understanding diffusion mr imaging techniques

CENTRAL NERVOUS SYSTEM: STATE OF THE ART S205

Understanding Diffu-sion MR Imaging Tech-niques: From ScalarDiffusion-weightedImaging to DiffusionTensor Imaging andBeyond1

Patric Hagmann, MD, PhD ● Lisa Jonasson, PhD ● Philippe Maeder, MDJean-Philippe Thiran, PhD ● Van J. Wedeen, MD ● Reto Meuli, MD, PhD

The complex structural organization of the white matter of the braincan be depicted in vivo in great detail with advanced diffusion mag-netic resonance (MR) imaging schemes. Diffusion MR imaging tech-niques are increasingly varied, from the simplest and most commonlyused technique—the mapping of apparent diffusion coefficient val-ues—to the more complex, such as diffusion tensor imaging, q-ballimaging, diffusion spectrum imaging, and tractography. The type ofstructural information obtained differs according to the techniqueused. To fully understand how diffusion MR imaging works, it is help-ful to be familiar with the physical principles of water diffusion in thebrain and the conceptual basis of each imaging technique. Knowledgeof the technique-specific requirements with regard to hardware andacquisition time, as well as the advantages, limitations, and potentialinterpretation pitfalls of each technique, is especially useful.©RSNA, 2006

Abbreviations: ADC � apparent diffusion coefficient, SE � spin echo, 6D � six-dimensional, 3D � three-dimensional

RadioGraphics 2006; 26:S205–S223 ● Published online 10.1148/rg.26si065510 ● Content Codes:

1From the Department of Radiology, Lausanne University Hospital (CHUV), Rue du Bugnon, 46, CH-1011 Lausanne, Switzerland (P.H., P.M.,R.M.); Signal Processing Institute, Ecole Polytechnique Federale de Lausanne, Lausanne, Switzerland (P.H., L.J., J.P.T.); and MGH Martinos Cen-ter for Biomedical Imaging, Harvard Medical School, Charlestown, Mass (V.J.W.). Recipient of an Excellence in Design award for an education ex-hibit at the 2005 RSNA Annual Meeting. Received February 28, 2006; revision requested April 21 and received May 25; accepted June 9. All authorshave no financial relationships to disclose. Supported by Swiss National Science Foundation 2153-066943.01 and 3235B0-102863, by NIH 1R01-MH64044, and by Yves Paternot. Address correspondence to P.H. (e-mail: [email protected]).

©RSNA, 2006

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TEACHING POINTS

IntroductionDiffusion-weighted magnetic resonance (MR)imaging, boosted by established successes in clini-cal neurodiagnostics and powerful new applica-tions for studying the anatomy of the brain invivo, has been an important area of research inthe past decade. Current clinical applications arebased on many different types of contrast, suchas contrast in relaxation times for T1- or T2-weighted MR imaging, in time of flight for MRangiography, in blood oxygen level dependencyfor functional MR imaging, and in diffusion forapparent diffusion coefficient (ADC) imaging.Even more advanced techniques than these are inuse today for the study of neural fiber tract anat-omy and brain connectivity.

Over the years, increasingly complex dataacquisition schemes have been developed, whilethe theoretical foundations of diffusion MR imag-ing have come to be better understood. For theradiologist who wants to use these techniques inclinical practice and research, it is important tounderstand a few key principles of diffusion imag-ing so as to select the appropriate technique foranswering a specific question. The article there-fore begins with an explanation of the physics ofwater diffusion and the ways in which the greatcomplexity of diffusion in the brain, the main or-gan targeted for investigation with diffusion MRimaging, can be described. Next, the basic prin-ciples that underlie diffusion contrast encodingwith MR imaging are described to enable thereader to understand the relation between theMR imaging signal and diffusion as well as thelimitations of simple diffusion imaging tech-niques. This discussion provides a context for thedescription of diffusion spectrum imaging, themost complex diffusion MR imaging technique,which provides the largest body of informationand the greatest detail. With the general prin-ciples of diffusion MR imaging in mind, the rangeof current diffusion MR imaging techniques, fromthe simplest to the most sophisticated, is then re-viewed with an emphasis on the underlying as-sumptions and hypotheses, advantages, and po-tential pitfalls of each. The technical require-ments (hardware capabilities, acquisition time)for each type of diffusion imaging examination,and the types of data provided by each type, arecompared.

The Physics andRepresentation of Diffusion

Molecular diffusion, or brownian motion, wasfirst formally described by Einstein in 1905 (1).The term molecular diffusion refers to the notionthat any type of molecule in a fluid (eg, water) israndomly displaced as the molecule is agitated bythermal energy (Fig 1). In a glass of water, themotion of the water molecules is completely ran-dom and is limited only by the boundaries of thecontainer. This erratic motion is best described instatistical terms by a displacement distribution.The displacement distribution describes the pro-portion of molecules that undergo displacementin a specific direction and to a specific distance.To illustrate this idea, we can perform an imagi-nary experiment. Let us imagine that we launch,at time t � 0, a given number N of labeled watermolecules in water, and we measure their indi-vidual displacement after a given time interval �(hereafter, diffusion time interval). For each dis-placement distance r, we count the number n oflabeled water molecules that are displaced thatdistance. We use the resultant data to plot a histo-gram of the relative number of labeled molecules(n/N) versus displacement distance (r) in a singledirection. Most of the molecules travel short dis-tances, and only a few travel farther (Fig 2). Typi-cally, the displacement distribution for free watermolecules is a Gaussian (bell-shaped) function.At 37°C, with a diffusion time interval of � � 50msec, the characteristic distance (standard devia-tion of the Gaussian distribution) typically is 17�m, which means that about 32% of the mol-ecules have moved at least this far, whereas only5% of them have traveled farther than 34 �m (2).

Figure 1. Diagram shows the diffusion-driven ran-dom trajectory (red line) of a single water moleculeduring diffusion. The dotted white line (vector r) rep-resents the molecular displacement during the diffusiontime interval, between t1 � 0 and t2 � �.

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TeachingPoint

Teaching Point In a glass of water, the motion of the water molecules is completely random and is limited only by the boundaries of the container. This erratic motion is best described in statistical terms by a displacement distribution. The displacement distribution describes the proportion of molecules that undergo displacement in a specific direction and to a specific distance.

A histogram like that in Figure 2 is adequatefor the display of one-dimensional data, but it isnot practical for visualizing displacement in mul-tiple dimensions. A useful approach is instead tocolor-code the probability. With such a represen-tation, the one-dimensional problem can be visu-alized as a colored displacement axis (x-axis) inwhich blue codes for high and red for low prob-ability (Fig 2). According to this rule, we can rep-resent actual three-dimensional (3D) diffusion asa 3D image in which the probability of displace-ment in three intersecting planes is coded in color(Fig 3a). The central voxel of the image is theorigin, and its value codes for the probability, orthe proportion of molecules (n/N) that do not

Figure 2. (a) Histogram shows a typical displace-ment distribution due to diffusion in a one-dimensionalmodel. For each displacement distance r (x-axis) thereis a corresponding probability n/N (y-axis), which is theproportion of molecules within a voxel that were dis-placed that distance within a time interval � (the dura-tion of the diffusion experiment). The top of the histo-gram is centered on zero, indicating that most mol-ecules had the same position at t � 0 and t � �. Theproportion of molecules that traveled the given distancer is indicated by the dotted red line. The horizontalcolor bar, in which blue signifies a high probability andred a low probability of displacement, shows the sameGaussian distribution. (b) Histogram shows a typicaldisplacement distribution due to flux (ie, nonzero aver-age displacement). All the molecules have moved thegiven distance r, as shown by N/N � 1.

Figure 3. Diffusion within a single voxel. (a) Dia-gram shows the 3D diffusion probability density func-tion in a voxel that contains spherical cells (top left) orrandomly oriented tubular structures that intersect,such as axons (bottom left). This 3D displacement dis-tribution, which is roughly bell shaped, results in asymmetric image (center), as there is no preferentialdirection of diffusion. The distribution is similar to thatin unrestricted diffusion but narrower because there arebarriers that hinder molecular displacement. The cen-ter of the image (origin of the r vector) codes for theproportion of molecules that were not displaced duringthe diffusion time interval. The color bar (right) showsthe spectrum used in color coding to represent prob-ability, from the lowest value, which is indicated by red,to the highest, which is indicated by blue. (b) Diagramshows the diffusion probability density function withina voxel in which all the axons are aligned in the samedirection. The displacement distribution is cigarshaped and aligned with the axons. (c) Diagram showsthe diffusion probability density function within a voxelthat contains two populations of fibers intersecting atan angle of 90°. The molecular displacement distribu-tion produces a cross shape.

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undergo displacement between t � 0 and t � �.This 3D diagram represents the displacementdistribution. A simple practical analogy is a dropof dye falling in a glass of water. On a photographtaken at t � �, the dye will have been diluted (dif-fused), and the relative color density will indicatethe proportion of dye molecules displaced a givendistance.

Diffusion in a homogeneous medium is welldescribed as having a Gaussian distribution. De-pending on the type of molecule, the temperatureof the medium, and the time allowed for diffu-sion, the distribution will be wider or narrower.The spread of the Gaussian distribution is con-trolled by a single parameter: variance (�2). Vari-ance, in turn, depends on two variables, so that�2 � 2 � D � �, where D, the diffusion coefficient,characterizes the viscosity of the medium or theease with which molecules are displaced. The dif-fusion coefficient for water at 37°C is approxi-mately D � 3 � 10�9 m2/sec. The longer the diffu-sion time interval, the larger the variance, becausethere is more time in which molecules may bedisplaced.

Molecular Displace-ment, Diffusion, and Flux

To describe the global behavior of a population ofwater molecules contained in an imaging voxel,we use the term displacement distribution. Equiva-lent terms to the latter are displacement probabilitydensity function and image of molecular displacement.In the present article, these terms are used inter-changeably. When molecules are agitated by ther-mal energy alone (ie, when molecular displace-ment takes place through the process of diffu-sion), the displacement distribution is centered.This means that the average or net displacementof the molecular population is zero. Factors otherthan heat also may contribute to molecular dis-placement. For example, a pressure gradient in apipe may affect molecular displacement. In anideal setting with no turbulence and no friction,all molecules undergo the same nonzero displace-ment r. Such a setting produces a very differentdisplacement distribution, in which the histogramis zero everywhere except in the position r, whichhas the value N/N � 1 (Fig 2b) because all themolecules have been displaced the same distance.This type of displacement is called flux. In flux,molecules are displaced over a nonzero averagedistance. Although diffusion and flux may occurtogether, for the sake of simplicity we have chosenin the present article to focus on diffusion only.

Therefore, the word displacement is often replacedwith the more specific term diffusion.

Diffusion in a Complex MediumAs mentioned earlier, a water molecule in a glassof water moves randomly and, given sufficienttime, may circumnavigate the internal contents ofthe glass but cannot go beyond it. The same istrue for water molecules within impermeablespheres that may be introduced into the glass ofwater (Fig 3a). The water molecules inside eachsphere diffuse within the restricted space of thatsphere, and the water molecules outside thespheres move randomly around them. Accord-ingly, the displacement distribution associatedwith a volume (ie, voxel) that contains the imper-meable spheres and their surround will be ratherdifferent from that associated with the same vol-ume before the spheres were introduced. The dif-ference reflects the presence of water restriction.Because molecules inside the sphere cannot movebeyond its boundaries, and because moleculesoutside cannot penetrate the sphere, the expecteddisplacement distance is reduced. It is difficult topredict the shape of the resultant displacementdistribution, but it will be more or less bell shapedand markedly narrower than that for unrestricteddiffusion, if the diffusion time interval is suffi-ciently long (Fig 3a). As in free diffusion, the dis-placement is isotropic, with no preferential direc-tion. To approximate the biological reality, onecould introduce into the glass of water a popula-tion of semipermeable spheres with a membranethat water molecules can cross with some resis-tance. Such intermediate conditions will producea displacement distribution that is not as narrowas that for a volume containing impermeablespheres but narrower than that for a volume withfree diffusion.

Biological tissues are highly heterogeneous me-dia that consist of various compartments and bar-riers of different diffusivities. In terms of its cyto-histologic architecture, a tissue can be regarded asa porous structure made up of a set of more orless connected compartments in a networklike

Figure 4. Diagram shows the cellular elementsthat contribute to diffusion anisotropy.


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arrangement. The movement of water moleculesduring diffusion-driven random displacement isimpeded by compartmental boundaries and othermolecular obstacles in such a way that the actualdiffusion distance is reduced, compared with thatexpected in unrestricted diffusion. A definingcharacteristic of neuronal tissue is its fibrillarstructure. Neuronal tissue consists of tightlypacked and coherently aligned axons that are sur-rounded by glial cells and that often are organizedin bundles. As a result, the micrometric move-ments of water molecules are hindered to agreater extent in a direction perpendicular to theaxonal orientation than parallel to it (Fig 3b).Consequently, molecular displacement parallel tothe fiber typically is greater than that perpendicu-lar to it. When diffusive properties change withthe direction of diffusion, the prevailing conditionis anisotropy, and the associated displacementdistribution is no longer isotropic and Gaussian,like that in unrestricted diffusion, but cigarshaped. Of course, the distribution may be evenmore complicated if the underlying tissue con-tains fibers with various orientations (Fig 3c) (3).

Experimental evidence suggests that the tissuecomponent predominantly responsible for theanisotropy of molecular diffusion observed inwhite matter is not myelin, as one might expect,but rather the cell membrane (4) (Fig 4). Thedegree of myelination of the individual axons andthe density of cellular packing seem merely tomodulate anisotropy. Furthermore, axonal trans-port, microtubules, and neurofilaments appear toplay only a minor role in anisotropy measured atMR imaging (4).

Diffusion Representedby a Six-dimensional Image

The image data acquired with computed tomog-raphy (CT) or MR imaging are usually 3D data.Every position in 3D space is associated with agray level that encodes the linear attenuation co-efficient at CT or the relative signal intensity atMR imaging. In mathematical terms, the 3D im-age is a function of the position variable p (a 3Dvector) and is designated as ƒ(p). Furthermore,the brain is a highly compartmentalized and het-erogeneous medium, with a different cytoarchi-tecture in different locations. Accordingly, if thelocal displacement distribution were measured invarious brain locations (voxels), there would be asmany different 3D displacement distributions asthere are voxels. To describe diffusion properly insuch a medium, every voxel position p must beassigned a diffusion probability density function(equivalent to the displacement distribution).Since the visual representation of a diffusionprobability density function is a 3D image, thenatural result of the combination of the two vari-ables p and r is a six-dimensional (6D) image.The 6D image fully characterizes diffusion in aheterogeneous medium, as it depicts the propor-tion of molecules ƒ(p,r) in voxel position p thathave been displaced a distance r (Fig 5). In otherwords, instead of each individual position beingassigned a single gray level as in CT or standardMR imaging, each position p is associated witha new 3D image on which molecular displace-ment is encoded. The resultant 6D image rep-resents the function of three position variables

Figure 5. Left part of diagram shows that standard imaging methods provide one value(gray level) for every 3D position p. That value or gray level may code for the linear x-rayattenuation coefficient at CT or for the relative signal intensity at MR imaging. Right part ofdiagram shows that in diffusion imaging every 3D position p (voxel) is associated not with agray level but with a 3D image that encodes the molecular displacement distribution in thatvoxel. The value measured at the coordinates p,r—ƒ(p,r)—indicates the proportion of mol-ecules in the voxel that have moved the given distance r.


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TeachingPoint

Teaching Point A defining characteristic of neuronal tissue is its fibrillar structure. Neuronal tissue consists of tightly packed and coherently aligned axons that are surrounded by glial cells and that often are organized in bundles. As a result, the micrometric movements of water molecules are hindered to a greater extent in a direction perpendicular to the axonal orientation than parallel to it.

(3D position vector p) and three displacementvariables (3D displacement vector r). This con-cept of multidimensionality may not be intuitiveto nonspecialists in mathematics but is nonethe-less essential for understanding diffusion imaging.

Representing 6DData in Three Dimensions

In standard 3D imaging, there is little differencebetween the data that are a function of position pand their representation on the display monitor asa section in which the function intensity is en-coded in gray levels. However, the distinctionbetween the two is more important when the dataare six dimensional, as six dimensions cannot berepresented straightforwardly in a single section;specific computer visualization techniques mustbe used to reduce the overwhelming amount ofinformation in six dimensions to the most impor-tant features. Typically, at diffusion imaging,there is less interest in obtaining a detailed diffu-sion profile than in determining the direction ofthe most rapid diffusion, because the latter pa-rameter likely corresponds to the orientation ofaxons or other fibrillar structures. One possibleapproach would be to replace the diffusion prob-ability density function with an isosurface, whichis a surface that passes through all points of equalvalue, or, in other words, where the value of ƒ(r)is a constant (Fig 6). A more commonly usedtechnique that is less sensitive to noise involvesthe computation of the orientation distributionfunction from the displacement distribution (Figs6, 7). An orientation distribution function may beconsidered a deformed sphere whose radius in agiven direction is proportional to the sum of val-ues of the diffusion probability density function inthat direction. For ease of visualization, we colorcode the surface according to the diffusion direc-tion ([x,y,z] � [r,b,g], where r � red, b � blue,and g � green). An orientation distribution func-tion or isosurface can be plotted for each indi-vidual MR imaging voxel in a section (Fig 8).

A General Descriptionof Diffusion Contrast Encoding

To depict the displacement distribution, diffusionmust be linked to the signal intensity measured at

MR imaging. As previously mentioned, watermolecules move randomly in the presence of ther-mal energy. In 1950, Hahn noted that the motionof spins (ie, hydrogen protons of the water mole-cule) in the presence of a heterogeneous magneticfield led to a decrease in signal intensity (5). In1956, Torrey established the fundamental equa-tions used to describe the magnetization of spinsin an MR spectroscopy experiment (6). Sincethen, these equations have come to be regarded asthe most fundamental equations in diffusion im-aging.

The results of the first MR spectroscopyexperiment specifically designed to measurediffusion were reported in 1965 by Stejskal andTanner (7). In their experiment, the investigatorsused a pulsed gradient spin-echo (SE) sequence,a technique based on the observation that spinsmoving in the magnetic field gradient directionare exposed to different magnetic field strengthsdepending on their position along the gradientaxis. As is well known in MR imaging, an ad-equately applied magnetic field influences thephase of the spins, with the degree of influencedepending on the strength of the field. Comparedwith a classic SE sequence, the pulsed gradientSE sequence includes two additional diffusion

Figure 6. Diagram shows two approaches that maybe used to simplify the visual representation of 3D dif-fusion data: replacement of the displacement distribu-tion with an isosurface, and computation of the orien-tation distribution function (ODF).


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Teaching Point An orientation distribution function may be considered a deformed sphere whose radius in a given direction is proportional to the sum of values of the diffusion probability density function in that direction.

Figure 7. Diagram shows how an orientation distribution function (ODF) is computedand represented. Left: Image of a section through a schematized 3D displacement distribu-tion. The value of the orientation distribution function was computed along two axes (yellowlines). Center: Histograms represent the displacement distribution along the two axes. Thevalue of the orientation distribution function along those axes equals the area under thecurve for each axis. In this example, the two areas under the curve are respectively small andlarge, indicating that there is much less diffusion in the one direction than in the other.Right: The sum of the areas under the curve is represented by a deformed sphere in whichthe lengths of the two radii (yellow lines) are short and long, corresponding to little diffusionand much diffusion, respectively. To compute the orientation distribution function, the areaunder the curve is computed for every direction.

Figure 8. Orientation distribution function map of a coronal brain section. For every brainposition p, an orientation distribution function is plotted to characterize the local diffusionprobability density function. It is easy to identify the corticospinal tract, in which the domi-nant color is blue, and the corpus callosum, in which red is predominant. More difficult tosee are the cingulum and the arcuate fasciculus, depicted predominantly in green, and themiddle cerebellar peduncle, in red.


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gradient pulses (Fig 9). The first of the two gradi-ent pulses in this sequence introduces a phaseshift that is dependent on the strength of the gra-dient at the position of the spin at t � 0. Beforethe application of the second gradient pulse,which induces a phase shift dependent on the spinposition at t � �, a 180° RF pulse is applied toreverse the phase shift induced by the first gradi-ent pulse. Since the diffusion-encoding gradientcauses the field intensity (ie, phase shift) to varywith position, all spins that remain at the samelocation along the gradient axis during the twopulses will return to their initial state. However,spins that have moved will be subjected to a dif-ferent field strength during the second pulse andtherefore will not return to their initial state butwill experience a total phase shift that results indecreased intensity of the measured MR spectro-scopic signal. The longer the displacement dis-tance is, the higher the phase shift and the greaterthe decrease in signal will be. Hence, the resultantimage shows low signal intensity in regions wherediffusion along the applied diffusion gradient ishigh.

A diffusion gradient can be represented asa 3D vector q whose orientation is in the direc-tion of diffusion and whose length is proportionalto the gradient strength. The gradient strength,or more often the diffusion weighting, is some-times expressed in terms of the b value, which isproportional to the product of the square of thegradient strength q and the diffusion time interval(b � q2 � �).

q-Space Explainedin Analogy to k-Space

According to basic MR imaging principles (8,9),the measured signal at conventional MR imagingis phase and frequency encoded. It is the result ofthe application of gradients in different directionsand with different intensities at specific momentsof the acquisition sequence. The values of themeasured signal are organized in a coordinatesystem known as k-space. Performing the acquisi-tion enables the filling of k-space. To transformthe raw MR imaging data from k-space into a po-sition-encoded visual image, a mathematical op-eration known as a Fourier transform is applied(Fig 10) (9,10).

The process in diffusion MR imaging is analo-gous. Let us first define a new 3D space, calledq-space, the coordinates of which are defined by avector q (11). The application of a single pulsedgradient SE sequence produces one diffusion-weighted image that corresponds to one position

in q-space or, more precisely, that depicts the dif-fusion-weighted signal intensity in a specific posi-tion q for every brain position. Repeated applica-tions of the sequence with gradients that vary instrength and in direction (ie, with variations of q)allow data sampling throughout q-space. Like thedata from conventional MR imaging, in whicha Fourier transform is applied to the data in

Figure 9. Diagram shows the pulsed gradient SE se-quence used for diffusion MR imaging. Two diffusion-encoding gradient (Gdiff ) pulses are added to the stan-dard SE MR imaging sequence to introduce a phaseshift proportional to molecular displacement along thegradient direction. � � duration of the diffusion-en-coding gradient, � � diffusion time interval, Gphase �phase-encoding gradient, Gread � readout gradient,Gslice � section-selective gradient, RF � radiofrequencypulse, t � acquisition time. The diffusion-encodinggradient often is symbolized by the vector q , which isequal to the product of � � � � Gdiff, where � is the gyro-magnetic ratio; thus, it represents the effective diffusiongradient.

Figure 10. Diagram shows the process with which astandard position-encoded MR image is obtained.First, the MR signal that was generated by the applica-tion of phase- and frequency-encoding gradients issampled to fill k-space (a coordinate system used toorganize the signal measurements). Next, the raw data(k-space images) are subjected to a mathematical op-eration known as a Fourier transform to reconstruct animage in the standard position space.


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k-space, the q-space data are subjected to a Fou-rier transform in every brain position. The resultis a displacement distribution in each brain posi-tion (ie, voxel) (Fig 11). In other words, a singleapplication of the pulsed gradient SE sequenceproduces one brain image with a given diffusionweighting. Multiple repetitions of the sequence,each with a different diffusion weighting, are nec-essary to sample the entirety of q-space; the resultis hundreds of brain images, each of which re-flects the particular diffusion weighting used. Onemust then imagine that the data are reorganizedso that in every brain position there is a q-space

signal sample that consists of hundreds of valuesand that in every brain position a Fourier trans-form relates the raw q-space data to the diffusionprobability density function (Fig 12).

q-Space is always sampled for a specific diffu-sion time interval �, which is determined by theduration of the interval between the two gradientpulses. The diffusion time interval can be variedto enhance different properties. For example, alonger interval produces better directional resolu-tion. Imagine diffusion within an axon: With a

Figure 11. Diagram shows the process with which a 3D diffusion probability density func-tion is obtained for one voxel (one brain position). In A, a 3D grid that represents q-space,each yellow dot corresponds to an MR signal sampling point. The signal is sampled at eachpoint by varying the direction and strength of the diffusion gradient (q vector) of the pulsedgradient SE sequence. With a single application of the pulsed gradient SE sequence, onepoint in q-space is sampled for each brain position simultaneously, and the result is one dif-fusion-weighted image. In B, the left panel shows sections through the MR signal sampled inq-space for a specific brain position (one voxel), and the right panel shows the diffusionprobability density function in the same voxel after a 3D Fourier transform of the MR signalin q-space is performed. The cross-shaped appearance of the diffusion probability densityfunction is often seen in voxels in the brainstem, where axons of the corticospinal tract crosswith axons of the middle cerebellar peduncle.

Figure 12. Series of diffusion-weightedMR brain images obtained with variationsin the direction and strength of the diffu-sion gradient in the pulsed gradient SEsequence. Each image shows the signalsampled at one point in q-space (one yel-low dot). Every sampling point in q-spacecorresponds to a specific direction andstrength of the diffusion gradient.


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very short diffusion time interval, there is a similaramount of diffusion in every direction. When theinterval is longer, diffusion perpendicular to thedirection of the axon stops when the moleculesreach the axon wall, while diffusion along the longaxis of the axon continues. Thus, a longer intervalincreases the distinction between the signals indifferent directions; however, it also leads to alower signal-to-noise ratio.

To describe the parameters applied in sam-pling q-space, the term “b value” is often used.The b value is proportional to the product of thediffusion time interval and the square of thestrength of the diffusion gradient. All diffusionimages should be compared with a reference im-age that is not diffusion weighted (a standardSE image)—in other words, one for which thestrength of the diffusion gradient is zero (q � 0and b � 0).

Diffusion Spectrum ImagingDiffusion spectrum imaging may be described asthe reference standard of diffusion imaging be-cause it is the practical implementation of theprinciples derived earlier and is the diffusion im-aging technique that has a sound basis in physicaltheory (12). Suitable for in vivo application, itprovides a sufficiently dense q-space signalsample from which to derive a displacement dis-tribution with the use of the Fourier transform.The technique was first described by Wedeen etal (13).

If established practice is followed, 515 diffu-sion-weighted images are acquired successively,each corresponding to a different q vector, thatare placed on a cubic lattice within a sphere witha radius of five lattice units. The lattice units cor-respond to different b (or q) values, from b � 0(which corresponds to the centerpoint of thesphere) to, typically, b � 12,000 sec/mm2 (whichis a very high b value). The Fourier transform iscomputed over the q-space data. If the imagingmatrix size is 128 � 128 � 30, the same numberof Fourier transform operations will be necessaryas the diffusion probability density function iscomputed for every brain location.

Traditionally, 515 images were considerednecessary to obtain data of good quality, althoughthe acquisition of that number of images is verytime consuming. With improvements in MR im-aging hardware and techniques in recent years,and in view of additional very recent experience,fewer sampling points seem to be necessary; theprobability density function can be reconstructedwith approximately 257 or even 129 images bysampling only one hemisphere in q-space. Of

course, the signal-to-noise ratio and angular reso-lution may change accordingly. The time for im-aging of both brain hemispheres thus can be re-duced from approximately 45–60 minutes to aslittle as 10–20 minutes, an acquisition time thatmakes the technique feasible in a clinical setting(14).

With the application of the Fourier transformover q-space in every brain position, a 6D imageof both position and displacement is obtained.Diffusion at each position is described by the dis-placement distribution or the probability densityfunction, which provides a detailed description ofdiffusion and excellent resolution of the highlycomplex fiber organization, including fiber cross-ings. Since diffusion spectrum imaging is mostlyused for fiber tractography, in which only direc-tional information is needed, the probability den-sity function is normally reduced to an orientationdistribution function by summing the probabili-ties of diffusion in each direction (Fig 7).

From the Simplest to theMost Sophisticated Technique

Diffusion-weighted MR ImagingDiffusion-weighted MR imaging is the simplestform of diffusion imaging. A diffusion-weightedimage is one of the components needed to recon-struct the complete probability density functionas in diffusion spectrum imaging. A diffusion-weighted image is the unprocessed result of theapplication of a single pulsed gradient SE se-quence in one gradient direction, and it corre-sponds to one point in q-space. Even though suchan image is rather simple, it does contain someinformation about diffusion. In Figure 13, the leftsplenium of the corpus callosum appears bright,whereas the right splenium appears dark. In re-gions such as the right splenium, where the maindiffusion direction is aligned with the applied dif-

Figure 13. Diffusion-weighted image (right) fromsignal sampling at a single point in 3D q-space (left).Brain areas where diffusion is intense in the direction ofthe applied gradient ( q� ) appear darker because of adecrease in the measured signal that results fromdephasing.


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fusion gradient, the intensity of the signal is mark-edly decreased, and the region therefore appearsdarker on the image. In the ventricles, diffusion isfree and substantial in all directions, including theapplied gradient direction, and therefore the en-tirety of the ventricles appears dark. Despite itssimplicity, diffusion-weighted imaging is routinelyused in investigations of stroke (15). Indeed, inacute stroke, the local cell swelling produces in-creased restriction of water mobility and hence abright imaging appearance due to high signal in-tensity in the area of the lesion. The benefit ofdiffusion-weighted imaging is that the acquisitiontime is short, since only one image is needed.

ADC and TraceThe problem of diffusion-weighted imaging isthat the interpretation of the resultant images isnot intuitive. To resolve this problem, let us as-sume that the diffusion has no restrictions andthat its displacement distribution therefore can bedescribed with a free-diffusion physical model,which is a 3D isotropic Gaussian distribution. Inthis model, the physical diffusion coefficient D isreplaced by the ADC, which is derived from theequation ADC � �b ln(DWI/b0), where DWI isthe diffusion-weighted image intensity for a spe-cific b value and diffusion gradient direction, de-fined as in the previous section, and b0 is a refer-ence image without diffusion weighting. Thus, toobtain an image of the ADC values, two acquisi-tions are necessary.

The ADC is very dependent on the direction ofdiffusion encoding. To overcome this limitation,one can perform three orthogonal measurementsand average the result to obtain a better approxi-mation of the diffusion coefficient. This methodis equivalent to the derivation of the trace fromthe diffusion tensor, described in more detail inthe next section.

Diffusion TensorImaging and Derived ScalarsFor ADC imaging, we have assumed that diffu-sion follows a free-diffusion physical model and isdescribed by an isotropic Gaussian distribution.This model often is too simplistic, especially if weare interested in the orientation of axonal bundlesin which diffusion is expected to be anisotropic(ie, not the same in all directions). For purposesof discussion, then, let us assume that diffusionremains Gaussian but may be anisotropic. Inother words, diffusion may be cigar or discshaped but also may be spherical, as in isotropicdiffusion. Anisotropic Gaussian distributionshave six degrees of freedom instead of one.Therefore, to fit our model, we must sample atleast six points in q-space with q 0 (diffusion-weighted images) and one point with q � 0 (refer-ence image) (Fig 14). In general, a b value of ap-proximately 1000 sec/mm2 is used. To fit the re-sultant data to the model, we must solve a set of

Figure 14. Series of diffusion-weightedimages obtained for diffusion tensor imag-ing, in which q-space is sampled in at leastsix different directions and in which a non–diffusion-weighted reference image is ob-tained. The direction but not the strengthof the diffusion gradient is changed foreach sampling.


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six equations like the equation given earlier. Theresult is a diffusion tensor (instead of a diffusioncoefficient) that is proportional to the Gaussiancovariance matrix (instead of the Gaussian vari-ance) (16). This diffusion tensor is a 3 � 3 matrixthat fully characterizes diffusion in 3D space, as-suming that the displacement distribution isGaussian. The diffusion tensor is usually repre-sented by an ellipsoid or an orientation distribu-tion function (Fig 15).

The mathematical properties of the diffusiontensor make it possible to extract several usefulscalar measures from diffusion tensor images.The mean diffusion, also known as the trace, iscomputed by averaging the diagonal elements ofthe matrix (16). The result is an image like that inFigure 16a and is the same as the result obtainedby estimating the ADC in three orthogonal direc-tions. The direction of the diffusion maximum iscalled the principal direction of diffusion and canbe directly obtained by computing eigenvectorsand eigenvalues of the tensor. Eigenvectors areorthogonal to one another, and, with eigenvalues,describe the properties of the tensor. Eigenvaluesare ordered as 1 � 2 � 3, and each corre-sponds to one eigenvector. The eigenvector thatcorresponds to the largest eigenvalue (1) is theprincipal direction of diffusion. If the eigenvaluesare significantly different from each other, diffu-sion is said to be anisotropic (Fig 15). If 1 ismuch larger than the second eigenvalue, 2, thediffusion is cigar shaped (Fig 15). If 1 and 2 aresimilar but are much larger than 3, the diffusionis said to be planar or disc shaped. When all theeigenvalues are approximately equivalent, diffu-sion is isotropic and may be represented as asphere (17).

The relationship between the eigenvalues re-flects the characteristics of diffusion. To describethe shape of diffusion with a scalar value, frac-tional anisotropy is most often used (16). How-ever, other measures, such as those described byWestin et al (17), are available. Fractional anisot-ropy is computed by comparing each eigenvaluewith the mean of all the eigenvalues (��), as inthe following equation:

FA � � 32 � 1 - ��2 � 2 - ��2 � 3 - ��2

12 � 2

2 � 32 ,

where FA is the fractional anisotropy. The frac-tional anisotropy of a section of diffusion tensorscan be seen in Figure 16b.

The ellipsoid or the orientation distributionfunction is the most accurate method for visualiz-ing the diffusion tensor data, but sometimes it isdifficult to represent it over an imaging section ona display monitor (18). Color coding of the diffu-sion data according to the principal direction ofdiffusion may be a more practical way of visualiz-ing the data (16). In the color coding system thatwe use, red corresponds to diffusion along theinferior-superior axis (x-axis); blue, to diffusionalong the transverse axis (y-axis); and green, todiffusion along the anterior-posterior axis (z-axis).The intensity of the color is proportional to thefractional anisotropy. An example of this colorcoding scheme is shown in Figure 16c.

The diffusion tensor model performs well inregions where there is only one fiber population(ie, fibers are aligned along a single axis), where itgives a good depiction of the fiber orientation.However, it fails in regions with several fiberpopulations aligned along intersecting axes be-cause it cannot be used to map several diffusionmaxima at the same time. In such areas, imagingtechniques that provide higher angular resolutionare needed.

Diffusion Tensor Imagingand Diffusion Spectrum ImagingBecause of the limited number of applied diffu-sion gradients and degrees of freedom, the diffu-sion tensor model is incapable of resolving fibercrossings. In contrast, diffusion spectrum imaging

Figure 15. Diagram of diffusion tensors. In A, thediffusion tensor is shown as an ellipsoid (an isosur-face) with its principal axes along the eigenvectors(1,2,3). In B, the diffusion tensor is shown as an ori-entation distribution function.


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TeachingPoint

TeachingPoint

Teaching Point This diffusion tensor is a 3 X 3 matrix that fully characterizes diffusion in 3D space, assuming that the displacement distribution is Gaussian. The diffusion tensor is usually represented by an ellipsoid or an orientation distribution function.

Teaching Point The diffusion tensor model performs well in regions where there is only one fiber population (ie, fibers are aligned along a single axis), where it gives a good depiction of the fiber orientation. However, it fails in regions with several fiber populations aligned along intersecting axes because it cannot be used to map several diffusion maxima at the same time. In such areas, imaging techniques that provide higher angular resolution are needed.

is not predicated on any particular hypothesisconcerning diffusion. Accordingly, its capabilityto resolve the diffusion probability density func-tion depends only on the resolution in q-space,and its capability to resolve fiber crossings de-pends only on the related angular resolution. InFigure 17, images obtained with the two methods

are juxtaposed. The regions in which the moststriking difference can be seen are the pons,where the corticospinal tract and middle cerebel-lar peduncle cross, and the centrum semiovale,

Figure 16. Extraction of scalar values from diffusion tensor imaging. (a) Image showsmean diffusion, which is the trace of the diffusion tensor. An image of ADC averaged overthree orthogonal directions would have a similar appearance. (b) Image shows the fractionalanisotropy, which is computed from the eigenvalues of the diffusion tensor. (c) Color-codedimage shows the orientation of the principal direction of diffusion, with red, blue, and greenrepresenting diffusion along x-, y-, and z-axes, respectively. The color intensity is propor-tional to the fractional anisotropy.

Figure 17. Comparison be-tween diffusion tensor anddiffusion spectrum imagingin regions that contain fibercrossings. In A, a color-codedcoronal diffusion image showsthe pons (B) and the centrumsemiovale (C), in which diffu-sion is depicted by both diffu-sion tensor images (B-DTI,C-DTI) and diffusion spec-trum images (B-DSI, C-DSI).In the pons, the middle cer-ebellar peduncle crosses thecorticospinal tract. In the cen-trum semiovale, the cortico-spinal tract crosses the corpuscallosum and the arcuate fas-ciculus. In the circled sections(C-DTI, C-DSI), it can beseen that diffusion tensor im-aging is not capable of resolv-ing fiber crossings, whereasdiffusion spectrum imaging is.


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where the corticospinal tract crosses the corpuscallosum and the arcuate fasciculus.

With regard to acquisition times, diffusion ten-sor imaging has a clear advantage over diffusionspectrum imaging in that it requires a minimumof only seven images, whereas diffusion spectrumimaging requires several hundred images. Diffu-sion spectrum imaging previously involved longacquisition times, but with constant improve-ments the acquisition time is decreasing (14).

Increased AngularResolution with q-Ball ImagingWe have seen, on one hand, that diffusion tensorimaging is insufficient in many brain areas for ac-curately mapping the orientation of major tracts.On the other hand, we would like to have avail-able a faster technique than diffusion spectrumimaging, which is time consuming for routineclinical applications, although improvements inthis regard are currently being evaluated. q-Ballimaging is an attempt to combine the best at-tributes of these two techniques (19). Althoughwe decided for illustrative purposes to discussq-ball imaging only, there are many other heuris-tic methods, such as those based on persistentangular structure (20) and spherical deconvolu-tion (21). All these techniques are based on anidentical or nearly identical scheme that consistsof rather dense sampling of the signal within asphere with a constant high b value in q-space.The orientation distribution function is estimatedfrom the resultant data by using various algo-rithms.

Like diffusion tensor imaging, q-ball imaging isbased on a hypothesis about the shape of the dif-fusion probability density function. This hypoth-esis is complex and demands a more in-depthconsideration of the spatial frequency content ofthe signal in q-space than can be provided in thepresent article. Here, we consider only a specifictype of diffusion probability density function forwhich q-ball imaging provides an adequate basis.We assume that the compartments inside a voxelconsist of a set of straight and very thin pipes withimpermeable walls. Water molecules inside the

pipes are assumed to diffuse uniformly along thelength of the pipes but to have no transverse mo-tion. The diffusion probability density function inthis case would look like a pincushion. With thismodel, diffusion can be reconstructed by sam-pling points in q-space on a sphere with a con-stant radius, at a high b value (typically, �4000sec/mm2). The data are reconstructed by usingthe Funk-Radon transform, an algorithm that canbe described as follows: Suppose that we want toknow the diffusion intensity (ie, the value of theorientation distribution function) in a directionthat corresponds to the North Pole and that theMR signal has been sampled over the globe. If weadd together the values of the signal intensitymeasured along the equator, the sum will be pro-portional to the diffusion intensity at the NorthPole. If we redefine the location of the North Poleas, for example, Lausanne and redefine the equa-tor accordingly, the value of the orientation distri-bution function at Lausanne can be computed ina similar fashion. The same can be done to recon-struct the orientation distribution function for anypoint (eg, Boston, Stockholm, Brussels) on theglobe (Fig 18).

Unlike diffusion tensor imaging, q-ball imagingcan account for multiple crossing fibers within asingle voxel and therefore can provide realisticdepiction of areas of complex fiber architecture,such as the centrum semiovale and the pons.With q-ball imaging, the images obtained re-semble those acquired with diffusion spectrumimaging. However, further validation studiesmust be performed to determine whether q-ballimaging provides high-quality depiction of all re-gions of the brain and whether the reconstructedimages are accurate.

Diffusion MR TractographyBrain fiber tractography is a rendering method forimproving the depiction of data from diffusionimaging of the brain. Although a detailed discus-sion of tractography is beyond the scope of thisarticle, a short introduction is necessary becausetractography is one of the most powerful toolsdeveloped to aid image interpretation. The pri-mary purpose of tractography is to clarify the ori-entational architecture of tissues by integratingpathways of maximum diffusion coherence. Fi-bers are grown across the brain by following from


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voxel to voxel the direction of the diffusion maxi-mum. The fibers depicted with tractography areoften considered to represent individual axons ornerve fibers, but they are more correctly viewed inphysical terms as lines of fast diffusion that followthe local diffusion maxima and that only generallyreflect the axonal architecture. This distinction isuseful because, for a given imaging resolution andsignal-to-noise ratio, lines of maximum diffusioncoherence (ie, the computer-generated fibers)may differ from the axonal architecture in somebrains. Tractography adds information and inter-est to the MR imaging depiction of the humanneuronal anatomy.

The connectivity maps obtained with tractog-raphy vary according to the diffusion imaging mo-dality used to obtain the diffusion data. For ex-ample, diffusion tensor imaging provides a Gauss-ian approximation of the actual displacementdistribution, and since the representation of thatdistribution is restricted to variations of an ellip-soid, this method creates various biases in the

tractography result. In contrast, diffusion spec-trum imaging with tractography overcomes manyof those biases and allows more realistic mappingof connectivity. The tractography result also de-pends on the tracking algorithm used. Determin-istic fiber tracking from diffusion tensor imaginguses the principal direction of diffusion to inte-grate trajectories over the image (22) but ignoresthe fact that fiber orientation is often undeter-mined in the diffusion tensor imaging data. Toovercome this limitation of the data, Hagmannand colleagues, as well as other investigators, in-vestigated statistical fiber tracking methods basedon consideration of the tensor as a probabilitydistribution of fiber orientation (23–25).

The application of fiber tractography to datasuch as those obtained with diffusion spectrumimaging or q-ball imaging results in the depictionof a large set of fiber tracts with a more complex

Figure 18. Diagram showsthat in q-ball imaging, pointson a shell with a constant bvalue are acquired in q-space.At least 60 images are neces-sary to reconstruct an orienta-tion distribution function thatis realistic.


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geometry (26). The greater complexity obtainedwith this method, compared with that from trac-tography with diffusion tensor MR imaging data,is due to the consideration of numerous intersec-tions between fibers that can be resolved or differ-entiated. The difference between tractographyperformed with diffusion tensor imaging data andtractography performed with diffusion spectrumimaging data can be seen in Figure 19.

ConclusionsWater diffusion is produced by the random mo-tion of water molecules because of thermal en-ergy. The molecular displacement depicted atdiffusion MR imaging is best described at thelevel of a selected molecular population—typi-cally, the water molecules contained in a voxel—by calculating the probability density function ordisplacement distribution. The 3D diffusionprobability density function is shaped by localtissue structure, which hinders molecular dis-placement. Because biological tissue is heteroge-neous, with a different tissue architecture in

Figure 19. Comparison of fiber tractography based on diffusion tensor imaging(DTI) versus fiber tractography based on diffusion spectrum imaging (DSI) in twohealthy volunteers. The diffusion spectrum imaging data were obtained with a3.0-T imager and a twice-refocused SE pulse (repetition time msec/echo timemsec � 3000/154; bmax � 17,000 sec/mm2; voxel size of 3 � 3 � 3 mm); tractogra-phy was performed according to the method described in reference 26. The diffu-sion tensor imaging data were obtained with a 1.5-T imager and a single-shot echo-planar sequence (1000/89; b � 1000 sec/mm2; voxel size of 1.64 � 1.64 � 3 mm);tractography was performed as described in reference 23. Because diffusion spec-trum imaging provides higher angular resolution, fiber crossings are better resolvedand fibers from different tracts are more clearly separated. The most visible differ-ences between the two axial views (bottom row) are the greater predominance ofred, which represents decussating callosal fibers that connect both the parietal andthe temporal lobes, and the more uniform distribution of callosal fibers that projectinto the frontal lobe, on the diffusion spectrum image. These differences reflecttypical errors of diffusion tensor imaging tractography in areas where fibers cross.


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different anatomic positions, a 3D displacementdistribution must be calculated for every 3Dvoxel, to produce a 6D image that depicts bothposition and displacement. This 6D image is bestobtained with diffusion spectrum imaging, thereference standard. Diffusion spectrum imagingis a rather complex and demanding technique(Table 1), with stringent hardware requirements.Many simpler diffusion imaging techniques alsoexist that can provide important informationabout diffusion and tissue structure; however, theinformation they provide is partial and often hy-pothesis based, and those who use such tech-niques must be aware of their limitations. Imag-

ing of the ADC and trace are extremely simplemethods and provide only basic information,namely an estimate of the variance of the diffu-sion function. Diffusion tensor imaging and q-ballimaging are hypothesis-based simplifications thatare used to shorten image acquisition time andreduce hardware requirements. Like diffusionspectrum imaging, they can be used to obtainmaps of the orientation distribution functions.Care must be taken when interpreting diffusion

Table 1Technical Requirements of Diffusion MR Imaging Techniques

TechniqueandReference

3.0 T andHigh Gradient

StrengthCapabilities

No. ofGradient

Directions

MaximalGradientStrength

(sec/mm2)

AcquisitionTime

(min)* Postprocessing Display

Diffusion-weightedimaging (15)

Optional 1 �1000 1–3 None Gray-scale sec-tions

Trace andADC imag-ing (16)

Optional �3 �1000 2–4 Simple summa-tion, usuallyperformed auto-matically by theimaging system

Gray-scale sec-tions

Diffusion ten-sor imaging(16)

Optional �6 �1000 3–6 Simple matrixoperation, usu-ally performedautomaticallyby the imagingsystem

Gray-scale sec-tions for derivedscalars (eg,trace, fractionalanisotropy),color-codedsections for dif-fusion direction,ellipsoid recon-struction of ori-entation distri-bution function,tractography

q-Ball imaging(19)

Desirable �60 �4000 10–20 Complex filteredback-projectionwith many pa-rameters

Trace, generalfractional an-isotropy, orien-tation distribu-tion function,tractography

Diffusion spec-trum imag-ing (12)

Verydesirable

�200 �8000 15–60 Complex (filteredFourier trans-form and radialprojection withmultiple param-eters)

Trace, generalfractional an-isotropy, prob-ability densityfunction, orien-tation distribu-tion function,tractography

*It is assumed that 30 axial sections are acquired, each with a thickness of 3 mm.


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tensor imaging data and q-ball imaging data, asthere may be brain areas in which the underlyinghypotheses are not applicable, whereas diffusion

spectrum imaging is limited only by factors suchas k- and q-space resolution and signal-to-noiseratio. Tractography is a visualization techniquethat can be used to extract lines of maximum dif-fusion coherence from any orientation distribu-tion function map. These lines reflect the anat-

Table 2Advantages and Drawbacks of Diffusion MR Imaging Techniques

Technique Information Obtained Advantages Drawbacks

Diffusion-weightedimaging

Diffusion measurement inone direction

Short acquisition time, nopostprocessing, imageseasy to interpret. Exami-nation well tolerated bypatients. Adequate hard-ware capabilities readilyavailable.

Provides unidirectional dif-fusion measurementonly, limited informa-tion. Voxel intensity isnot a natural physicalunit but a measure ofrestriction.

Trace and ADCimaging

Estimated diffusion coeffi-cient

Short acquisition time,nearly no (or automated)postprocessing, imageseasy to interpret. Voxelintensity has physicalmeaning. Examinationwell tolerated by patients.Adequate hardware capa-bilities readily available.

Hypothesis based (hypoth-esis not always true).Limited information (nomeasurement of orienta-tion or anisotropy).

Diffusion tensorimaging

Estimated diffusion tensor Short acquisition time,some postprocessing re-quired (automated onrecent imaging systems).Provides informationabout diffusion orienta-tion and anisotropy. Ex-amination well toleratedby patients. Adequatehardware capabilitiesreadily available.

Hypothesis based (hypoth-esis not always true).Does not provide accu-rate map of complex fiberarchitecture. Tractogra-phy results are vulnerableto severe artifacts.

q-Ball imaging Estimated map of orienta-tion distribution functionvalues

Feasible with reasonableacquisition time. Pro-vides information aboutdiffusion orientation andanisotropy, accurate de-piction of fiber crossings.Examination tolerated bymost patients.

Hypothesis based. Al-though results seem cor-rect in important brainareas, accuracy is notguaranteed in all brainregions. Further valida-tion is required. Hard-ware requirements arehigh.

Diffusion spectrumimaging

Full 3D diffusion probabil-ity density function map,true 6D images

Principle based, hypothesisfree, has already receivedtheoretical and practicalvalidation. Provides ac-curate depiction of fibercrossings with a specificangular resolution. Mapsthe entire field of diffu-sion, providing 6D dataand increasing the possi-bility of quantitation.Provides diffusion tensorinformation.

Hardware requirements arehigh, and acquisitiontime is comparativelylong. Whole-brain stud-ies were not tolerable forpatients. Recent im-provements in hardwareand imaging techniqueshave made shorter acqui-sition times possible, al-lowing future patientstudies.


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omy of the axonal trajectories. Many uses areforeseen for fiber tractography, from single-tractanalysis to whole-brain connectivity analysis(27,28). The technical requirements and the re-sults that can be achieved with each diffusion MRimaging method are described in Table 1. Theradiologist should weigh the pros and cons (Ta-ble 2) of each technique and, depending on thequestion addressed and the equipment available,choose the most adequate. It is our hope that theinformation in this article will be helpful in mak-ing that decision.

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RG Volume 26 • Special Issue • October 2006 Hagmann et al

Understanding Diffusion MR Imaging Techniques: From Scalar Diffusion-weighted Imaging to Diffusion Tensor Imaging and Beyond

Patric Hagmann, MD, PhD et al

Page S206 In a glass of water, the motion of the water molecules is completely random and is limited only by the boundaries of the container. This erratic motion is best described in statistical terms by a displacement distribution. The displacement distribution describes the proportion of molecules that undergo displacement in a specific direction and to a specific distance. Page S209 A defining characteristic of neuronal tissue is its fibrillar structure. Neuronal tissue consists of tightly packed and coherently aligned axons that are surrounded by glial cells and that often are organized in bundles. As a result, the micrometric movements of water molecules are hindered to a greater extent in a direction perpendicular to the axonal orientation than parallel to it. Page S210 An orientation distribution function may be considered a deformed sphere whose radius in a given direction is proportional to the sum of values of the diffusion probability density function in that direction. Page S216 This diffusion tensor is a 3 × 3 matrix that fully characterizes diffusion in 3D space, assuming that the displacement distribution is Gaussian. The diffusion tensor is usually represented by an ellipsoid or an orientation distribution function. Pages S216 The diffusion tensor model performs well in regions where there is only one fiber population (ie, fibers are aligned along a single axis), where it gives a good depiction of the fiber orientation. However, it fails in regions with several fiber populations aligned along intersecting axes because it cannot be used to map several diffusion maxima at the same time. In such areas, imaging techniques that provide higher angular resolution are needed.

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RadioGraphics 2006; 26:S205–S223 ● Published online 10.1148/rg.26si065510 ● Content Codes:

understanding diffusion mr imaging techniques

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