in a numberof regions. Our diffusion anisotropydata can be explained more consis-tently by considering these larger-scale architectural patterns of thewhite matter.

If we could neglect on nullify theeffect of noise on the distribution ofthe eigenvalues of D, then the relativemagnitudes of the three eigenvalueswithin each voxel would be sufficient

to characterize white matter fiber an-chitecture. Several architectural para-digms are suggested. Each fiber pat-

tenn corresponds to a distinct shape ofthe corresponding diffusion ellipsoid.

A1 � A2 � A3.-This is the typical

distribution of the eigenvalues that

we would expect in a medium in whichdiffusion is isotropic at a microscopic

level, as in free water. We must con-siden, however, that apparent isot-

ropy could result from structures thatare anisotnopic at the microscopiclevel but that are randomly orientedwithin the voxel. In white matter, thiscould occur where fibers cross in aspherically symmetric pattern. On ourimages, this pattern is evident in some

regions of the centrum semiovale atthe intersection of fibers of the nadia-tion of the corpus callosum, associationfibers, and fibers of the corona radiata.

A1 >> A2 � A3.-This configurationcorresponds to a cigar-shaped diffu-sion ellipsoid that is cylindrically

symmetric. This distribution of eigen-

values is consistent with the arrange-

ment of white matter fibers in parallelbundles with their longitudinal axisaligned with c1, the eigenvector asso-ciated with Xi. In the anatomic regionsthat we have considered in this study,this pattern is found in the pyramidaltract and in the corpus callosum.

A1 � A2 >> A3.-This configurationcorresponds to a cylindrically sym-

metric diffusion ellipsoid that is pan-cake- or pizza-shaped. This distribu-tion of eigenvalues is consistent withwhite matter fibers that have theirlongitudinal axes oriented either or-thogonally or randomly in the planethat contains E1 and E2 (where E2 is the

eigenvector associated with X2). Fiberscould be regularly oriented withinsheets, but those sheets could them-

selves be stacked within a voxel sothat the voxel-averaged orientationappears random in the El-E2 plane.This pattern is not highly representedin the brain. We found it in peripheralregions of the centrum semiovale, es-pecially at the intersection of longassociation fibers with fibers of the

corona radiata.A1 > A2 > A3.-This configuration

corresponds to an asymmetric diffu-sion ellipsoid whose semimajor axesare all unequal. In general, this sug-gests the presence of fibers that run in

multiple directions within the voxelbut that maintain, on average, a pref-erential direction. It could representintermediate stages between the cigarand pancake configurations, depend-ing on the relative magnitude of eacheigenvalue. This is the pattern repre-sented in the majority of voxels in thewhite matter of the brain. Given thecomplicated direction field of whitematter fibers in the brain, this is notsurprising. The degree of asymmetryis variable in different regions. For

instance, the posterior limb of the in-ternal capsule and the optic radiationdo not exhibit cylindrical symmetry(see Table 3), but their degree ofasymmetry is lower than that of theU fibers and the centrum semiovale.

Experimental Design Issues inDiffusion Tensor MR Imaging

Many technical obstacles have im-peded the widespread implementa-tion of diffusion imaging and diffu-sion tensor imaging in the clinic.These include a dearth of gradientcoils capable of producing sufficientlystrong magnetic field gradient pulsesto produce diffusion sensitization, theabsence of fast imaging sequences that

produce high-quality DW images, andthe difficulty in controlling for motionartifacts.

Gradient calibration and b-matrix com-

putation.-Errors in the estimated dif-

fusion tensor can originate from gra-

dient miscalibration, miscalculation ofthe b-matrix, or both. The effect ofimaging gradients on the b-matrix hasbeen extensively described previously(30) and will not be discussed here. Ourexperience suggests that with imaging

parameters typical of a clinical study, ifthe imaging gradients are refocused im-mediately after they are applied, their

contribution to the b-matrix, and thusthe echo attenuation, is minimal. If thesequence is not optimally designed,

however, the contributions of imaging

gradients (cross terms) can be treatedin the estimation of D.

Number ofsampling directions-To

estimate the entire diffusion tensor,one must apply diffusion gradientsalong at least six noncollinear direc-tions (20). Typically, this is achievedby applying different combinations ofx, y, and z diffusion gradient pulsessimultaneously. Because one gener-ally does not know the distribution offiber directions in the tissue a priori, itis prudent to sample these gradient

directions uniformly. However, hard-ware limitations introduce constraintson the maximum gradient amplitudeone can apply and thus on the maxi-mum diffusion attenuation achievablein a DW image. In most cases, the sur-face along which the diffusion gradi-ent vector has a maximum length is acube. To maximize the S/N per unittime in a DW image, one should ap-ply gradients that point to the verticesof this cube (43). However, this sam-pling strategy yields only four inde-

pendent gradient directions, while sixare required to adequately describediffusion anisotropy in all white mat-ten regions.

The methods proposed by Conturoet al (43) and Hsu and Mon (44) are inprinciple appropriate for characteriza-tion of anisotropy in regions of thenormal brain, such as the pyramidal

tract and the corpus callosum, where

cylindrical symmetry of diffusion is veri-fled. We do not know, however, if theseregions will still exhibit cylindrical sym-

metry in pathologic conditions.Here, we decided to sample six gra-

dient directions isotropically by ap-plying combinations of diffusion gra-dient pairs. Even more efficient gradientconfigurations that still maintain anisotropic sampling pattern can beachieved by increasing the numberof gradient directions.

Recently, isotropicalby weightedsequences have been proposed (45,46). These produce DW images whosecontrast is proportional to Trace(D)


by effectively applying multiple gra-

dients with different directions withinthe same sequence. This interestingacquisition scheme, however, has anintrinsically low S/N per unit time as

compared with a multiple-directionsampling pattern and provides no infor-mation about diffusion anisotropy.

Number ofdiffusion increments foreach direction-In brain tissue, wherethere is a large range in the observedprincipal diffusivities (eigenvalues), itis prudent to obtain DW images with

a range of b-matrix values. A good

rule of thumb to ensure that the vari-ance of the estimated principal diffu-sivity, X1, is acceptably low is to seethat its b value is approximately equalto l/X1. It is easy to see that b values of300-400 sec/mm2 obtained with con-ventional gradients (10 mT/m) aremuch lower than the 1/X2 and l/X3we measured in some white matterfiber tracts and thus are too small toprovide adequate estimates of the dif-fusivity perpendicular to the fibers.Errors in the estimation of the diffu-sivity perpendicular to the fibers havelittle effect on the value of Tnace(D)but can substantially affect accuracyand the precision of the measurementsof anisotropy. Therefore, in clinicalMR systems equipped with bow-powergradients, a reliable assessment of an-isotropy may be difficult to attain.

Voxel-by-voxel computation versussignal intensity averaging within a

ROI.-If one wishes to characterizediffusion adequately in a heteroge-

neous, anisotropic medium such as thehuman brain, it is necessary first to de-termine diffusion parameters derived

from D (eigenvalues, anisotropy indices,etc) within each voxel and then to aver-age them within an anatomic ROl ratherthan first to average the signal intensitywithin the entire ROI and then calculate

the diffusion parameters of interest. Sig-nab intensity averaging within a ROI,like decreasing image resolution, effec-

lively powder averages the quantities ofinterest. In particular, measures of diffu-sion anisotropy will often be reduced bysignal intensity averaging within a ROI.

Misregistration caused by eddy cur-

rents-Cane should be taken to elimi-nate not only motion artifacts, butalso eddy currents, which tend tocause shearing and dilation in DWimages, as described above.

Summary and Clinical Perspective

The acquisition of the entire diffu-sion tensor allows one to producemaps of distinct intrinsic features ofthe diffusion process, such as the av-erage diffusivity, diffusion anisotropy,

and the principal directions of diffu-sion. The resulting images are easierto interpret than conventional diffu-sion images, such as DW images andADC maps, whose contrast resultsfrom a complicated combination ofmean diffusion, anisotropy, and fiberdirection.

In the normal brain, differences inlocal fiber architecture and organiza-tion are reflected in a highly variabledegree of diffusion anisotropy withindifferent white matter regions. Forexample, diffusion anisotropy is muchlower in subcortical regions, wherethe direction field of fibers is less co-herent than it is in the corpus calbo-sum or the pyramidal tract, where

fibers are more homogeneously on-ented. However, in the latter regions,the degree of diffusion anisotropy isapproximately three times higherthan what was previously reported.The assumption of cylindrical symme-try of diffusion, which is widely used,also is not supported by experimentalfindings in many brain white matterregions.

Scalar quantities derived from thediffusion tensor can be used to seg-ment normal brain tissue into CSF,gray matter, and white matter com-partments, as well as to classify tissueson the basis of their diffusion proper-ties. Moreover, the rotationally invari-ant quantities derived from D, suchas the lattice anisotropy index and

Trace(D), can be used in conjunctionwith other intrinsic MR quantities,such as Ti and T2, in multiparametricimage analysis.

In summary, diffusion tensor imag-ing provides a quantitative and infor-mative description of diffusion in an-isotropic and heterogeneously orientedmedia, which is impossible to achieveby using DW images or ADCs acquiredin two or three orthogonal directions.However, the acquisition and process-ing of a diffusion tensor data set re-quires the estimation of more param-etens than does conventional diffusionimaging; therefore, it is intrinsicallymore time-consuming. So, from aclinical perspective, one must ascer-tam whether the additional benefitsprovided by diffusion tensor imagingexceed the additional costs.

Clinical requirements effectivelydictate the preferred method to use tomeasure water diffusion properties inthe human brain. If one is interestedin determining whether a patient hashad an acute ischemic event, DW im-ages acquired with gradients applied

in only one direction might suffice. Ifit is necessary to determine the extentand severity of the infarct, or if it is

advisable to perform a follow-upstudy of acute ischemia, we necom-mend determining Trace(D), perhapsby using the method proposed by

Conturo and colleagues (43), who ap-plied a direction pattern of the diffu-sion gradients that is especially effi-cient in terms of S/N pen unit time.However, if one is interested in per-forming quantitative studies in which

diffusion anisotropy could also be in-formative, we recommend acquiring

the entire diffusion tensor. Thiswould apply to long-term studies ofstroke, where it has already been ob-served that changes in diffusion an-isotropy indicate Wablerian de-generation and gliosis (47), as wellas to a variety of other neunologic

disorders, which include the assess-ment of incomplete white mattermaturation, demyelination, tumorgrowth, and degenerative dis-eases. #{149}

References1. Merboldt KD, Hanicke W, Frahm J. Self-

diffusion NMR imaging using stimulated

echoes. J Magn Reson 1985; 64:479-486.

2. Le Bihan D, Breton E, Lallemand D, Gre-

nier P, Cabanis E, Laval-Jeantet M. MR

imaging of intravoxel incoherent motions:application to diffusion and perfusion in

neurologic disorders. Radiology 1986; 161:401-407.

3. Taylor DC, Bushell MC. The spatial map-ping of translational diffusion coefficients

by the NMR imaging technique. Phys MedBiol 1985; 30:345-349.

4. Le Bihan D, Turner R, Douek P, Patronas

N. Diffusion MR imaging: clinical appli-cations. AJR 1992; 159:591-599.

5. Warach 5, Chien D, Li W, Ronthal M, Edel-man RR. Fast magnetic resonance diffu-sion-weighted imaging of acute humanstroke. Neurology 1992; 42:1717-1723.

6. Moseley ME, Cohen Y, Mintorovitch J, etal. Early detection of regional cerebralischemia in cats: comparison of diffusion-

and T2-weighted MRI and spectroscopy.Magn Reson Med 1990; 14:330-346.

7. Doran M, HajnalJV, Van Bruggen N, KingMD, Young IR, Bydder GM. Normal andabnormal white matter tracts shown by MRimaging using directional diffusion weighted

sequences. J Comput Assist Tomogr 1990;14:865-873.

8. HajnalJV, Doran M, Hall AS. MR imag-

ing of anisotropically restricted diffusion

of water in the nervous system: technical,

anatomic, and pathologic considerations.Comput Assist Tomogr 1991; 15:1-18.

9. Moseley ME, Cohen Y, Kuchanczyk J, et al.Diffusion-weighted MR imaging of aniso-tropic water diffusion in cat central ner-vous system. Radiology 1990; 176:439-445.

10. Cleveland GG, Chang DC, Hazlewood CF.Rorschach HE. Nuclear magnetic reso-nance measurement of skeletal muscle: an-isotropy of the diffusion coefficient of theintracellular water. Biophys J 1976; 16:1043-

1053.

11. Reese TG, Weisskoff RM, Smith RN, RosenR, Dinsmore RE, van Wedeen J. Imagingmyocardial fiber architecture in vivo withmagnetic resonance. Magn Reson Med1995; 34:786-791.


12. Yang Y, Shimony JS, Xu 5, Gulani V, Daw-

son MJ, Lauterbur PC. A sequence formeasurement of anisotropic diffusion byprojection reconstruction imaging and itsapplication to skeletal and smooth muscle

(abstr). In: Proceedings of the Society ofMagnetic Resonance 1994. Berkeley, Calif:Society of Magnetic Resonance, 1994; 1036.

13. Muller MF, Prasad PV, Bimmler D, Kaiser

A, Edelman RR. Functional imaging ofthe kidney by means of measurement ofthe apparent diffusion coefficient. Radiol-ogy 1994; 193:711-715.

14. Wu JC, Wong EC, Arrindell EL, Simons KB,

Jesmanowicz A, Hyde JS. In vivo determi-nation of the anisotropic diffusion of waterand the Ti and T2 times in the rabbit lensby high-resolution magnetic resonance im-aging. Invest Ophthalmol Vis Sci 1993; 34:2151-2158.

15. Sakuma H, Nomura Y, Takeda K, et al.

Adult and neonatal human brain: diffu-sional anisotropy and myelination withdiffusion-weighted MR imaging. Radiology1991; 180:229-233.

16. Le Bihan D, Turner R, Douek P. Is water

diffusion restricted in human brain whitematter? An echo-planar NMR imagingstudy. Neuroreport 1993; 4:887-890.

17. Nomura Y, Sakuma H, Takeda K, TagamiT, Okuda Y, Nakagawa T. Diffusional an-isotropy of the human brain assessed withdiffusion-weighted MR: relation with nor-mal brain development and aging. AJNR

1994; 15:231-238.18. BrunbergJA, Chenevert TL, McKeever PE,

et al. In vivo MR determination of waterdiffusion coefficients and diffusion anisot-ropy: correlation with structural alterationin gliomas of the cerebral hemispheres.

AJNR 1995; 16:361-371.19. Pierpaoli C, Basser PJ. Toward a quantita-

tive assessment of diffusion anisotropy.Magn Reson Med 1996; 36:893-906.

20. Basser PJ, Mattiello J, LeBihan D. Estima-lion of the effective self-diffusion tensor

from the NMR spin echo. J Magn Reson B1994; 103:247-254.

21. Basser PJ, Mattiello J, LeBihan D. MR dif-fusion tensor spectroscopy and imaging.Biophys J 1994; 66:259-267.

22. Le Bihan D. Diffusion and perfusionmagnetic resonance imaging. New York,NY: Raven, 1995.

23. Jezzard P. Pierpaoli C. Diffusion mapping

using interleaved spin echo and STEAMEPI with navigator echo correction (abstr).In: Proceedings of the Society of Magnetic

Resonance 1995. Berkeley, Calif: Society ofMagnetic Resonance, 1995; 903.

24. Asato R, Tsukamoto T, Okumura R, Miki Y,

Yoshitome E, Konishi J. A navigator echotechnique effectively eliminates phase shiftartifacts from the diffusion weighted headimages obtained on the conventional NMR

imager (abstr). In: Book of abstracts: Soci-ely of Magnetic Resonance in Medicine1992. Berkeley, Calif: Society of Magnetic

Resonance in Medicine, 1992; 1226.25. Ordidge RJ, Helpemn JA, Qing ZX, Knight

RA, Nagesh V. Correction of motionalartifacts in diffusion-weighted MR imagesusing navigator echoes. Magn Reson Imag-ing 1994; 12:455-460.

26. Anderson AW, Gore JC. Analysis and cor-

rection of motion artifacts in diffusionweighted imaging. Magn Reson Med 1994;32:379-387.

27. de Crespigny AJ, Marks MP, Enzmann DR.

Moseley ME. Navigated diffusion imag-ing of normal and ischemic human brain.Magn Reson Med 1995; 33:720-728.

28. Marks MP, de Crespigny A, Lentz D, Enz-mann DR, Albers GV, Moseley ME. Acuteand chronic stroke: navigated spin-echodiffusion-weighted MR imaging. Radiology1996; 199:403-408.

29. Stejskal EO, Tanner JE. Spin diffusionmeasurements: spin echoes in the presenceof time-dependent field gradient. J ChemPhys 1965; 42:288-292.

30. Mattiello J, Basser PJ, LeBihan D. Analyti-cal expression for the b matrix in NMR dif-fusion imaging and spectroscopy. J MagnReson 1994; 108:131-141.

31. Henkelman RM. Measurement of signalintensities in the presence of noise in MR

images. Med Phys 1985; 12:232-233.32. Bevington PR. Data reduction and error

analysis for the physical sciences. NewYork, NY: McGraw-Hill, 1969.

33. Press WH. Eigensystems. In: Numerical

recipes in C: the art of scientific computing.2nd ed. New York, NY: Cambridge Univer-sity Press, 1992; 478-481.

34. Pierpaoli C, Mattiello J, Le Bihan D, Di

Chiro C, Basser PJ. Diffusion tensor im-aging of brain white matter anisotropy(abstr). In: Proceedings of the Society ofMagnetic Resonance 1994. Berkeley, Calif:Society of Magnetic Resonance 1994; 1038.

35. Pierpaoli C, Basser PJ. New invariant “lat-

tice” index achieves significant noise re-duction in measuring diffusion anisotropy(abstr). In: Proceedings of the InternationalSociety of Magnetic Resonance in Medicine1996. Berkeley, Calif: International Societyof Magnetic Resonance in Medicine, 1996;1326.

36. Pierpaoli C, Baratti C,Jezzard P. Fast ten-sor imaging of water diffusion changes ingray and white matter following cardiacarrest in cats (abstr). In: Proceedings of the

International Society of Magnetic Reso-nance in Medicine 1996. Berkeley, Calif:International Society of Magnetic Reso-nance in Medicine, 1996; 314.

37. Blinkov 5, Glezer I. The human brain in

figures and tables. New York, NY: Plenum,1968.

38. Weil A, Lassek A. The quantitative distri-bution of the pyramidal tract in man. ArchNeurol Psychiatry 1929; 22:495-510.

39. Tomasch J. A quantitative analysis of thehuman anterior commissure. Acta Anat

1957; 30:902-906.40. Blinkov 5, Ivanitskii G. The number of

glial cells in the human brain: computercalculation. Biofizika 1965; 10:817-825.

41. Friede R. A histochemical study of di-

aphorase in human white matter withsome notes on myelination. J Neurochem1961; 17-30.

42. Yakovlev P, Lecours A. The myelogeneticcycles of regional maturation of the brain.Philadelphia, Pa: Davis, 1967.

43. Conturo TE, McKinstry RC, Akbudak E,Robinson BH. Encoding of anisotropicdiffusion with tetrahedral gradients: a gen-eral mathematical diffusion formalism andexperimental results. Magn Reson Med1996; 35:399-412.

44. Hsu EW, Mon S. Analytical expressions

for the NMR apparent diffusion coefficientsin an anisotropic system and a simplified

method for determining fiber orientation.Magn Reson Med 1995; 34:194-200.

45. Wong EC, Cox RW, Song AW. Optimizedisotropic diffusion weighting. Magn ResonMed 1995; 34:139-149.

46. Mon 5, van ZijI PCM. Diffusion weight-ing by the trace of the diffusion tensor witha single scan. Magn Reson Med 1995; 33:41-52.

47. Pierpaoli C, Barnett A, Penix L, De Graba T,Basser PJ, Di Chiro G. Identification offiber degeneration and organized gliosis instroke patients by diffusion tensor MRI(abstr). In: Proceedings of the InternationalSociety of Magnetic Resonance in Medicine1996. Berkeley, Calif: International Societyof Magnetic Resonance in Medicine, 1996;563.

diffusion tensor mrimaging ofthe human brain’...tensor inaclinical setting. materials and methods...

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