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Visualizing White Matter Pathwaysin the Living Human Brain: DiffusionTensor Imaging and BeyondChristopher P. Hess, MD, PhD, Pratik Mukherjee, MD, PhD*

N E U R O I M A G I N GC L I N I C S

O F N O R T H A M E R I C A

Neuroimag Clin N Am 17 (2007) 407–426

- Magnetic resonance diffusion imagingtechniques

Diffusion weightingDiffusion tensor imagingHigh angular resolution diffusion imagingDiffusion spectrum imagingThree-dimensional fiber tractography

- Normal human white matter pathwaysClassification of white matter fibers

Supratentorial brainBrainstem

- Case study: callosal agenesis- Diffusion magnetic resonance imaging

limitations and future development- Summary- Acknowledgments- References

Through its superb tissue contrast, magnetic res-onance imaging (MR imaging) has revolutionizedthe scientific and clinical study of the human brain.By exploiting differences in proton density, T1 andT2 relaxation, and macroscopic flow, abnormalitiescan be localized to a resolution that is typically onthe order of 1 mm. Much of the brain’s function,however, derives from its organization at muchsmaller spatial scales. The normal cerebral cortexand deep gray matter contain more than 100 billionneuronal cell bodies and their supporting struc-tures. The information-carrying portion of thewhite matter consists of axons, which form an elab-orate network of circuits interconnecting processingunits within gray matter and relaying informationto the body by way of the spinal cord and cranialnerves. Because neurologic and psychiatric disor-ders affect white matter in different ways, the ability

1052-5149/07/$ – see front matter ª 2007 Elsevier Inc. All rightneuroimaging.theclinics.com

to visualize the complex ‘‘wiring’’ of the brain pro-vides an important window into the operation ofthe human mind.

Diffusion MR imaging differs from other MR im-aging modalities in that it can be used to infer infor-mation about structures much smaller than thespatial resolution of the image. It may therefore beconsidered a ‘‘microstructural’’ imaging technique.Conventional techniques for eliciting the connec-tivity between different brain regions are based onhistologic tissue analysis or on meticulous dissec-tion of post-mortem specimens. Such approachesare not only invasive and not applicable to the invivo study of the human brain but are also highlylabor intensive and subject to the inherent prob-lems associated with tissue fixation. In contrast, dif-fusion MR imaging is a tool for straightforward,rapid ‘‘virtual dissection’’ of the living human brain.

This work was funded in part by NIH NS40117, NIH 1 T32 EB001631-01A1, joint funding from General ElectricHealthcare Technologies and the Life Sciences and Informatics Program award number LSIT01-10107, as partof the University of California’s Industry University Cooperative Research Program, and a seed grant from theDepartment of Radiology of the University of California, San Francisco.Neuroradiology Section, Department of Radiology, University of California at San Francisco, 505 ParnassusAvenue, Box 0628, San Francisco, CA 94143-0628, USA* Corresponding author.E-mail address: pratik@radiology.ucsf.edu (P. Mukherjee).

s reserved. doi:10.1016/j.nic.2007.07.002

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The purpose of this article is fourfold: (1) to pro-vide a brief overview of the theoretic principles un-derlying diffusion tensor imaging (DTI) and newernon-tensor diffusion MR imaging methods, such ashigh angular resolution diffusion imaging (HAR-DI); (2) to review the white matter tracts that arecommonly visualized in the normal human brainusing DTI and HARDI; (3) to use callosal agenesisas a clinical example of how diffusion MR imagingcan be used in the study of aberrant white matterconnectivity, and finally; (4) to summarize severalcurrent research directions in diffusion MR imagingthat may ultimately find practical use in systemsneuroscience and in clinical neuroradiology.

Magnetic resonance diffusion imagingtechniques

Diffusion weighting

Water molecules, the principal constituents of thebrain, are in constant motion caused by randomthermal fluctuation. Within an artificial environ-ment such as a test tube filled with pure water, mo-lecular mobility can be quantified by MR imagingusing the diffusion (or self-diffusion) coefficient,a physical constant that expresses the mean dis-placement of water molecules in a given time inter-val. In biologic tissues, the motion of water isinfluenced not only by properties inherent to themolecules themselves, but also by the surroundingenvironment in which diffusion takes place. In thissetting, diffusion can be described using theapparent diffusion coefficient (ADC), distinguishedfrom the self-diffusion coefficient in that it includesthe empiric aggregate of all factors that determinethe nature of local molecular diffusion. ADC is atissue-specific biologic marker whose value variesthroughout the brain, depending on active trans-port and passive diffusion of water, microscopicbarriers to diffusion such as cell membranes and or-ganelles, and compartmentalization of water withincell bodies, axons, and glia [1]. Expressed in units ofarea per unit time (typically mm2/s), the ADC canbe viewed as a measurement of the average rate ofdiffusion within a voxel.

In a homogeneous medium in which protons areequally likely to diffuse in any direction, diffusionis said to be isotropic, and a single measurement ofADC suffices to characterize the medium. In contra-distinction, diffusion in white matter tracts is direc-tionally dependent— that is, the trajectory ofmolecules caused by thermal motion is more likelyto occur along certain orientations than others.These three-dimensional constraints on the move-ment of water protons cause diffusion to exhibitdirectional anisotropy. The anisotropy of diffusioncan be measured using MR imaging and has an

important biologic meaning—the average directionof proton diffusion preferentially aligns with theorientation of axonal fibers within white mattertracts. To adequately characterize the directional an-isotropy, it is necessary to obtain measurements ofADC along several different directions. Heuristi-cally, it is thus useful to view ADC as a surface inthree dimensions that varies depending on the an-gular direction in which it is measured. The infor-mation encoded by the shape of the ADC surfaceallows inference of the orientational structure ofthe underlying neural architecture.

The critical element of an MR pulse sequence thatsensitizes it to proton diffusion is the diffusion gra-dient. Diffusion gradients can be incorporated intovirtually any pulse sequence, but are most com-monly used in a spin-echo experiment by placingidentical gradient pulses before and after the 180�

refocusing pulse. It is important to point out thatdiffusion gradients are applied independently andin addition to the phase-encoding and readout gra-dients used for spatial encoding and typically havemuch larger magnitudes. Mathematically, the diffu-sion gradient is a vector quantity that has magni-tude (the strength of the diffusion gradient) anddirection (the angular orientation in which the gra-dient is applied). Applied along any single orienta-tion, the diffusion gradient causes the signal to beattenuated according to the equation

S=S0 5 e�b ADC;

where S is the measured diffusion-weighted signal,S0 is the signal that would be obtained without dif-fusion weighting, and b is the strength of the diffu-sion-weighting for the experiment (determined bythe timing and strength of the diffusion gradients).Larger values of ADC result in greater signal attenu-ation. This equation allows the recovery of the ADCvalue for any directional diffusion measurement.

Overall the magnitude of the diffusion-weightedsignal depends on two factors: (1) the three-dimen-sional angular orientation in which the diffusiongradients are applied during image acquisition,and (2) the strength of diffusion weighting applied,as parameterized by the b value for the acquisition.The strength, duration, and relative timing of thediffusion gradients with respect to the 180� refocus-ing pulse determine the b value. Fig. 1 illustrates theeffect of these two parameters on the appearance ofa diffusion-weighted image in a normal adult vol-unteer. For any specific b value, the resulting imagecontrast depends on the relative angular differencebetween individual fiber tracts and the directionof diffusion weighting. For a fixed direction of thediffusion gradient, increasing the value of b results

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Fig. 1. Effect of b value and directional encoding on diffusion-weighted images acquired at the level of thecentrum semiovale. When no diffusion weighting is applied (b 5 0 s/mm2), the resulting image is typicallyT2-weighted. As the value of b increases from b 5 0 s/mm2 to b 5 3000 s/mm2, image contrast increases andthere is greater sensitivity to the angular direction of diffusion encoding. Reconstruction from these diffusion-encoded data involves synthesizing the angular dependence of the image intensities to infer the parenchymalmicrostructure within each voxel.

in progressive signal attenuation from moleculesdiffusing over smaller and smaller distances. In gen-eral, larger b values impart higher overall contrastand greater sensitivity to directional encoding todiffusion-weighted images.

In what follows, the authors refer to the processof systematically varying the strength and directionof the applied diffusion gradients as one of obtain-ing diffusion-encoded images. Each diffusion encod-ing yields a single diffusion-weighted imagewhose intensity is a function of fiber orientationand the length scale over which diffusion is probed.To characterize the three-dimensional structure ofdiffusion, it is necessary to acquire multiple diffu-sion-encoded images along different orientations,and to make certain assumptions about the proper-ties of diffusion in the brain. Depending on theassumed nature of diffusion, it is possible tosynthesize a set of measured diffusion-weightedimages in different ways so as to ultimately charac-terize the underlying white matter architecture.

Diffusion tensor imaging

To date the diffusion tensor remains the most widelyapplied mathematic model used to represent theangular variability of diffusion in three dimensions[2,3]. Equivalent to assuming a Gaussian probabil-ity for diffusion along any single direction, the ten-sor effectively fits the angular variation of the ADC

to the geometric shape of a three-dimensional ellip-soid. The six unique parameters that define the ten-sor are deduced from at least six diffusion-encodedimages acquired along non-collinear directions[4–6].

An intuitive and biologically meaningful param-eterization of the diffusion ellipsoid results whenthe tensor is subjected to a mathematic operationtermed eigendecomposition. As illustrated in Fig. 2,this description of the tensor recasts the ellipsoidin terms of a unique set of three eigenvectors thatrepresent the orientations of the major, medium,and minor principal ellipsoid axes, and three corre-sponding eigenvalues that quantify the value of theADC along each axis. Depending on the magnitudeof the eigenvalues, the diffusion ellipsoid may takeon one of three basic shapes [7]. When diffusion isequally likely along any direction, the ellipsoid isnearly spherical. Alternatively, when there is a singledominant direction for diffusion, as may be thecase for a large and coherently oriented fiber tract,the ellipsoid is cigar-shaped (prolate). Finally, if dif-fusion is hindered along one axis but equally likelyalong the other two, the ellipsoid assumes a pill-shaped morphology (oblate). In fact, any tensorcan be decomposed as a sum of these three cardinalshapes.

The two most widely used numeric descriptorsof the tensor, fractional anisotropy (FA) and majoraxis, are also easily interpreted using the geometric

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Fig. 2. Geometric interpretation of the tensor using the diffusion ellipsoid. The re-parameterized tensor ob-tained from a set of diffusion-weighted measurements has principal, intermediate, and minor eigenvalues(l1, l2, l3) and corresponding eigenvectors (e1, e2, e3). These values define the relative magnitude and direction,respectively, of diffusion along three spatial dimensions within each voxel. Depending on the underlying prob-ability of intravoxel diffusion, the tensor may take on one of three cardinal shapes—prolate, spherical, or ob-late. Although coherent pathways such as the corpus callosum generally adopt the highly oriented prolatemorphology, crossing fiber tracts may result in oblate or even spherical morphologies.

parameterization of the diffusion ellipsoid. FA iscalculated from the three eigenvalues and charac-terizes the degree to which the diffusion ellipsoidis anisotropic. When the large majority of fiberswithin any single voxel are organized along a singledirection, the ellipsoid is long and narrow. The FAin this case is large, approaching its maximumvalue of 1. At the opposite extreme, when diffusionis nearly isotropic and the tensor is roughly spher-ical in morphology, the value of FA approximateszero. The other important parameter derivedfrom the tensor is the major axis of the diffusionellipsoid. This is given by the angular orientationof the eigenvector that corresponds to the largesteigenvalue (the principal eigenvector), and definesthe direction in which the diffusion of water isleast hindered. It is worth noting that FA is a puta-tive marker of fiber density and myelination [1],and the principal eigenvector reflects the dominantorientation of white matter fascicles within eachvoxel.

To facilitate visual interpretation of diffusion ten-sor data, diffusion ellipsoid parameters are oftenused to derive color-encoded directional anisotropymaps. To construct these images, the principal axisof the diffusion ellipsoid for each voxel is convertedto a unique color in RGB (red-green-blue) color-space. The intensity of the assigned color is thenweighted according to the value of FA. In the mostcommonly applied color scheme [8], used for theconstruction of the anisotropy maps shown inFigs. 3 and 4, the anterior–posterior orientation isassigned to green, the left–right orientation is as-signed to red, and the craniocaudal orientation isassigned to blue. As these images illustrate, highlyisotropic diffusion within the cerebrospinal fluidspaces is characterized by small values of FA, andthus appears black in the color FA maps. The bright-est voxels, in contrast, correspond to tightly packed,highly oriented, and largely myelinated white mat-ter bundles, such as the corpus callosum. Becausecortical and deep gray matter structures contain

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Fig. 3. Axial (left) and coronal (right)DTI color maps obtained in a normalvolunteer. Images were acquired at3T with 55 diffusion-encoding direc-tions and b 5 1000 s/mm2, using par-allel imaging on an 8-channel phasedarray head coil (acceleration factor2). Axial images are shown from thelevel of the centrum semiovale (topleft) to the level of the anterior com-missure (bottom left), and coronalimages are shown anteriorly fromthe genu of the corpus callosum(top right) posteriorly to the sple-nium of the corpus callosum (bottomright). ac, anterior commissure; alic,anterior limb of the internal capsule;cc-b, corpus callosum (body); cc-g,corpus callosum (genu); cc-s, corpuscallosum (splenium); cg, cingulategyrus; cr, corona radiata; cs, centrumsemiovale; ec, extreme capsule; fmj,forceps major; fmn, forceps minor;fx, fornix (crus, body, columns); ilf, in-ferior longitudinal fasciculus; iof, in-ferior occipitofronal fasciculus; mcp,middle cerebellar peduncle; ml, me-dial lemniscus; plic, posterior limbof the internal capsule; scp, superiorcerebellar peduncle; sfo, superiorfronto-occipital fasciculus; slf, supe-rior longitudinal fasciculus; tap, ta-petum; ts, temporal stem; unc,uncinate fasciculus.

primarily cell bodies with no well-defined orienta-tion, these areas have low anisotropy and are seenas dark pixels with no single dominant directionof diffusion on color FA maps.

Careful inspection of Figs. 3 and 4 also demon-strates a substantial drawback of the tensor model.In areas in which fiber tracts cross, diverge, bend, orare otherwise partial volume-averaged within a sin-gle voxel, there is a relative falloff in anisotropy incomparison to surrounding white matter. This ‘‘arti-factual’’ reduction of FA in regions of complex whitematter architecture precludes accurate numericquantitation of single-tract anisotropy and presentsa significant obstacle to fiber tracking algorithms(see later discussion) [9–12]. For example, thishas been shown to interfere with DTI fiber trackingof many portions of the corticospinal tract in clini-cal applications, such as presurgical white mattermapping of patients who have brain tumors [13].

Decreasing voxel size may help to reduce partialvolume averaging of fiber tracts in some brain re-gions, but requires sacrificing signal-to-noise ratio(SNR) and yields less accurate tensor estimates.Moreover, axonal projections in certain brainregions, such as the centrum semiovale and thehighly compact brainstem decussations, are knownto interdigitate at a spatial scale that is orders ofmagnitude smaller than can be resolved using MRimaging.

High angular resolution diffusion imaging

One seemingly straightforward approach to recov-ering the subvoxel white matter architecture lostin the tensor model is to fit more than one tensorto directional measurements of the ADC. Unfortu-nately multitensor fitting is numerically challeng-ing, and more important, the peaks of the ADCfunction may not actually correspond to dominant

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directions of distinct fiber populations [14]. Theshortcomings of multitensor models have recentlyspawned the development of several novel methodsfor recovering multiple fiber orientations usingmeasurements of diffusion obtained at a fixedb value. Collectively referred to as techniques forhigh angular resolution diffusion imaging (HAR-DI), these have shown great promise and are cur-rently the subject of intense research. The mostpopular methods that have been developed includeq-ball imaging (QBI) [15,16], spherical deconvolu-tion [17], FORECAST [18], persistent angular struc-ture [19], and the diffusion orientation transform[14]. These approaches each rely on a different as-sumption about the underlying probability of waterdiffusion, but together share the common goal of

Fig. 4. Sagittal DTI color maps obtained in a normalvolunteer subject. Images in the figure are shownfrom the midsagittal plane (top) to the midsagittalsection of the temporal lobe (bottom). All DTI acqui-sition and display parameters are the same as inFig. 3.

overcoming the inability of the tensor to representmore than one fiber orientation.

Data acquisition for HARDI is similar to DTI inthat measurements are obtained at a fixed value ofdiffusion weighting b. Unlike DTI, however, HARDIuses much larger b-values (b 5 3000 mm2/s orhigher) and requires that dozens or even hundredsof diffusion-weighted measurements be obtained toseparately resolve subvoxel fiber populations. As il-lustrated schematically in Fig. 5, diffusion encod-ings are acquired at points uniformly distributedover the surface of a sphere and synthesized to re-construct a three-dimensional surface termed theorientation distribution function (ODF). This sur-face is analogous to the diffusion ellipsoid in thatit quantifies the likelihood of diffusion along anyangular direction, and its peaks coincide with theorientations of distinct fiber populations.

Akin to spatial resolution, a related but separateconcept important for the interpretation of HARDIODFs is that of angular resolution [20]. Ideally, twocrossing subvoxel fiber populations would result inan ODF that is comprised of two intersecting lines.In practice, however, the contribution of each pop-ulation to the ODF has a finite width because of thetrue underlying coherence of diffusion (ie, ‘‘anisot-ropy’’) and the measurement uncertainty in the di-rectional estimates. As discussed, the magnitude ofdiffusion weighting determines the spatial scaleover which water diffusion is evaluated. The mostsignificant contribution of diffusion-weighted im-age contrast when b values of 3000 mm2/s or higherare used is from the fraction of water moleculesthat, on average, are coincident with the directionof encoding over a long distance. As the value ofb decreases, this fraction increases, because overshort distances, diffusion is more likely to occuralong any direction just by random chance. Fig. 6illustrates how this phenomenon changes the shapeof the ODF. With large b values, the ODF has sharpprofiles that more clearly delineate the orientationof individual fiber tracts. Decreasing the value ofb has a peak-broadening effect that imposes anoverall rounding to the shape of the ODF that limitsthe detection of individual crossing tracts. Angularresolution and b value are thus inversely propor-tional—the accurate separation of fiber bundlescrossing at more shallow angles requires largerb values.

Although the tradeoffs that govern angular reso-lution, b value, and SNR differ between distinctHARDI methods and have not yet been completelycharacterized, two general rules of thumb are clear.First, whereas angular resolution increases withb value, SNR decreases with this heavier diffusionweighting. A larger number of diffusion encodingsthus must be acquired to achieve an equivalent

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Fig. 5. High-angular resolution diffusion imaging (HARDI). In contrast to DTI, diffusion measurements are ob-tained with large b values and along many different diffusion-encoded directions. On the left, the measurementsphere is depicted as a multifaceted polygon in which the individual vertices correspond to unique directions fordiffusion encoding with a fixed value of b (b 5 3000 s/mm2 for the data shown). These measurements are com-bined mathematically to generate orientation distribution functions (ODFs) for each voxel using a methodcalled q-ball imaging. The q-ball ODFs are unimodal, similar to the tensor, when there is a single, dominant di-rection of diffusion within a voxel. Unlike the tensor, however, q-ball ODFs have the flexibility to take on morecomplex forms to represent multiple intravoxel populations of diffusing protons when fiber tracts cross, bend,or are otherwise partial volume-averaged. Example unimodal ODFs are shown for the posterior limb of the in-ternal capsule (bottom left) and the callosal splenium (bottom right), and example bimodal ODFs are shown forthe anterior corona radiata (top left) and at the boundary between the callosal genu and cingulum (top right).

Fig. 6. The importance of b value and angular resolution for the detection of fiber crossings. Simulated q-ballorientation distribution functions derived from HARDI for fiber populations crossing at 90� (first row) and at70� (second row) for data acquired with b 5 4000 s/mm2 (first column) and at b 5 1000 s/mm2 (second column).As the magnitude of diffusion weighting increases, separate peaks corresponding to different intravoxel whitematter tracts are more readily resolved. Note that orthogonal fiber crossings are just barely resolved at the typ-ical diffusion weighting used for DTI (top right), but fibers intersecting at more shallow angles merge and arenot detected separately (bottom right). HARDI techniques such as q-ball imaging require large b values toachieve high angular resolution and resolve shallow fiber crossings.

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SNR for a larger value of b. Second, because largerb values lead to a more complex ODF morphologywith sharper peaks and troughs, a larger number ofdiffusion measurements must be obtained to accu-rately reconstruct an ODF from more heavily diffu-sion-weighted data. As explained in the nextsection, this is equivalent to increasing the radiusof the measurement sphere in q-space and requiresthat a greater sampling density be used. The num-ber of diffusion encodings that must be acquiredfor sufficient SNR and for accurate recovery of theODF places a limit on the maximum value ofb that can be used in practice, because this ulti-mately determines the experiment time. To achievepractical imaging times of 15 minutes or less, initialclinical applications of HARDI, as discussed in thisarticle, have used b values that are typically on theorder of 3000 mm2/s.

Diffusion spectrum imaging

To this point, the authors have focused on methodssuch as DTI and HARDI in which diffusion-en-coded data are collected over the surface of a sphere,in which the radius of the sphere is defined bya fixed b value. Measurements of diffusion, how-ever, need not be constrained to fall on a sphericalshell and can be performed with multiple b values.The space in which diffusion-encoded measure-ments are obtained through deliberate choice ofdiffusion gradients, referred to as q-space, has a re-ciprocal relationship with diffusion probability[21]. The larger the b value, the larger the radiusin q-space. Direct recovery of the diffusion proba-bility distribution function that governs water diffu-sion within each voxel is possible by acquiringdiffusion measurements over a three-dimensionallattice of points in q-space. As might be imaginedwhen implemented in vivo, this so-called diffusionspectrum imaging (DSI) approach leads to a farmore complete characterization of diffusion thaneither DTI or HARDI [22] that may ultimatelymake it possible to meaningfully study diffusionwithin more complex microenvironments, such asthe cortical gray matter. DSI has not yet been widelyapplied clinically, because it is notoriously time-in-tensive. Typical imaging times of several hours havelimited its use to highly motivated human volun-teers or animal experiments, although this maychange with continued improvements in MR imag-ing technology.

Three-dimensional fiber tractography

Because white matter pathways in the brain arethree-dimensional structures, voxel-based represen-tations, such as DTI color anisotropy maps andHARDI ODF arrays, are inherently limited. A so-phisticated knowledge of neuroanatomy is still

required to visualize the spatial trajectory of fiberpathways. Three-dimensional fiber tractography as-sists in this process by using DTI, HARDI, or DSI toderive clinically relevant anatomic maps of whitematter connectivity. The first algorithms to beused for three-dimensional DTI tractography arebased on the serial propagation of streamlinesfrom manually defined seed points along the orien-tation of the principal eigenvector of the diffusiontensor for neighboring voxels [23–25]. These sim-ple methods are classified as deterministic stream-line tractography. Reviewing the implementationdetails of these techniques and comparing their rel-ative strengths and weaknesses is beyond the scopeof this article, and the reader is referred to a techni-cal review of this subject for more information [26].Only the essential features of three-dimensionalfiber tracking methods are outlined here.

Deterministic tractography can be performed inone of two ways: (1) by initiating the streamlinesfrom seed points placed within a manually drawnregion of interest (ROI) encompassing part of thewhite matter pathway to be traced; or (2) by so-called brute force seeding of all the voxels in thebrain that exceed a certain minimum threshold FAvalue followed by selection of only those stream-lines that pass through a manually defined ROI en-compassing part of the white matter pathway to betraced [24]. Although more computationally expen-sive, the latter brute force approach is generally con-sidered to be superior, because it can detect somefibers that are missed if seed points are restrictedonly to the ROI used to initiate tracking. A priorianatomic knowledge of the course of white matterpathways can be further used to ‘‘dissect’’ out spe-cific tracts by placing multiple ROIs along the ex-pected trajectory of the pathway and filtering outthe streamlines that do not pass through all theROIs [24].

The most widely used of the deterministicstreamline tractography methods is known as fiberassignment by continuous tracking (FACT) [23,26].Fig. 7 shows an example of FACT-based fiber track-ing of ascending and descending tracts that passthrough manually placed ROIs in the posteriorlimbs of the internal capsule. Typical parametersthat can be adjusted to alter the results of fibertracking include the minimum FA threshold to ini-tiate tracking from a voxel, the minimum FA thresh-old to continue tracking through a voxel, and themaximum turning angle for the streamline betweenany two voxels. For example, if the streamline en-counters a voxel with FA 5 0.10 and the minimumthreshold to continue tracking is FA 5 0.20, thenthe streamline terminates. Fig. 7 shows the resultsfor fiber tracking with two different FA thresholds:0.20 and 0.40. Note that the higher threshold traces

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Fig. 7. Three-dimensional deterministic streamline DTI tractography of fibers passing through the posterior limbsof the internal capsules. Diffusion images were obtained at 3T with 25 diffusion-encoding directions and b 5

1000 s/mm2, using parallel imaging on an 8-channel phased array head coil (acceleration factor 2). Coronal pro-jections are displayed of only those streamlines passing through regions of interest (ROIs) placed in the posteriorlimbs of both internal capsules (left and center) or only the right internal capsule (right). With a minimum FAthreshold of 0.4 (left), only the central portions of the tracts within the internal capsule and centrum semiovaleare identified. Lowering the FA threshold to 0.2 enables visualization of more peripheral fibers of the coronaradiata ramifying with the neocortex (green arrows). Note, however, that only the most superomedial and in-ferolateral projections of the corona radiata can be seen; DTI tracking of the rest of the corona radiata isblocked at the centrum semiovale by crossing fibers of the corpus callosum and the superior longitudinal fascic-ulus (see Fig. 9). Also, lowering the FA threshold to 0.2 produces more spurious tracks, such as streamlines thatcross the midline at the corpus callosum (red arrow) and at the central pons (yellow arrow), the latter ascendingin the contralateral internal capsule (blue arrow). These spurious streamlines are the result of mistracking alongcrossing fiber pathways in the supratentorial brain (Fig. 9) and the infratentorial brain (Fig. 12).

only the central cores of the tracts, because, as a gen-eral rule, the FA is highest near the middle of a tractand falls off at the periphery. Exceptions include re-gions of complex white matter architecture, whereFA is lower because of the presence of crossing fi-bers. Decreasing the minimum FA threshold forstarting or continuing streamlines, or increasingthe maximum turning angle, serves to increase thenumber and length of streamlines identified bythe fiber tracking algorithm. The tradeoff, however,is that these changes also increase the number ofspurious tracks, ie, streamlines that do not corre-spond anatomically to actual axonal pathways.

Three-dimensional DTI tractography has provenuseful not only for scientific studies in cognitiveneuroscience [27,28], but also for clinical applica-tions, such as presurgical and intraoperative visual-ization of axonal pathways for tumor resection[13,29]. The pitfalls of DTI tractography, however,should be understood before using this tool for sci-entific or clinical purposes. DTI fiber tracking mayfail in two different ways. The first is the failure toidentify, in part or in whole, white matter tractsthat are anatomically present. The second is thegeneration of spurious tracks that are not anatomi-cally correct. Both of these limitations are usually

related to the inability of DTI to adequately describediffusion in areas of complex white matter architec-ture where multiple fiber pathways of different ori-entations intersect or are otherwise partial volumeaveraged within a voxel. This shortcoming is exem-plified by fiber tracking of the pyramidal tract, partof which crosses through fibers of the superior lon-gitudinal fasciculus and corpus callosum in its paththrough the centrum semiovale. As can be seenfrom Fig. 7, DTI tractography delineates only partof the corona radiata, because streamlines enteringregions of complex white matter terminate prema-turely. This has been shown to interfere with preop-erative DTI tractographic mapping of the pyramidaltract before glioma resections [13]. Moreover, thepresence of complex white matter can cause thestreamlines to deviate from their assigned pathwayand extend along crossing pathways instead. Fig. 7shows examples of this ‘‘mistracking.’’

Several different HARDI and DSI fiber trackingmethods are currently under development to allowaccurate tractography through these areas of com-plex white matter architecture [30–33]. Examplesof HARDI tractography using streamline and prob-abilistic techniques are shown in Fig. 8. Proba-bilistic tractography differs from deterministic

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Fig. 8. Three-dimensionalHARDI tractography of thefibers of the corpus callos-um. Diffusion images wereobtained at 3T with 55 dif-fusion-encoding directionsand b 5 3000 s/mm2, usingparallel imaging on an 8-channel phased array headcoil (acceleration factor 2).At top, q-ball orientationdistribution functions(ODFs) derived from HARDIare shown for voxels of thecallosal striations (top left)and centrum semiovale(top right). The ODFs inthe corpus callosum areunimodal, because they rep-resent only a single popu-lation of fibers. The ODFsin the centrum semio-vale are bimodal, becausethey represent two crossingfiber populations, those ofthe corpus callosum (red)extending along the left–right orientation and those

of the pyramidal tract (blue) extending along the up–down orientation. Unlike DTI, tractography using thisHARDI information allows propagation of the streamlines along the callosal fibers (yellow lines) throughthe region of crossing tracts without premature termination and without mistracking along the crossing fiberpathway. At the bottom, probabilistic tractography of corpus callosal fibers using the bootstrap technique iscompared for DTI (bottom left) and HARDI (bottom right). Because HARDI tractography is not hindered bythe presence of crossing fibers, it is capable of visualizing many more fibers of the callosal radiation thanDTI tractography. Images courtesy of Jeffrey I. Berman, PhD and Roland G. Henry, PhD of the University ofCalifornia, San Francisco.

streamline fiber tracking in that connectivity is de-termined by propagation along a wide front ratherthan along a single streamline. Results can be ex-pressed in terms of the probability of connectivitybetween two regions, taking into account the uncer-tainty in the diffusion measurements along thepaths between the regions [34,35]. Although DTIis a natural fit for deterministic streamline methods,because it provides a single orientation for propa-gating streamlines, HARDI is a better fit for proba-bilistic tractography, because orientationdistribution functions are a suitable basis for deter-mining connection probabilities.

Normal human white matter pathways

Classification of white matter fibers

Neuroradiologic evaluation of brain connectivitybegins with a working knowledge of normal tracto-graphic anatomy. By correlating with known whitematter pathways discovered through traditional grossanatomic dissection and histologic tract-tracing

methods, a detailed atlas of the connectional anat-omy of the human brain revealed by DTI has beenelaborated in several recent articles [36,37] andeven one textbook [38]. HARDI techniques havejust begun to be applied to the normal brain, butvalidation with known tract anatomy in the ma-caque monkey has been undertaken [39]. In whatfollows, the authors survey some of the larger neu-ronal pathways that are routinely visualized by DTIand provide selected examples in which HARDI canbe applied to better understand complex white mat-ter architecture in instances in which the tensormodel is equivocal.

A fairly straightforward method for categorizingwhite matter tracts distinguishes among (1) projec-tion fibers that connect cerebral cortex to subcorti-cal structures, such as the deep gray nuclei andspinal cord, (2) commissural fibers interconnectinggray matter regions in different cerebral hemi-spheres, and (3) association fibers linking differentbrain regions within the same cerebral hemisphere.Note that, in general, projection fibers tend to

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appear blue on DTI color maps because of theirlargely craniocaudal orientation, commissuraltracts appear red, because they course left–right be-tween the two hemispheres, and association fibersappear green, because they usually connect anteriorand posterior regions within the same hemisphere.Exceptions exist to this general rule, however; for ex-ample, the optic radiation is a projection tract butappears green on DTI color maps because of itslargely anteroposterior orientation. Bearing this inmind, the location and orientation of tracts canthen be used to define their function in the normalbrain or the implications of their dysfunction in thediseased brain.

Supratentorial brain

Commissural pathwaysThe corpus callosum is the largest commissuraltract in the human brain, containing some 200 mil-lion fibers that interconnect homologous regions ofcortex across the midline. In the midsagittal plane,the callosum is clearly seen as a large red bundleon DTI color maps (see Figs. 3 and 4). Gross ana-tomic and DTI studies have demonstrated a rostro-caudal topographic organization for callosalfibers—fibers interconnecting the frontal lobespass through the genu, posterior frontal and parie-tal fibers through the body, and occipital fibersthrough the splenium [40,41]. Posteriorly withinthe corpus callosum, it has also been demonstratedwith DTI tractography that fibers maintain an ante-rior–posterior organization that directly corre-sponds to the foveal–peripheral organization ofvisual information processing on the dorsal–ventralvisual cortex [42,43]. Tractography of the callosumpermits its subdivision into functionally distinctsub-segments by incorporating cortical connectivityinformation [44,45]. Depending on the spatial lo-cation of insults to the callosum, clinical featuresof callosal disconnection may include hemispatialneglect, left hemialexia, amnestic disorders or the‘‘alien hand’’ syndrome of intermanual conflict.DTI fiber tractography has been used to directly vi-sualize the structural correlate of posterior callosaldisconnection syndrome caused by traumatic axo-nal shearing injury to the splenium [46] and post-operatively after resection of a hemorrhagicarteriovenous malformation [47].

Lateral to the midline, callosal projections be-come more difficult to resolve using DTI, becausethey intersect with other fiber bundles within thecentrum semiovale and corona radiata. For exam-ple, anteriorly within the centrum there is a lossof anisotropy as callosal striations intersect withthe descending pyramidal tract and the superiorlongitudinal fasciculus within the subcortical fron-tal lobe. As Fig. 9 illustrates, this three-way crossing

is manifest by a dark area on coronal DTI colormaps. The subvoxel fiber crossings in this regionof the brain are accurately reproduced using a HAR-DI technique known as q-ball imaging. Althoughthe original implementation of q-ball imagingrequired well in excess of 100 diffusion-encodingdirections for adequate visualization of crossingfiber tracts [15,16], a new q-ball ODF reconstruc-tion technique using a spherical harmonic basisenables visualization of complex white matterarchitecture with many fewer diffusion-encodingdirections, resulting in reduced scan times of 15minutes or less [20]. All of the HARDI resultsshown herein are derived from q-ball reconstruc-tion of data acquired at 3T with 55 diffusion-encod-ing directions and b53000 s/mm2, using parallelimaging on an 8-channel phased array head coil(acceleration factor 2). In Fig. 9, the q-ball ODFs ex-hibit separate peaks for each of the three fiber tracts.Fig. 10 shows how, at the forceps minor, the path ofinterhemispheric connections through the genu ofthe corpus callosum is also well visualized usingHARDI. Posteriorly, fibers arising from the corpuscallosum can be similarly discerned as separatefrom the sagittal stratum.

Though considerably smaller than the corpuscallosum, the anterior commissure is the secondlargest interhemispheric fiber bundle in the humanbrain. This tract connects homologous regions ofthe temporal and orbitofrontal cortex through thelamina terminalis to allow interhemispheric trans-fer of visual, auditory, and olfactory information[48]. Similar to the callosum, this pathway is clearlydepicted on DTI color maps as a thin, round, redbundle in the midline, passing through to the col-umns of the fornix. Tract dissection studies separatethis commissure into smaller anterior and largerposterior limbs. The former are not discernable us-ing diffusion MR imaging at typical voxel sizes, butthe latter can be followed laterally underneath thestriatum to a point at which the fibers diverge intotwo separate tracts, one arching anteriorly into thetemporal lobe and the other extending posteriorlyinto the occipital lobe. Distinct clinical features oflesions to the anterior commissure have not beendescribed, presumably a consequence of the bilat-eral representation of olfaction in the brain, whichseems to be the primary source of informationrelayed by this structure.

Projection pathwaysThe pyramidal tract, which contains the neuronalaxons responsible for controlling the movementof the face and the extremities, was among the firsttracts to be studied using diffusion MR imaging.The topographic organization of its fibers is main-tained throughout its course through the corona

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Fig. 10. DTI and HARDI reconstructions of the complex white matter of the forceps minor. At center is an axialDTI color map at the level of the corpus callosum, with the right forceps minor enclosed in the yellow box. Close-up of q-ball ODFs (left) within the right forceps minor accounts for the loss of anisotropy seen on the DTI colormap. Specifically, the anterior corona radiata (cr) intersects with fibers passing through the genu of the corpuscallosum (cc). Posteriorly, intravoxel partial volume averaging of the callosal striations and superior fronto-occipital fasciculus (sfo) also results in bimodal ODFs. There is also partial volume averaging medially of fiberswithin the genu of the corpus callosum with those of the cingulum (cg).

Fig. 9. Coronal DTI and HARDI reconstructions of the complex white matter architecture of the centrum semi-ovale. At center is a coronal DTI color map at the level of the posterior limbs of the internal capsules. Diffusionimages were obtained at 3T with 55 diffusion-encoding directions and b 5 3000 s/mm2, using parallel imagingon an 8-channel phased array head coil (acceleration factor 2). The three-way intersection of the craniocaudallyoriented descending pyramidal tract (pt), the mediolaterally oriented interhemispheric corpus callosal (cc) stri-ations, and the anterior–posterior oriented superior longitudinal fasciculus (slf) occurs within the centrum semi-ovale (yellow box). On the DTI colormap, this portion of the centrum semiovale consequently has reducedfractional anisotropy in comparison to surrounding white matter. Q-ball orientation distribution functions(ODFs) from HARDI plotted for each voxel (right) allow separate resolution of the intersecting tracts. Notethe trajectory of commissural fibers of the callosal striations en route to the middle frontal gyrus (mfg) afterpassing through the centrum semiovale. The DTI color map and the q-ball ODFs are color-shaded accordingto the scheme used in Figs. 3 and 4 (see color ball at bottom left). The grayscale background of each voxel inthe q-ball ODF array reflects the generalized fractional anisotropy (GFA) in that voxel, where GFA representsthe HARDI generalization of the FA measure of anisotropy from DTI.

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radiata, internal capsule posterior limb, cerebral pe-duncle, and brainstem. As might be expected fromits predominantly craniocaudal trajectory, DTIcolor maps depict the corticospinal tract predomi-nantly in blue. Corticobulbar fibers, which arisemore laterally on the convexities, are not separatelyresolved within the crossing fiber populations ofthe centrum semiovale. The corticobulbar tractagain converges within the genu of the internal cap-sule, joining the adjacent corticospinal tract to ulti-mately terminate within brainstem cranial nervenuclei. As discussed earlier in reference to the cor-pus callosum, HARDI depicts the separate three-way crossing fibers within the centrum semiovale(see Fig. 9), including projections for facial move-ment whose cell bodies lie on the lateral motorstrip. Recent work has shown that, unlike DTI trac-tography, HARDI and DSI tractography can accu-rately delineate the course of these fibers throughthe centrum [32,49].

In addition to pyramidal projections, careful trac-tography can identify discrete extrapyramidal pro-jections that link cortical gray matter to deep graynuclei. Behrens and colleagues have describeda probabilistic tractography technique capable ofdetecting thalamocortical pathways, and in doingso also parcellated the putative spatial locations ofindividual thalamic nuclei [34]. Using a similarmethodology, Lehericy and colleagues [50,51]were able to follow the course of fibers from thesupplementary motor and primary motor cortexto the striatum. Their approach results in a spa-tial–functional segmentation of the caudate andputamen that allows separation of distinct sensori-motor and associative components. As portions ofthese cortical–subcortical projections traverse areasof complex white matter, HARDI can be expected toallow further characterization of these short subcor-tical projection pathways.

Association pathwaysThe largest association tract in the human brain isthe superior longitudinal fasciculus (SLF), whichis a bidirectional tract that connects different re-gions of the cerebral cortex within the same hemi-sphere. DTI studies have divided this pathway intofour components, each sub-serving a different func-tion: SLF I–III and an arcuate fascicle [52]. DTIcolor maps depict the largest portion of this massiveintrahemispheric tract as a long green structurewithin the centrum semiovale and corona radiata.Its long course renders this tract particularly diffi-cult to trace in its entirety using DTI. The arcuatefasciculus is of particular importance in the produc-tion and comprehension of language and isbelieved to represent the dominant connection be-tween Broca’s area and Wernicke’s area within the

language-dominant hemisphere. This tract is themost caudal portion of the SLF and is found lateralto the posterior horn of the lateral ventricle as itarches around the Sylvian fissure to connect the su-perior temporal gyrus and the inferior frontal gyrus.

The cingulum is the component of the limbic sys-tem that connects the subcallosal region to the tem-poral lobe within the same hemisphere and playsa role in cortical control of emotion and consolida-tion of memories as a part of the circuit of Papez. Asthe pathway linking the cingulate gyrus and ento-rhinal cortex, it is contiguous around the spleniumof the corpus callosum with the ipsilateral parahip-pocampal gyrus. The predominantly anterior–pos-terior orientation of this pathway makes it standout as a prominent green bundle superficial to thecorpus callosum on DTI color maps. Anteriorlywithin the cingulum, a region that has been sug-gested to play a role in risk-associated decision-making [53], a reduction in fractional anisotropyis often seen with tensor reconstruction [54]. Asthe DTI and HARDI results of Fig. 10 illustrate,the reduction in anisotropy may at least in part beattributable to partial volume averaging with adja-cent fibers of the callosal genu.

The stem of the temporal lobe serves as a conduitfor associative fiber tracts that link the temporallobe to other brain regions and is a not infrequentroute of spread for seizures, tumor, or infection.Because of partial volume averaging and fibercrossings, DTI tractography does not reliablydistinguish among the three primary neuronalpathways that traverse the temporal stem—theuncinate fasciculus, the inferior occipitofrontal fas-ciculus (IOF), and Meyer’s loop. Using three-dimensional MR imaging renderings together withgross anatomic dissection, Kier and colleagues[55] have described how the uncinate fasciculus isfound anteriorly within the temporal stem, andthe IOF and Meyer’s loop lie more posteriorly atthe level of the lateral geniculate nucleus. Further-more, the IOF is found superior and superficial toMeyer’s loop within the posterior temporal stem.HARDI also improves the ability to discriminatebetween these tracts in their course through thetemporal stem (Fig. 11). Improved tractographicanatomy of the temporal stem may prove usefulin the evaluation of schizophrenia, in which studieshave shown involvement of the uncinate fasciculus,in surgical planning for temporal lobectomy toavoid injury to Meyer’s loop, or in the evaluationof infiltrative glial tumors that extend along thecourse of the IOF.

Brainstem

In contrast to the supratentorial brain, the brain-stem and cerebellum have been the subjects of

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Fig. 11. Sagittal DTI and HARDI reconstructions of the left temporoparietal junction in the region of the tempo-ral stem. Fibers comprising the uncinate (‘‘hooklike’’) fasciculus, which connects the frontal and temporal lobes,lies anterior to the fibers of Meyer’s loop and the inferior occipitofrontal fasciculus (iof). Q-ball orientation dis-tribution functions in this region illustrate why DTI tractography in this region fails to delineate the full courseof these tracts. Superiorly, fibers en route to the superior frontal gyrus (sfg) are found above and anterior tofibers of the uncinate fasciculus (uf). The IOF is visualized in part just posterior to the uncinate fasciculus, ashas been described using gross anatomic dissection. Inferior to the uncinate fasciculus, the inferior longitudinalfasciculus (ilf) is visualized. Meyer’s loop contributes fibers to the inferior longitudinal fasciculus and can be seenseparately in their course along the temporal horn of the lateral ventricle.

a relatively small number of diffusion MR imagingstudies. This disparity in the literature reflects thetechnical challenge of obtaining high-resolutiondiffusion images in this region. To reveal the intri-cate array of small white matter projections that tra-verse this region with any meaningful clarity, veryhigh spatial resolution must be used. Moreover,the region often suffers from strong warping arti-facts that result from its proximity to air-filled re-gions, such as the pharynx and mastoid andparanasal sinuses. Despite these limitations, severalof the larger brainstem tracts can still be resolvedusing carefully performed DTI [56–59]. BrainstemDTI has been applied clinically in limited numbersof patients who have wallerian degeneration [60],amyotrophic lateral sclerosis [61,62], and otherneurodegenerative movement [63] and congenitaldisorders [64].

Fig. 12 shows axial DTI color maps of the brain-stem at the level of the upper pons in a normal vol-unteer subject. The largest tract, the corticospinaltract, is readily seen in blue through most of itscourse through the ventral brainstem. Other tractsthat are seen include the medial lemniscus andthe superior and middle cerebellar peduncles.Gray matter nuclei, such as the inferior olivary nu-clei, trigeminal nuclei, oculomotor nuclei, and sub-stantia nigra, may be identified on DTI and HARDIas discrete areas of low anisotropy, dependingon the spatial resolution. High anisotropy of

surrounding white matter delineates these struc-tures, making their localization much more precisethan previously possible and presenting the oppor-tunity for characterization of their anisotropy orother signal parameters.

Besides gray matter nuclei, other areas in whicha falloff in anisotropy is found are the result ofcrossing tracts or partial volume averaging of adja-cent tracts with different fiber orientations. HARDIis especially useful in the brainstem, where it can beapplied as a supplemental tool to DTI to allowmore confident interpretation of white matter anat-omy [65]. The ability to resolve multiple fiber ori-entations within a single voxel promises to allowaccurate tractography of the corticospinal tract,which is currently unreliable in these locations ofcomplex subvoxel fiber microstructure.

Case study: callosal agenesis

The tracts outlined in the previous section sub-servethe different large-scale cognitive networks thatcontrol language, praxis, and social and emotionalbehavior [66,67]. Brain function is altered whenthese pathways are interrupted, classically by meansof a focal lesion, such as a tumor, infarct, traumaticaxonal shearing injury, or demyelinating plaque.Disconnection syndromes such as conductive apha-sia result from this type of lesion. Lesions that indi-rectly result in selective tract degeneration, such as

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Fig. 12. DTI and HARDI reconstructions of the brainstem. At top left is an axial DTI color map of the upper pons,showing projection fibers of the pyramidal tract (pt) and medial lemniscus (ml) and the transverse pontocere-bellar fibers (tpf). Pontocerebellar fibers of the middle cerebellar peduncle (mcp) are also shown with their de-cussation anteriorly (d-mcp). The fibers of the superior cerebellar peduncle (scp) lie posteriorly. The q-ball ODFarray at right shows several regions of complex white matter architecture, most prominently at the crossings ofthe pyramidal tract with the transverse pontocerebellar fibers. The yellow box highlights one voxel with sucha fiber crossing, and the corresponding ODF is magnified at bottom left, and is shown reoriented into the cor-onal plane. The presence of these fiber crossings helps explain the mistracking that may occur in the pons withDTI tractography (see Fig. 7).

post-ischemic wallerian degeneration and amyotro-phic lateral sclerosis, can also be considered vari-ants of classic disconnection syndromes. Theconcept of connection disorders can be furtherbroadened to include neurologic conditions thatarise from abnormally enhanced connections ora combination of disconnection and hyperconnec-tion [28,67]. In this section, the authors provideexamples of aberrant connectional anatomy fromcallosal agenesis, a developmental disorder thatlends itself well to analysis by diffusion MRimaging.

Callosal dysgenesis serves as an excellent modelfor studying neuronal plasticity, because much ofthe functional capacity of the brain seems to beretained through the dynamic rewiring of axonalcircuits during embryogenesis. Believed to be the re-sult of a yet undiscovered pathologic insult during inutero brain development, the spectrum of callosalabnormalities ranges from partial to completeabsence. Concordant with the putative neuronal re-organization of the dysgenetic callosum, the clinicalimplications of callosal dysgenesis differ signifi-cantly from well known callosal disconnection

syndromes that may occur with callosal infarcts,surgical transection, or other insults that take placefollowing completion of embryogenesis. Individ-uals who have developmental abnormalities ofthe callosum may be completely asymptomatic ormay present with various clinical symptoms that in-clude language deficits, motor dysfunction, or men-tal retardation. In general, the presence and severityof symptoms is highly dependent on the presenceof one of many congenital or metabolic diseasesthat are often associated with callosal agenesis.

Conventional anatomic imaging in patients whohave complete agenesis of the corpus callosumshows typical features of colpocephaly, centripetallyradiating sulci that extend from the cortical surfaceto the ventricular margin, downward displacementof the cingulate gyrus, and Probst bundles [68].Hypogenesis and agenesis of the corpus callosumare also associated with noncallosal abnormalities,including interhemispheric cysts, lipomas, ano-malous cortical development, and generalizeddiminution in white matter volume [69].

Paralleling these gross anatomic abnormalities,DTI in patients who have callosal agenesis shows

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absence of the midline interhemispheric connec-tions through the callosum and prominent Probstbundles medial to the lateral ventricles (Fig. 13)[70,71]. The functional role of these large, aberranttracts has yet to be elucidated in humans, but ini-tial work has been undertaken to determine theirtopographic organization. Their predominantlygreen color on DTI color maps suggests a princi-pally anterior–posterior orientation for these het-erotopic callosal fibers that failed to cross themidline. Analysis using DTI tractography also re-veals that much of the Probst bundle has a spatialarrangement that is unique from the expected tra-jectory of normal callosal fibers. Fibers ventrallywithin the Probst bundle seem to have a longerlongitudinal course that links the parietal andoccipital lobes with the frontal lobes, and fibersdorsally within the bundle have a U-shaped config-uration that connects medial cortical regions [71].This difference in the spatial composition of fibersbetween the Probst bundle and the normal corpuscallosum may reflect reorganization that occurs inresponse to absence of interhemispheric tracts inthe developing brain.

HARDI can supplement the DTI findings of cal-losal agenesis through its improved characteriza-tion of complex white matter architecture. As anexample, in contrast to the three-way crossingsseen in the centrum semiovale of normal subjects(see Fig. 9), absence of the interhemispheric con-nections in this region of the acallosal brain yieldsODFs that show only two-way crossings of pyrami-dal tract projections and the superior longitudinalfasciculus (Fig. 13). Anteriorly within the Probstbundles, a transition from longitudinally orientedODFs to mediolaterally oriented ODFs can beseen, possibly corresponding to fibers that, on exit-ing the bundle, form hairpin turns that return to thebundle on histochemical tract tracing studies inacallosal mice [72].

Diffusion magnetic resonance imaginglimitations and future development

Diffusion MR imaging has undergone significantdevelopment over the past decade, and the largenumber of studies in animals and humans confirm-ing results previously derived using gross anatomic

Fig. 13. Evaluating connectivity in the acallosal brain using diffusion MRI. Coronal (left) and sagittal (right) DTIand HARDI reconstructions show absence of normal interhemispheric fiber tracts passing through the corpus cal-losum. Within the centrum semiovale, q-ball ODF arrays show the descending corticospinal tract (cst) and supe-rior longitudinal fasciculus (slf) but lack the mediolaterally oriented crossing fibers emanating from the corpuscallosum. The aberrant Probst bundles (pb) are seen medial to the corticospinal tract. In addition, sagittal recon-struction shows that, although the ventral portions of the Probst bundles consist primarily of long anterior–pos-terior oriented fiber tracts, the dorsal portions have both medial–lateral and craniocaudal fiber populations.These likely represent shorter pathways that interconnect medial regions of the cerebral cortex within thesame hemisphere.

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dissection and histochemical tract-tracing stand asa testament to the validity of the methodology. Nev-ertheless, there remain several technical and bio-logic challenges preventing its more widespreadapplication. For example, although several whitematter atlases have now been made available, a sys-tematic validation of DTI tractography has yet to beundertaken for the large majority of neuronal path-ways that have been cataloged using the technique.Furthermore, the tracts delineated using DTI trac-tography lack polarity—there is at present nomethod that allows the differentiation of afferentand efferent connections. As an alternative to directintraoperative cortical stimulation, the orientationof tracts may in the future be inferred by using com-bined functional MR imaging-diffusion MR imag-ing paradigms.

The advent of approaches such as HARDI hasallowed the discrimination of individual intravoxelfiber populations in regions of complex white mat-ter in which DTI has been unsuccessful. Thesemathematic techniques for reconstruction of multi-modal diffusion have had little impact on the un-derlying physics that govern the measurement ofdiffusion-weighted MR imaging data, in that diffu-sion remains an SNR-limited modality. On onehand, increasing spatial resolution should allowmore accurate characterization of fiber orientations,because this decreases the likelihood that fiberpathways cross, twist, or loop within a voxel. Theconcomitant loss of signal that comes with smallervoxel sizes, however, increases the uncertainty withwhich the parameters of the tensor or other diffu-sion models are estimated. SNR is even more criti-cal at large b values, the regime in which HARDItechniques are typically applied for improving an-gular resolution. The recent translation of diffusionMR imaging approaches to magnetic field strengthsof 7T or higher and to phased array head coils withincreasing numbers of receiver elements promisesto increase the available SNR, such that higher spa-tial and angular resolution can be more reliablyachieved. The most recent approaches for diffusionMR imaging aim to improve the SNR tradeoff be-tween angular and spatial resolution by fusingDTI and HARDI information over concentric shellsin q-space rather than acquiring diffusion data onlyon a single sphere [14,73].

The clinical application of tractography requiresnot only an understanding of connectional anat-omy on the part of the interpreter, but also a refer-ence standard with which to compare tractmorphology and tract-specific parameters, such asanisotropy. Several investigators have proposedmethods for spatial normalization of diffusion ten-sor data [74,75] to spatially co-register tracto-graphic maps. Such methods will be necessary to

accurately compare tracts between individuals orto follow changes in tractographic anatomy withinthe same individual over time. Moreover, the anal-ysis of tracts in patients who have various neuro-logic disorders is still evolving. Most existingstudies that specifically measure tract parametershave investigated tract-averaged anisotropy ormean diffusivity. Methods for quantifying tractmorphology [76] may offer further insights intothe normal variability of individual pathways andserve to identify those tracts that fall outside thelimits of normal.

Summary

Biologic connectionism holds as its central tenetthat the cognitive, behavioral, and motor functionsof the brain are derived from the complex intercon-nections of simple neural processing units. Muchcan be learned about the human mind throughthe study of the brain’s connections in normaland diseased states. In this review, the authorshave summarized the essential features of the ten-sor model of diffusion, outlined newer approachesto overcoming the limitations of the tensor, andprovided normal and clinical examples of whitematter anatomy derived using the tensor andmore sophisticated HARDI approaches. DiffusionMR imaging is a powerful adjunct to techniquesfor studying brain function that has already haddramatic scientific impact, and with further devel-opment will continue to become part of routineclinical practice.

Acknowledgments

Experiments in subjects who had agenesis of thecorpus callosum were done in collaboration withElliott H. Sherr, MD, PhD, of the University of Cal-ifornia, San Francisco (UCSF). The authors alsothank Daniel B. Vigneron, PhD, Duan Xu, PhD,of UCSF, and Eric T. Han, MSE of General ElectricMedical Systems for many helpful discussions.

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