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FEATURE ARTICLE

Diffusion Magnetic Resonance Imaging:Its Principle and ApplicationsSUSUMUMORI* AND PETERB. BARKER

Diffusion magnetic resonance imaging (MRI) is one of the most rapidly evolving techniques in the MRI field. This

method exploits the random diffusional motion of water molecules, which has intriguing properties depending on the

physiological and anatomical environment of the organisms studied. We explain the principles of this emerging

technique and subsequently introduce some of its present applications to neuroimaging, namely detection of

ischemic stroke and reconstruction of axonal bundles and myelin fibers. Anat Rec (New Anat) 257:102–109, 1999.

1999 Wiley-Liss, Inc.

KEY WORDS: brain imaging; magnetic resonance imaging; diffusion MRI; diffusion tensor imaging; stroke; fiber reconstruction

It is truly amazing to realizethat more

than two decades after the invention

of magnetic resonance imaging

(MRI),8 this technology is still evolv-

ing with considerable speed. The tech-

nique of dif fusion-weighted im aging

(DWI) is one of the most recent prod-

ucts of this evolution. Briefly speak-

ing, this approach is based on the

measurement of Brownian motion of

molecules. It has been long, but notwidely, known that nuclear magnetic

resonance is capable of quantifying

diffusional movement of molecules.17

In the1980s, a method that combines

this diffusion measurement with MRI

was introduced, which is now widely

called d i f fu s i o n i m a gi n g .18,10,9 This

techniquecan characterize water diffu-

sion properties at each picture ele-

ment (pixel) of an image. The first

important application of diffusion MRI

emerged at center stage of the M RI

community in early1990s when it wasdiscovered that DWI can detect stroke

in its acute phase.14 Around the sametime, scientists had also noticed thatthere is a peculiar property of waterdiffusion in highlyordered organssuchasbrains.13,11,5,6,19 In theseorgans, wa-ter does notdiffuseequallyin all direc-tions, a property called anisotropic

dif fusion. For example, brain waterdiffuses preferentially along axonal fi-ber directions. We now believe that i t

is possible to use this diffusion prop-erty as a probe to study the structureof spatial order in living organs non-invasively. In this tutorial, We willexplain the physical principles of thisemergingtechnology andintroduceitspresent applications.

C O N V EN TI ON A L M RI

Before explaining diffusion MRI, wewill briefly go over principles of con-ventional MRI —proton density and

T2-weighted imaging—because they

share some important analogies withdiffusion M RI. In MRI , we usuallyobserve water protons, because theyare by far thedominant chemical spe-cies observable by magnetic reso-nance. MRI is anextraordinarily versa-tile techniquebecause of its capabilityof producing various types of contrastin the images, or so-called, weighting.

Water protonshavecharacteristic MRIproperties depending on their physi-cal and chemical environments. Vari-

oustypes of MRI techniques havebeen

designed to use the difference in such

MRI properties of water in different

tissues to differentiateregions of inter-

est.

In order to explain the concept of

theconventional MRI , weusetheanal-

ogy of a gyroscope(Fig. 1). In an M RIexperiment, we first excite water pro-

tons in a sample (or human in our

case) with the imposition of a strongmagnetic field. This is similar to start-

ing the rotation of millions of gyro-

Drs. Mori and Barker are faculty mem-bers in the Department of Radiology,The Johns Hopkins University Schoolof Medicine, Baltimore, Maryland.*Correspondence to: Susumu Mori,Ph.D., Johns Hopkins University Schoolof Medicine, Department of Radiology, 217Traylor Bldg.,720 Rutland Ave., Baltimore,MD 21205. Fax: (410) 614-1948; E-mail:[email protected]

Figure 1. Analogy of MRI signal to a gyro-

sco pe. A fter excitation of protons in MRI, the

signal behaves like a gyroscop e that pre-

ce sses at a fixed rate. If the p osition of the

gyroscope is projected to a horizontal plane,

such precession ca n be p resented a sa rotat-

ing vector. The p osition of the vector is ca lled

phase.

102 THE ANA TOMIC AL REC ORD (NEW A NAT.) 257:102–109, 1999



scopessimultaneously. The gyroscopeswill start to precess, and it is thisprecession-equivalent of water pro-

tons that produces signals (electriccurrents in a receiver) in MRI. If themovement of the gyroscope is pro-

jected to a horizontal plane, thepreces-sion can be presented as a rotatingvector as shown in Figure1. The posi-tion of this vector is called the phase.

In a standard proton density image,

the visual contrast is determined bytheconcentration of water, or thenum-ber of gyroscopes in our analogy.Namely, the more water in a givenregion, the brighter the region willappear. The morefrequently used, but

more difficult to understand, proto-cols generate so-called r e l a x a t i o n -

weighted images, such as T2-weightedimages. After the excitation, there are

several mechanisms through whichthe signal eventually diminishes, orrelaxes. The T2 relaxation can be ex-

plained by a loss of coherence or syn-chrony between the gyroscope rota-

tions. Right after the excitation, all thegyroscopes have the same phase (Fig.

2).However, astimegoes by, thephasesof gyroscopes becomerandomized be-cause each gyroscope precesses at

slightly different speed due to variousreasons such as local non-homegene-

ity of themagnetic field. Becausewhat

we observe is the vector sum withdifferent phases, this randomization

of the phaseleads to theloss of signal

in MRI, which iscalled T2 relaxation.Depending on the location of water

protons related, for example, to patho-logical conditions, the time required

for T2 relaxation varies, resulting in

different degrees of signal loss. This inturn can be used for the diagnosis of

certain diseases. The exact mecha-nism that confers longer or shorter T2

relaxation is not completely under-

stood. One thing we are sureof is thatwhen water is in an environment

where i t can freely tumble (e.g., less

viscosity or less macromolecules withwhich to interact), therelaxation tends

to take longer. One typical example isthe formation of edema, which leads

to significant slowing of therelaxation

and a prolonged T2-weighted signal.

TheT2 weighting can beobtained byinserting a weighting period in be-tween the excitation and data acquisi-

tion (Fig. 3) and this time period

(strictly speaking from the time pointof excitation to the beginning of the

acquisition) is called echo t ime (TE).

Depending on the TE, the amount of T

2 weighting varies. We can obtain a

heavily weighted image by increasing TE , while the use of the shortest pos-

sible TE produces minimally T2-

weighted images. E xamples of thelightly weighted (short TE ) and heavily

T2-weighted (long TE ) images areshown in Figure 4. Regions in the

brain that have slow T2 relaxation

show up bright, such as cerebrospinalfluid (CSF). Whitematter has faster T2

relaxation and consequently looksdarker. Theminimally T2-weighted im-age in F igure 4a is referred as ‘‘protondensity,’’which meanstheimageis notweighted by anything but water con-centration (in other words, ‘‘protondensity’’).

DIFFUSIO N WEIGH TING

Weighting of MR I by diffusion canalso be explained using theanalogy tothe gyroscope. J ust as the rate of theprecession of the gyroscope is propor-tional to the strength of gravity, inMRI the rate of the precession is pro-

portional to the strength of the mag-net. For example, in a typical MRImagnet of 1.5 tesla (T), therate of theprecession is about 64 MHz. Becausethe strength of magnetic field is keptas homogeneous as possible, this pre-cession rateis also very homogeneousacross the magnet. This homogeneitycan be disturbed linearly by using aso-called pulsed field gradient. Thestrength (slope) of the gradient, itsdirection, and the time period can becontrolled. As an example, Figure 5shows a diagram of an x gradient. As a

result of this gradientapplication, pro-tons start to precess at a different ratealong the x-axis. With an analogy totheT2 relaxation process(Fig. 2), suchdifferences in the precession rate leadto dispersion of the phase and signalloss(Fig. 6). However, if another gradi-ent pulse is subsequently applied withthe same direction and time periodbut of opposite magnitude, such dis-persion can berefocused or re-phased,therefore, the first gradient is calledthedephasing gradient and the secondonethe rephasing gradient.

From Figure6, it can beunderstoodthat this refocusing can not be perfectif theprotonsmoved in between a pairof the gradient applications. Thus, byapplying a pair of gradientpulses afterthe excitation and before the data ac-quisition, we can sensitize the image(make the resultant image sensitive)

Wa te r proton s ha ve

c ha ra c te ristic M RI

p ro p e rtie s d e p e n d in g o n

the ir p hy sic a l a nd

c he m ic a l e nviro nm e nts.

Va rio us typ e s of M RIte c h n iq u e s h a v e b e e n

d e sig ne d to use the

d iffe re nc e in suc h M RI

p rop e rtie s of w a ter in

d iffe re nt tissue s to

d iffe re ntia te re g ion s of

inte re st.

Figure 2. Mechanism of T2 relaxation. Phase

of eac h proton isgradually randomized after

excitation due to slightly different precession

rates. As a result, the vector sum (indicated

by thick arrows) dec reases over the time,

which meanssignal lossin MRI.

Figure3. M echanism of T2 weighing. By insert-

ing a wa iting period in between excitation

and data ac quisition, we ca n o btain relax-

ation weighting. For T2 weighting, a scheme

called spin-echo is inserted (in this ca se, the

spin-echo time iside ntica l to the T2-weighting

period). The length of the inserted element

determinesthe degree of weighting. Gray inten-

sity incirclesdepic tsrelative image intensity.

FEATURE ARTICLE THEA NATOM ICA L REC ORD (NEW ANAT.) 103



to motional processes such as flow ordiffusion. The amount of the diffu-sional signal lossby thegradient appli-cation is known to obey an equation

S

S 0 e

2G

2

2(/3)D e bD

where S 0 is the signal intensity with-out the diffusion weighting (no gradi-ent application) and S is the signalwith the gradient application (Fig. 7).D is a diffusion constant. The equationindicates that the higher the diffusionconstant, the larger the signal loss.

The parameter is a nuclear constantcalled gyromagnetic ratio. It is intu-itively understandablethattheamountof signal loss depends on the timebetween thetwo pulses indicated by,because there i s more time for watermolecules to diffuse and, thus, therefocusingof theprecessing protonsisless perfect. Signal lossis also larger if the gradient pulses are stronger (G)and/or longer (). Most commonly, wechange thestrength of thegradients toobtain various amounts of the diffu-sion weighting.

The result of a DWI experiment on ahuman brain is shown in Figure 8. I tcan be seen that signal intensity de-creases as gradient strength increasesand that the extent of the signal decay

depends on the diffusion constants of brain water. For example, signal fromthe cerebrospinal fluid (CSF) region(indicated by a white arrow in F igure8) decays faster and therefore gives a‘‘darker’’ image than that of brain mat-ter. Although thesediffusion-weightedimages areuseful, their absoluteinten-

sity or contrast is not always a directindicator of the diffusion constant ateach pixel of the image. This is be-cause DWI areaffected bynot only thedegree of diffusion weighting (b -valuedependent), but also other contrastingmechanisms, such as T 2, and/or pro-

ton density. To appreciate the amountof water diffusion, the degree of thesignal decay (or theslopeof thedecay)is more important than the absoluteintensity of the images. Recalling Fig-ure 7, if such signal decay (S(b) ) isplotted in logarithmic scale, diffusionconstant at each pixel can beobtainedfrom the slope. The calculated diffu-sion constants at each pixel can thenbe mapped to create an image calledan apparent dif fusion constant (ADC)image (Fig. 8).

DIFFUSIO N M RI C A N DETEC T

STROKE IN ITS A C UTE PHA SE

In 1991, i t was found that the ADC of brain water drops drastically in theevent of ischemia.14 Although the ex-act mechanism of the drop is still notknown, it is almost certain that thebulk of the effect is related to thebreakdown of membranepotential. Be-cause this technique is one of the fewradiological techniques that can de-tect strokein its acutephase, theimpli-

Figure 4. Examples of p roton d ensity ( a ) and T2 ( b ) weighted imag es. Echo time for proton

density was 5 msand that for T2 weighted image was 80 ms. Repetition time was 3 s for both

images.

Figure 5. An example of an x -gradient. The direc tion along the magnet bore isd efined a s z,

along which the main the magnetic field aligns. Grad ient unitsintroduc e linear magnetic field

inhomogeneity with a spec ified time period, magnitude, and direction. As a result, the

precession rates varyin the sample depe nding on the position of the protons.

104 THE ANATOMIC AL REC O RD (NEW A NAT.) FEATURE ARTIC LE



cation is significant. An example of theADC drop is shown in Figure9a.

M EASURED DIFFUSIO N

C O NSTAN T DEPEND S O N A

DIREC TIO N O F THE

M EASUREM EN T

By the time the ADC drop due toischemia was reported, researchershad also noticed that there was astrong contrast in the ADC map of brains, which variesdepending on thedirection of themeasurement.13,11,5,6,19

This effect i s demonstrated in Figure9b–d. Note that MR I can measuremolecular diffusion along any desireddirectional axis byusingthreeindepen-dent gradient units that are orthogo-nal each other (x , y , and z , see Fig. 5).It can be seen that the orientation-dependent contrast is so great in Fig-ure 9b–d, that the location of isch-emia, compared to artifactual signals,can no longer be easily differentiated.

It is now known that this orientation-dependent contrast is generated by

dif fusion ani sotropy ; in other words,

water diffusion hasdirectionality.

3

Thisconcept is explained in Figure 10.

When water is freely diffusing (F ig.

10a), it diffusion is isotropic (no direc-

tionality) and themeasured ADC does

not depend on the axis of thegradient

application. However, water in living

systems is often contained in very

ordered structures that restrict its dif-

fusion along certain axes. An example

is shown in Figure 10b in which a

water molecule is confined in a cylin-

drically shaped tube. In this case, a

diffusion constant measured along the

z axis is larger than those along x andy . In practice, such an ordered biologi-

cal structure does not usually align to

thephysical coordinate, x , y , and z (see

Fig. 10c) defined by orientation of an

MRI scanner. In this case, what we

measure using x , y , or z gradients is

diffusion along an oblique angle with

respect to the ordered structure.

From this example, it follows that

the result of diffusion measurement

along an axis depends on the orienta-

tion of the object in anisotropic me-dia. Therefore, anisotropic diffusioncan not be represented by one diffu-sion constant. We can fully character-izesuch a diffusion propertyby a 3 3

tensor, called diffusion tensor (D)’’;12,13

D 3D xx D xy D xz

D yx D yy D yz

D zx D zy D zz 4When a diffusion measurement is

made along thex, y, or z axis, what wemeasureisD xx , D yy , or D zz , respectively.

The meaning of this diffusion tensorcan be more easily understood usingso-called diffusion ellipsoids (Fig. 10,middle row). In an isotropic environ-ment, the diffusion tensor has onlydiagonal elements (D xx , D yy , and D zz ),all of which have the same value (Fig.

10a). Thus, the system can be charac-terized by only one value (D ) and thediffusion ellipsoid is spherical (thedif-fusion constant D is the diameter of thesphere). In an anisotropic environ-ment, the ellipsoid is elongated. Wecall the longest, middle, and shortestaxes of this ellipsoid principal axesandthethreediffusion constants along theaxes 1, 2, and 3. When theprincipalaxes happen to align to our physicalcoordinate x, y, and z, we can directlymeasure 1, 2, and 3 as shown inFigure 10b. In practice, they are al-

most never aligned (Fig. 10c) and thediffusion tensor has ninenon-zero val-ues. Because D xx , D yy , and D zz valueschange astheorientation of theobjectchanges, so does the measured diffu-sion constant using x -, y -, and z -gradient axes.

Figure 6. Gradientdiagram (upperrow) and signalp hases(lowerrow) undera pplication of a

gradient. The length of gray arrows indica tes the strength o f the magnetic field that is

non-uniform during the application of the gradients. After the first gradient ap plica tion, signals

lose their uniform phase (de phase) bec ause eac h proton starts to prece ss at different rates

depending o n itsp osition in spac e. Such a gradient app lica tion is indicated by b oxes in the

diagram representing duration and strength. After the second field a pplication o f op posite

magnitude, the system restoresuniform phase (rephase). Thisrepha sing isco mplete only when

spins do not move by Brownian motion (viz., d iffuse) during the time in b etween the two

ap plica tions of the gradient. The lessco mplete the rephasing, the more signal lossresults.

Figure 7. Relationship between gradient ap-

plica tion, signal loss, and diffusion co nstant

(D ). Gradient strength (G), duration (), and

sepa ration () affect the signal. When b -

value (2G 22( / 3)) is plotted ag ainst

the signal dec ay, the slope represents the

diffusion co nstant.




C O NTRAST CA USED BY THE

AN ISO TRO PY EFFEC T IS NO TDESIRABLE FO R STRO KE

DETECTIO N

In light of the previous discussion, itshould be more clear why the ADCmaps of a human brain in Figures9b–d can look so different dependingon the orientation of the diffusionmeasurement. For example, in Figure9b—where diffusion was measuredalong thex -axis—thebright part of thebrain has fibers oriented parallel to x ,

whereas those in the dark region areoriented perpendicular to it. Thisstrong contrast due to the anisotropyeffect is unwanted for the detection of thestroke.

One of the most intriguing proper-ties of thetensor is that certain combi-nations of the diffusion tensor ele-ments are not susceptible to contrastcaused by this anisotropy effect. Thesimplest and most widely used combi-nation is the so-called trace of thetensor (D xx D yy D zz ).22 In otherwords, if three ADC maps generated

using x-, y-, and z -gradient axes areadded all together, the image contrastis insensitive to the anisotropy effectin any one axis and no differencebetween gray and white matter re-mains. An example of this trace imageis shown Figure9a. It can beseen that

entire brain now has a very homog-enous ADC and a stroke region iseasily discerned as a dark patch (indi-cated by thewhite arrows).

STUDY O F BRAIN FIBER

STRUC TURES FRO M THE

A N ISO TRO PY EFFEC T

While anisotropyis anunwanted prop-erty of water diffusion for the detec-tion of stroke, it carriesvery intriguinginformation about brain neuronalstructures. Although we still do not

know exactly which neuronal struc-tures confer thediffusion anisotropy,7,4

there is muchevidencesuggesting thatmyelination and/or protein fiberbundles of axons are the most likelysource. For example, there is higheranisotropy in white matter than graymatter and in adult brains comparedwith thoseof newborns. It follows thatthe DWI technique should provide us

Figure 8. An example of a diffusion-weighted and an app arent diffusion c onstant (ADC)

imag e of a human brain. From a series of diffusion-weighted image sw ith different b -values, an

ADC image ca n be calculated. Onlyfrom ADC c an we purelya ppreciate diffusion properties

of waterat each pixel.

Figure 9. ADC images of a human brain with stroke. White arrow indicates area of darkness,

corresponding to damage from stroke.The image shown in a isa trace image which isobtained by

adding three ADC imagesrecorded using x -gradient (b ), y -gradient (c ),and z -gradient (d ). There is

strong contrast in the ADC imagesmeasured along a single axis(b–d), which isdue to the presence

of water molec ules diffusing along axonal fibers. This contrast isremoved in a. (Figure reproduc ed

from Ulug et al.21with permission.)




with entirely new information aboutaxonal fiber structures,which no otherradiological technique has been ableto previously.

To investigate axonal structures, wefirst have to fully characterize the dif-fusion ellipsoid ateach pixel. Themostintuitivemethod of characterization isto measurediffusion constants(or cre-ate ADC maps) along numerous direc-tions, from which we can deduce theshape of the ellipsoids. This can beachieved byusingthreegradient units.For example, if x and y gradients areapplied simultaneously, diffusion alonga direction 45degrees from thex and y

axis can be measured. I n this way, wecan measure diffusion along any de-sired angles. Tensor theory tells us if we measure the diffusion constantalong six independent axes, we cancalculate the complete shape of thediffusion ellipsoid.3,1,2,20 Namely, wecan obtain 1, 2, and 3 and theirdirections.

From this characterization of thediffusion ellipsoid at each pixel, wecan now obtain two important param-eters. One is called the anisotropy in-

dex, which indicates how anisotropic

the diffusion is—or in other words,

how elongated the ellipsoid is.15 This

indicates how packed and/or ordered

theaxonal fibers are in each pixel. The

simplest method to calculate this is to

take a ratio of 1 and 3, which are

diffusion constants along the longest

and shortest axes of a diffusion ellip-

soid. However, this method does not

havegoodstatistical stabilityand many

more elaborate ways to characterize

theanisotropy have been postulated.15

One example is shown in Figure 11b.

Compared to conventional T2 weighted

images (Fig. 11a), Figure 11b depicts

much moredetailedstructuresof whitematter tracts. This is understandable

because water diffusion anisotropy is

a moredirect indicator of thepresence

of packed fibers than T2 weighting,

which is affected by many other pa-

rameters. It has been reported that the

anisotropy index of white matter in-

creases during brain development pos-

sibly due to the process of myelina-

tion.16,23 Thus, there is an expectation

that this technique will be a sensitive

indicator of myelination abnormali-ties.

Besides the anisotropy index, thesecond important parameter we canobtain is thedirection of axonal fibers.Assuming water tendsto diffuse alongfibers, this can beachieved byidentify-

ing the direction of the longest axis of diffusion ellipsoids i n a given imagesection. An example is shown in Fig-ure 11c. In this figure, some promi-nent fibers can be easily appreciated,

which are indicated by color-coding.

Once we know the fiber direction ateach pixel, it then should be possibleto reconstruct three-dimensional (3D)fiber structures by connecting theirpassagethrough multiple imageslices.We have pursued this goal of brainfiber mapping by acquiring high-reso-lution 3D diffusion MR I data usingfixed rat brains.12 An example of sucha 3D reconstruction is shown in Fig-ure 11d. This kind of information onwhite matter tracts waspreviously ob-tained only by invasive in vivo experi-ments such astracer techniques.

In the near future, we believe thatthe technique of 3D-diffusion MRI re-construction will bean important toolused to observewhite matter tracts of livehumansfor thestudy of connectiv-ity of brain functional centers, braindevelopment, and white matter dis-eases.

IN SUM M ARY

In this article, we introduced thecon-cept of diffusion M RI and its applica-

Figure 10. Relationship between a nisotropic d iffusion (uppe r row), diffusion ellipsoids (middle

row), and diffusion tensor (bottom row). When environment is isotropic (a ), water diffuses

equivalently in a ll direc tions. The diffusion ellipsoid of this system is spherica l a nd ca n be

depicted by one diffusion constant, D. When the environment is anisotropic, e.g. cylindrica l

(b,c), water diffusion has direc tionality. The diffusion ellipsoid of water in a cylinder iselongated

and has three principal axes, 1, 2, and 3. To fully cha rac terize such a system, 3 3 tensor is

needed a nd the valuesof the nine elementsdepe nd on the orientation of the principal axes.

In the ne a r future , w e

b e lie ve tha t the

tec hniq ue of 3D- d iffusion

M RI re c o nstruc tio n w ill

b e a n im p o rta nt too l

use d to ob se rve w hitem a tte r tra c ts of live

hum a ns fo r the stud y o f

c onne c tivity o f bra in

func tion a l c e nte rs, b ra in

d e ve lo p m e n t, a n d w h ite

m a tte r d ise a se s.




tions. The technique is already widelyused for the study of stroke. A newlyemerging application is dif fusion ten-

sor imaging, which allows us to study

axonal brain fiber structures. For bothtechniques, it is very important torealize that water diffusion in livingsystem is often anisotropic.

AC KNO WLEDG M ENTS

This research was funded in part by agrant from the American Federationof Aging Research, theWhitaker Foun-dation, and NI H (RO3 HD37931-01). Iwould like to thank Dr. Peter van Zijl

for giving suggestions and criticallyreviewing themanuscript.

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