Basic Concepts of MRImaging, Diffusion MRImaging, and DiffusionTensor Imaging

Eduardo H.M.S.G. de Figueiredo, BSca,*,Arthur F.N.G. Borgonovi, BScb,c, Thomas M. Doring, MScd,e

KEYWORDS

� Magnetic resonance imaging � Diffusion-weighted imaging� Diffusion tensor imaging

BASIC PHYSICS OF MAGNETIC RESONANCE

Magnetic resonance (MR) imaging stems from theapplication of nuclear magnetic resonance (NMR)to radiological imaging. The adjective “magnetic”refers to the use of magnetic fields and “reso-nance” refers to the need of matching thefrequency of an oscillating electromagnetic fieldto the “precessional” frequency of the spin ofsome nuclei in a tissue molecule.1

Interest in medical diagnostic possibilities ofNMR began in 1971, with the study by Damadian2

of the differences in relaxation times T1 and T2,among different tissues, and between normaland cancerous tissues.3 In 1973, the imagingarea for MR started with pioneering articles pub-lished by Lauterbur4 and Mansfield and Grannell,5

when the idea of spatial varying magnetic fields togive the localization information was firstintroduced.

The phenomenon of magnetic resonance isbased on the interaction between externalmagnetic fields and nuclei, which have a nonzeromagnetic moment. According to classical theoryof electromagnetism, individual nuclear moments

a GE Healthcare, Avenida das Nacoes Unidas, 8501, 3 anb Hospital das Clınicas, Avenida Dr. Eneas de Carvalho ABrazilc Hospital do Coracao, Avenida Dr. Eneas de Carvalho ABrazild Federal University of Rio de Janeiro, Avenida das AmeriRio de Janeiro, Brazile Clınica de Diagnostico por Imagem, Avenida das AmeriRio de Janeiro, Brazil* Corresponding author.E-mail address: eduardo.figueiredo@ge.com

Magn Reson Imaging Clin N Am 19 (2011) 1e22doi:10.1016/j.mric.2010.10.0051064-9689/11/$ e see front matter � 2011 Published by E

called spins in a static magnetic field B0 precesswith Larmor frequency w0 about B0. A bulk of spinsforms the net magnetization vector pointing alongB0. When radiofrequency (RF) is applied in thissystem at Larmor frequency, the spins absorbthe radiofrequency energy and the net magnetiza-tion vector flips by a certain angle in relation to B0.The net magnetization vector can be decomposedinto 2 components, a longitudinal componentparallel to B0 and a transversal component perpen-dicular to B0. As the transversal componentprecesses around a receiver coil, it inducesa current in that coil, in accordance with Faraday’slaw of induction. This current becomes the MRsignal.6

After stopping sending RF to the spins system,the MR signal decays mainly via 2 processes:loss of phase between spins and energy releaseto the environment. The loss of phase betweenspins can occur due to interaction spin-spin, andthis process is described as T2 relaxation, or itcan occur due to B0 inhomogeneities, describedas T2* relaxation. In both ways, the transversecomponent of net magnetization vector decreasesand even though there is energy in the system, the

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Fig. 1. In the classical view, a charged particlewith spincan be compared as a magnetic dipole such as a barmagnet. (Courtesy of GEHealthcare, Sao Paulo, Brazil.)

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MR signal decays. The interaction between spinsand the environment they insert, called spin-lattice interaction and described as T1 relaxation,causes the spins that form the net magnetizationvector to release their energy, and its longitudinalcomponent grows back along the B0 direction.The tissue relaxation characteristics are ex-

pressed in image contrast and are controlled bythe pulse sequence chosen. The “pulse sequence”is a sequence of RF pulses, magnetic field gradientpulses, signal sampling, and time periods betweenthem. RF pulses are basically responsible for exci-tation of spins and their manipulation to obtaina signal echo. Magnetic field gradients are respon-sible for selecting the slice to be imaged, spatiallyencoding the signal induced in receiver coils, usingfrequency and phase as location information andin some pulse sequences, gradients also controlthe image contrast. Spin echo and gradient echoare examples of pulse sequences that controlimage contrast, by applying RF pulses or gradientpulses, respectively.Although tissue relaxation characteristics are

the main source of contrast information, MRimages can represent other aspects of the biologicarchitecture. Random thermal motion of spins ina gradient field causes a phase shift of their trans-verse magnetization with respect to static spins,and can be used as a source of contrast usingproper pulse sequence. To better understandthis mechanism of image acquisition, a brief over-view of MR physics is presented in this article.

Magnetic Resonance Concepts

MR imaging works because, in the presence of anexternal magnetic field, one canmeasure the inter-action between protons in human body and theexternal magnetic field itself. Protons interactwith the external magnetic field, due to an intrinsicmagnetic characteristic called spin. The classicalview of spin is the effect of one charged parti-cleda proton, for exampledspinning arounditself, which creates a magnetic moment pointingperpendicularly toward a spinning axis (Fig. 1). Inthe presence of an external magnetic field, thisproton behaves similarly to a magnetic bar, tend-ing to align to the field and precesses around it.When we are dealing with individual protons, we

need to look at them through “quantummechanicalglasses,” and “not-so-intuitive” thoughts arepermitted under this treatment. A not-intuitivebehavior is that this proton can align in eithera parallel or an antiparallel orientation to theexternal magnetic field. There is a difference ofenergy between a parallel and an antiparallel state,and if this exact amount of energy ismatched by an

incident radiation and is delivered to the proton, itabsorbs this energy and changes from one stateto another. This phenomenon is called magneticresonance. The difference of energy statesdependson themagnitudeof theexternalmagneticfield B0 where this proton is inserted, and is ex-pressed in terms of the Larmor equation (1) as:

w0 5 yB0 (1)

In equation (1), w0 is the frequency needed fromthe incident electromagnetic field to match theenergy difference between states of nuclei, withthe gyromagnetic constant y in the presence of anexternal magnetic field of amplitude B0. The gyro-magneticconstant y is an important nucleuscharac-teristic. Human body abundance and propergyromagnetic constant make hydrogen nuclei (H1)the best choice for magnetic resonance imaging.But in MR imaging, we are not dealing with

a single spin and instead of a quantum mechanicsview, a classical treatment can be used to under-stand MR imaging physics. In a classicalmechanics view, spins in the presence of anexternal magnetic field B0 start to precess aroundB0, with an angular frequency w0 (Fig. 2). Theprecessional frequency is given by the same rela-tionship expressed in quantum mechanics treat-ment, the Larmor equation.The sum of many spins rotating around B0 forms

the magnetization vector M that points in the samedirection as B0. When RF wave in resonancefrequency w0 irradiates the bulk of spins, thequantum effect of states transition is analogousto flip the vector M by a certain angle in relationto B0. If RF in resonance frequency is applied bya certain time that flips the vector M 90�, this RFpulse is said to be a “90� RF pulse.” The samenomenclature applies to a “180� RF pulse.”Consider the following experiment: a bulk of

spins in the presence of external magnetic fieldB0. At this time, the equilibrium time, vector M,

Fig. 2. Precession of spin axis around B0. (Courtesy ofGE Healthcare, Sao Paulo, Brazil.)

Basic Concepts of MRI 3

possesses only the longitudinal component Mz. A90� RF pulse is applied. After turning RF off, vectorM has only the transversal component Mxy andunder the influence of B0 starts to precess aroundit. At this time, vector M induces current in thereceiver coil, according to Faraday’s law of induc-tion, and generates the MR signal (Fig. 3). When itpasses through the receiver coil a maximum signalis obtained, and when it is the farthest from the coila minimal signal is obtained. Plotting signal versustime, a sinusoidal function is to be expected.

But insteadof a simple sinusoidal function, a sinu-soidal functionwith amplitude decrease over time is

Fig. 3. In the transversal plane, rotating magnetiza-tion vector M induces current in receiver coil accord-ing to Faraday’s law of induction. (Courtesy of GEHealthcare, Sao Paulo, Brazil.)

obtained (Fig. 4). The signal represented in Fig. 4 iscalled FID (free induction decay), which decays dueto a process known as relaxation.

Relaxation Effects

Signal relaxation is a result of loss of phasebetween spins and energy release to the environ-ment where spins are inserted. Immediately aftera 90� RF pulse, all spins that form the Mxy vectorare pointing in the same direction, and they aresaid to be “in phase.” Turning RF off, they areset free to precess around B0, and they precesswith an angular frequency according to the Larmorequation. The first problem is that not all spins feelthe same static field, due to B0 inhomogeneities,and as they feel differently, they precess withdifferent frequencies. This difference causesa loss of phase between them and after sometime carrying out vector addition, it can be under-stood why the signal vanishes (Fig. 5). Thisprocess is called T2* decay or T2* relaxation,and effects of this nature can be restored once itis not a random effect but a scanner characteristic.

The same loss of phase described here canhappen even though scanner B0 homogeneity isperfect. Spins that form vector Mxy can interactwith each other, feeling the tiny magnetic field ofneighboring spins, in addition to B0, and eachspin starts to precesswith a different frequency, re-sulting in the same lossof phasecausedbyB0 inho-mogeneities. The central difference is that this lossof phase cannot be recovered once thermalmotionof spins is random. This process is called T2 relax-ation or T2 decay. T2* and T2 decay express expo-nential behavior (see Fig. 4) and are modeled interms of transversal components of vector M.

Another source of signal decay is spins giving upenergy, which are absorbed by an RF pulse to the

Fig. 4. MR signal amplitude (proportional to M vectormagnitude) as function of time. The exponentialdamped sine function is called FID and is character-ized by relaxation effect. (Courtesy of GE Healthcare,Sao Paulo, Brazil.)

Fig. 5. Signal loss due to dephasing between spins, caused by T2* and T2 relaxation. (Courtesy of GE Healthcare,Sao Paulo, Brazil.)

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environment. In terms of magnetization vectors,vector Mxy decreases and Mz increases overtime, until all energy has been released and thevector M has only a longitudinal component(Fig. 6), returning to equilibrium. The energyexchange is governed by the interaction betweenspins and the lattice, and it is called T1 decay orT1 relaxation.T1, T2, and T2* are tissue properties, and are

measured in seconds (T2* carries B0 inhomogene-ities information, caused by the tissue and thescanner). T1 is the time needed for Mz to achieveapproximately 63% of its initial value, after a 90�

RF pulse. T2 and T2* are the times taken for Mxy

to achieve approximately 37% of its initial value,after a 90� RF pulse, T2* being measured takinginto account inhomogeneity effects and T2 beingmeasured taking into account only spin-spin inter-actions. Image contrast contains all relaxationeffects, but usually they are weighted in one effect,meaning that differences in the gray scale mostlyrepresent differences in tissue relaxation

Fig. 6. The decay of transverse magnetization occursby means of T2 and T2* effects, while recovery oflongitudinal magnetization reflects energy transfer-ence to the environment. (Courtesy of GE Healthcare,Sao Paulo, Brazil.)

properties. Image weighting is controlled by pulsesequences.

Pulse Sequences

In the circumstance whereby the externalmagnetic field is not particularly uniform, dephas-ing between spins caused by field inhomogenei-ties are the main source of signal loss.Fortunately, this effect can be reversed by a well-known RF pulse sequence called the “spin echomethod.”The spin echo sequence is based on the appli-

cation of 2 RF pulses: a 90� RF pulse (or excitationpulse) followed by a 180� RF pulse (or refocusingpulse). The 90� RF pulse tips all spins that formthe vector M into a transversal plane and immedi-ately after they reach the plane, they are in phaseand Mxy has its maximum amplitude. After turningthe RF pulse off, spins start to precess and losephase by T2* relaxation effects. The 180� RF pulseis applied after a time t, defined as t5 TE/2 (t is setequal to 0 at the time the first 90� RF pulse isapplied), rotating the spins by 180� in relation tothe position they were in. At the end of refocusingthe pulse application, the spins localizationremains in the transversal plane, but “faster” spinswith higher precessional frequency are put behind“slower” spins with lower precessional frequency.The accumulated phase between spins caused byfield inhomogeneities through the time from t 5 0seconds to t5 TE/2 seconds is compensated aftera 180� RF pulse at the time t 5 TE seconds (calledecho time), TE/2 seconds after refocusing pulse.The whole picture is better understood inFigs. 7 and 8.The realignment of spins is called spin echo. It is

possible to apply many refocusing pulses aftera 90� RF pulse, collecting many spin echoes asshown in Fig. 8. B0 inhomogeneities are canceledin this method, because they are static in time, and

Fig. 7. Themechanismof spin echowith applicationof 180� RFpulse. (Courtesyof GEHealthcare, Sao Paulo, Brazil.)

Basic Concepts of MRI 5

the same B0 inhomogeneity that spins feel beforerefocusing pulse they also experience after it.But spin-spin interactions are not static in timeand T2 decay cannot be avoided. The longer thetime a spin echo is collected, the stronger a T2relaxation effect is presented.

Another important figure in pulse sequence isthe repetition time TR, the time between 2 excita-tion pulses. In the spin echo sequence, TR is thetime between 2 90� RF pulses applied in thesame location.

TR and TE are the main parameters in spin echosequence used to control contrast image weight-ing. Signal is acquired in echo time t5 TE, and ac-cording to parameters set in the sequence, thespin echo received in the receiver coil will expressdifferences among tissues, regarding protondensity (PD), and T2 or T1 relaxation.

Consider 2 different magnetization vectors, Ma

and Mb, possessing different PD, T1, and T2 prop-erties. At equilibrium state, M vector magnitudedepends on PD available in the tissue. A 90� RFpulse is applied in the system, andMa andMb relayinto the transversal plane. Dephase between spinsstarts at different rates, and a refocusing pulse isapplied at TE/2 to provide a spin echo at TE. If

Fig. 8. A spin echo experiment with acquisition of 2 echo

TE is short enough, T2 differences will not be rele-vant and the signal induced in the receiver coil willmostly represent PD properties. To fulfill this requi-site, TR must be kept long enough, to allow Mvectors to recover all their longitudinal magnetiza-tion and so that T1 differences will not influenceMxy vector after the next excitation pulse (Fig. 9).Therefore, PD-weighted images acquired witha spin echo sequence are obtained by using longTR and short TE.

If a T2-weighted image is desired, a long TR isneeded to avoid T1 influence through excitationpulse repetitions, but TE must be adequate toreflect T2 relaxation differences in signal ampli-tudes acquired (Fig. 10). The optimal TE to opti-mize contrast between Ma and Mb is the timewhen the difference between transverse magneti-zation of Ma and Mb is larger. Therefore, T2-weighted images acquired with a spin echosequence are obtained by using long TR andadequate TE.

To acquire T1-weighted images, a short TE isneeded for a signal echo not to reflect T2 differ-ences. After applying the first excitation pulse,Ma and Mb remain in a transversal plane and de-phasing between spins is caused by T2*

es. (Courtesy of GE Healthcare, Sao Paulo, Brazil.)

Fig. 9. Proton densityeweighted image acquired using long TR and short TE. (Courtesy of GE Healthcare, SaoPaulo, Brazil.)

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relaxation effects. The refocusing pulse is appliedat a short TE/2 time and the first echo acquiredrepresents PD differences. Then, T1 relaxationeffects become significant and Mz recovery startsto Ma and Mb. In order that all the followingechoes represent T1 differences, TR must beadequate and optimize T1 image contrastbetween Ma and Mb, and the next excitation pulsemust be applied at the time when longitudinalmagnetization Ma and Mb is larger (Fig. 11).Therefore, T1-weighted images acquired withspin echo sequences are obtained by usingadequate TR and short TE.Gradient echo (GRE) is another important pulse

sequence that, instead of using RF pulses torefocus spins, uses a gradient pulse, referring toa controlled linear change of magnetic fieldstrength during a short period. The gradient ischaracterized by its amplitude, representing howmuch field strength has changed in a certaindistance, and its polarity, representing the direc-tion of the change in field strength.

Fig. 10. T2-weighted imageacquiredusing longTRandade

In a GRE experiment, an excitation and 2gradient pulses are applied with different polaritiesand duration. The first gradient pulse is appliedafter the excitation pulse. While the first gradientis turned on the magnetic field amplitude changesregarding spatial location, and spins precess atdifferent frequencies according to the Larmorequation, causing a certain phase accumulationbetween them, and the signal diminishes. The firstgradient is then turned off and the second gradientis turned on, with the same amplitude and differentpolarity. Spins forced to precess slower thanthat feeling B0, in the presence of the first gradient,now are forced to precess faster in the presence ofthe second gradient and, after some time, theaccumulated phase between spins is compen-sated by inducing a signal echo generated bya gradient: a “gradient echo.”B0 inhomogeneities are not canceled in this

method, because a gradient echo is acquired bymanipulating the magnetic field, and the magneticfield felt by spins at the application of the first

quateTE. (Courtesyof GEHealthcare, SaoPaulo, Brazil.)

Fig. 11. T1-weighted image acquired using adequate TR and short TE. (Courtesy of GE Healthcare, Sao Paulo,Brazil.)

Fig. 12. During the application of a gradient, themagnetic field is modified linearly across the applica-tion direction. This change in magnetic field impliesa change in precessional frequency, according to theLarmor equation. (Courtesy of GE Healthcare, SaoPaulo, Brazil.)

Basic Concepts of MRI 7

gradient is not the same in the presence of thesecond gradient.

Frequency and Phase Encoding

Pulse sequences are not used just to obtaindifferent image contrasts but also to manipulatethe spins and form an image. This manipulationis performed by turning gradients on and off,inducing phase and frequency for the spins, andusing these properties as spatial information.GRE pulse sequence is used in the followingexplanation of image formation.

In a GRE pulse sequence, after the emission ofexcitation pulse, a gradient called “readoutgradient” is applied, firstly with a negative polarity(to sample high frequencies of symmetric signal)and afterwards with a positive polarity to placespins in phase and read the echo. When thisreadout gradient, also known as frequency encod-ing gradient, is applied, H1 spins precess atdifferent frequencies at the same time the axisgradient was applied (Fig. 12).

Although the signal induced in the receiver coilcontains all frequencies emitted by the tissues,there is a mathematical tool called Fourier trans-form (Fig. 13) that decomposes this signal inphases and frequencies. With the frequenciescontained in the signal and the previous knowl-edge of the readout gradient amplitude applied,it is possible to correlate signal frequency andspatial location toward an applied gradient.

Unfortunately, it is not possible to apply thesame strategy in the other axis, because it wouldchange the spins frequency twice and only thelast result would be obtained. To apply anothergradient in other direction simultaneously wouldnot be a solution, because magnetic fields would

Fig. 13. The Fourier transform indicates the frequen-cies contained in the signal.

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be vector summarized and just one frequencygradient would result. To solve this problem,phase information of spins is used. This informa-tion is added by applying a gradient called the“phase-encoding gradient” before the readoutgradient and perpendicular to it. The phase-encoding gradient is kept for a short period tomodify the magnetic field in the gradient direction,and during this short period spins precess atdifferent frequencies according to equation (1).When the phase-encoding gradient is turned off,spins precess at the same frequency again, butthey keep the phase memory acquired in the pres-ence of the gradient (Fig. 14). The accumulatedphase between spins depends on the gradientamplitude and duration.In the sampling time, each part of the subject to

be imaged will possess a bulk of spins withdifferent phase and frequency information, makingpossible the image formation. The pulse sequencecycle must be repeated until K-space is filled ina proper way to form the final image.

Fig. 14. Phase-encoding scheme representing 3 spins at diffBrazil.)

K-Space and Acquisition Time

After frequency and phase encoding, a continuoussignal emitted by the object to be studied isreceived by the receiver coil and sampled by theequipment, becoming a discrete signal. The signalsampled is converted in voltage and organized inthe K-space, which holds the raw data of theimage. As the signal is encoded in phase andfrequency, both are the coordinates of K-space(Fig. 15). The inverse Fourier transform of K-spacesignal magnitude is the usual magnetic resonanceimage, thus a good coverage of K-space isneeded to guarantee a reasonable image quality.Pulse sequence controls K-space coverage.

The phase-encoding gradient indicates the start-ing line in K-space to signal sampling, and thefrequency-encoding gradient indicates the sam-pling direction on this line. Refocusing pulses toecho acquisition inverts the sampling direction.The number of sampled points in K-space must

be higher or equal to the number of pixels thatcompose the final image, thus pulse sequencemust be repeated n times, varying the phase-encoding gradient amplitude to the entirecoverage of K-space, where n corresponds tothe matrix value in the phase direction; this is thefirst factor that hampers image acquisition time.The frequency encoding does not have a signifi-cant impact in acquisition time, because it takesthe readout gradient duration (on the order of milli-seconds). Nevertheless, the phase encoding toreceive one echo depends on the application ofone RF pulse, and TR must be taken into accountfor image contrast. Therefore, TR and phase-encoding steps are primarily the main aspectsthat affect image acquisition time, and usualmethods that optimize acquisition time are multi-slice acquisition (excitation of multiple slices inside

erent locations. (Courtesy of GE Healthcare, Sao Paulo,

Fig. 15. Image formation by phase and frequency encoding using Fourier transform. (A) Slice representation with3 vials of water. (B) Spin echo acquired from the entire slice with different phase encoding. (C) Fourier transfor-mation of the signal. (D) A new data set is assembled from the columns in (C). (E) Inverse Fourier transform of (D)produces the image. (Courtesy of GE Healthcare, Sao Paulo, Brazil.)

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a TR) and acquisition of multiple phase-encodingsteps inside a TR, using either RF pulses orreadout gradients, between phase-encodingsteps.

INTRODUCTION TO DIFFUSION MR IMAGINGPrinciples and Concepts

Diffusion refers to the transport of gas or liquidmolecules through thermal agitation randomly,that is, it is a function of temperature above 0 K.In pure water, collisions between molecules causea random movement without a preferred direction,called Brownian motion. This movement can bemodeled as a “random walk,” and its measure-ment reflects the effective displacement of themolecules allowed to move in a determinedperiod. The random walk is quantified by an Ein-stein equation: the variance of distance is propor-tional to 6Dt, where t is time and D is theproportionality constant called the diffusion coeffi-cient, expressed in SI units of m2/s.

According to Fick’s law, diffusion also occursfrom a region of higher concentration to a lowerconcentration.

In biologic tissue, there is a high probability thatwater molecules interact with structures such ascell membranes, macromolecules that reduce orimpede its motion (Fig. 16). Water exchange,between intracellular and extracellular compart-ments, as well as the shape of extracellular space

and tissue cellularity, affects diffusion. In this case,the term apparent diffusion coefficient (ADC)represents the measured diffusion constants andis commonly reported in cm2/s or mm2/s.

Isotropy and anisotropyIsotropy means uniformity in all directions. A dropof ink placed in the middle of a sphere filled withwater spreads over the entire volume, with nodirectional preference. If the same experiment isrepeated in a sphere filled with uniform gel therestriction is increased as compared with freewater, but is still isotropic, as the restriction isthe same in all directions.

Anisotropy implies that the property changeswith the direction. If a bundle of wheat straw withthe fibers parallel to each other is placed insidea glass of water, the ink will face severe restrictionin the direction perpendicular to the fibers andfacilitated along the fibers. This bundle is highlyanisotropic (Fig. 17).

Diffusion-Weighted Imaging

MR image contrast is based on intrinsic tissueproperties and the use of specific pulse sequencesand parameter adjustments. The image contrast isbased on a combination of tissue properties and isdenominated “weighted,” as the contribution ofdifferent tissue properties are present, but one ofthem is more expressive than the others.

Fig. 16. (A) Water molecules travel by “random walk” more freely than (B), as the freedom of this movement isreduced by barriers as cell membranes. The diffusion in (B) is restricted as compared with (A). Finally, ADC (B) isless than ADC (A). (Courtesy of GE Healthcare, Sao Paulo, Brazil.)

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Routine acquisitions have some degree of diffu-sion influence that is actually quite small. Somestrategies have been developed to make diffusionthe major contrast contributor, and dedicateddiffusion-weighted imaging (DWI) sequences areavailable nowadays on commercial scanners, aswell as several others as investigational sequencesthat may or not be available in clinical practice.

Diffusion sensitization schemeStejskal and Tanner7 introduced a method toimage and quantify DWI with MR imaging in1960, which was implemented in routine practiceby Le Bihan and colleagues8 in 1986. Thesequence was based on a spin echo sequencethat has symmetric diffusion sensitizing gradientsinserted before and after the 180� refocusing pulse(Fig. 18). The idea is as follows.

Fig. 17. The bundle offers no resistance to watermolecules in the diffusion direction parallel to thefibers but there is a severe restriction if perpendicular.In this case there is preferred water molecule directiondue to anisotropy. Outside the bundle, the watermolecules are in an isotropic environment and haveno preferred direction. (Courtesy of GE Healthcare,Sao Paulo, Brazil.)

Static water spins will experience a precise de-phase induced by the first diffusion sensitizinggradient lobe. The 180� pulse will cause a phasecompensation for the external field inhomogenei-ties. The second lobe will rephase the water spinsat the same amount they were dephased, asthe area is exactly the same and spins were inthe same position. Therefore, the signal of thestationary water spins echo is maintained as prac-tically unaltered.However,movingwater spinswill be in adifferent

position, so they will not be rephased at the sameamount by the second lobe, and the echo willhave a reduced signal. The degree of water motionis proportional to the signal attenuation.The diffusion-sensitizing gradients can be

applied to x, y, or z axes, as well as in a combina-tion of them. This direction is called the diffusion-sensitizing direction.The Stejskal-Tanner scheme can be applied on

top of pulse sequences as spin echo, but the mostused nowadays is in combination with spin-echo

Fig. 18. Stejskal-Tanner Scheme:2diffusion-sensitizinggradients inserted before and after 180� RF refocusingpulse using precisely controlled duration and distance.G, amplitude; d, durationof the sensitizinggradient;D,time between the 2 sensitizing gradient lobes.

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echo-planar imaging (SE-EPI). A combination withfast spin echo sequence takes longer, but is lesssensitive to distortions and susceptibility artifactsthan EPI.

Other strategies are also available but are lessused in routine practice, as many others are inthe research environment and become commer-cialized eventually.

Diffusion-weighting factorThe sensitivity of the diffusion sequence to watermotion can be varied by changing the gradientamplitude, the duration of the sensitizing gradi-ents, and the time between the gradient pair.

The diffusion-weighting factor is named b-valueand for the Stejskal and Tanner8 sequence thevalue is given in units of s/mm2 by (2):

b5g2:G2:d2ðD� d=3Þ (2)

where g is the gyromagnetic ratio, G is the strengthof the diffusion-sensitizing gradients; d is the dura-tion of the gradient pulse, and D is the time intervalbetween these gradients. A higher b-value isachieved by increasing the gradient amplitude andduration and by widening the interval between thegradient lobes. In most applications, the gradientamplitude is maximized and the gradient durationand interval changed to control the b-value.

The T2 shine-through phenomenaThe signal intensity observed in a diffusion-weighted image can be expressed as:

SðTE ;bÞ 5PD�e�TE=T2

��e�bD

�(3)

where S is signal intensity, k is a constant; PD isproton density, TE echo time, D diffusion coeffi-cient, and b the b-value.

As TR (repetition time) is usually long(5000e15,000 ms) and, in case of single shotscans, TR is virtually infinite, T1 contamination isminimal or null. TE is usually kept as low aspossible, usually 60 to 100 ms; therefore, theDWI may suffer from T2 contamination if long T2components are present. This phenomenon iscalled the “T2 shine-through artifact” and maycause misinterpretation as the signal may be artifi-cially hyperintense or isointense. Parametric ADCmaps are used to quantify diffusion, and are insen-sitive to T2 shine-through artifacts.

Intravoxel incoherent motionIntravoxel incoherent motion (IVIM) is the randommovement of the water inside a voxel, and causesthe signal to decay. One example is blood insidetortuous capillary vessels, where the measureddiffusion coefficient will be overestimated and fallinto the ADC denomination, instead of D. In 1988

Le Bihan and colleagues9 proposed the nameIVIM, instead of diffusion imaging, and D* as thepseudo-diffusion coefficient dependent on capil-lary geometry and blood velocity, estimated tobe 10 times larger than the diffusion coefficientof water. For high b-values, the perfusion effectsare significantly reduced and diffusion informationremains. For low b-values, the combined effect ofperfusion and diffusion is present. As IVIMmeasurement involves the acquisition of severalsmall b-values,10 eddy currents must be wellcompensated, and motion and single-shot EPIdiffusion must be used with high-performancegradients.

Echo-Planar Diffusion-Weighted Sequence

Echo-planar is an ultrafast acquisition, in which allK-space is sampled extremely fast. Althoughproposed by Peter Mansfield in 1978,11 it was im-plemented in routine practice in the 1990s, whenhigh-performance gradients and enhancedanalog-to-digital converters, image reconstruc-tors, and support electronics became available. Itis fast, robust, and widely available on most scan-ners today, but it is also sensitive to susceptibilityeffects that cause artifact and image distortions.The distortion degree depends on several imagingparameters, as well as magnetic susceptibility andfield strength.

EPI principlesThe EPI strategy to reduce acquisition time is tocollect several echoes, with phase and frequencyencoding, after the RF excitation pulse, the sameway as fast spin echo, but instead of producingan echo train using RF 180� refocusing pulses,EPI uses a series of oscillation gradient reversalsthat have both positive and negative polarities, togenerate “odd” and “even” echoes that takesignificantly less time to be generated (Fig. 19).

EPI can be implemented using different modessuch as SE-EPI (spin-echo EPI) or GRE-EPI(gradient-echo EPI), depending on the use of anRF echo or a gradient echo before the EPI echotrain. It can collect all echoes needed to acquirean image by using one excitation pulse (single-shot EPI), or splitting into separate shots. SE-EPIis used in conjunction with diffusion-sensitizinggradients, called EPI-DWI, and the single-shotapproach is mostly used.

EPI sequences are sensitive to the so-called off-resonance effects of water and fat spins: fat spinsaccumulate a huge phase shift, proportional totime, in collecting all echoes in a given TR and thefrequency distance between water and fat. Theeffect occurs in the phase direction, and the imageof fat can be typically displaced by pixels and is

Fig. 19. After a 90� excitation pulse and 180� refocusing pulse is applied, positive-negative gradient oscillationsgenerate frequency-encoded echoes, and the phase encoding is provided by the “blipped” phase encoding gradi-ents. In this case there is an echo train length of 7. (Courtesy of GE Healthcare, Sao Paulo, Brazil.)

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increased at higher field strengths. Therefore all EPIsequences, in practice, are fat-suppressed, anddifferent methods can be employed such asspatial-spectral fat suppression, frequency-selective fat suppression, or even short-tau inver-sion recovery (STIR) in combination with EPI-SE.The sampling period is typically the “flat-top”

part of the readout gradient (Fig. 20A). Water spinsalso accumulate phase shifts in areas near tissue-air or tissue-bone interfaces, which cause disrup-tions in the local field, and the results are mild tosevere distortions depending on the field strength,gradient performance, and sequence parameters(compare Fig. 20B with C). The longer thesampling time to collect the echo, the more timewater spins accumulate phase shift and the worseis the distortion. The echo spacing is the time fromthe middle of the echo top to the middle of thenext, and is directly related to the degree ofthe distortions. The shorter the echo spacing, the

Fig. 20. (A) Detail of the oscillating readout gradient echdistortion. (B) Single-shot EPI with 256 frequency matrix,direction on a low-performance gradient of 10 mT/m wfrequency matrix, with a gradient of 33 mT/m with 120 TBrazil.)

less the distortions; this concept is important tooptimize sequence parameters and achieve thebest results.High-performance gradients using appropriate

acquisition parameters improve EPI image qualitysignificantly (see Fig. 20C).

EPI-DWI practical aspectsA common implementation of EPI-DWI acquires 3separate orthogonal acquisitions with diffusionsensitization in each main gradient direction (X,Y, Z), which are automatically averaged into a finalcombined image (Fig. 21). Usually, 2 b-values areacquired, the first of which is generally b5 0 and iscalled “T2 image,” as no diffusion contribution ispresent and it is the same as a T2-weighted EPIimage. Different implementations allow the acqui-sition from a single to several b-values in the samescan, at the expense of acquisition time. Respira-tory and cardiac compensation can be used to

o spacing. Reduction of echo spacing greatly reducesresulting in severe distortion in the phase-encodingith 17 T/m/s slew rate. (C) Single-shot EPI with 256/m/s slew rate. (Courtesy of GE Healthcare, Sao Paulo,

Fig. 21. The diffusion sensitization gradients were applied in directions SI (B), RL (C), and AP (D). Image (A) is theaverage of (B), (C), (D), and is usually denominated combined or “isotropic” image. The white arrow points tosplenium of corpus callosum that has restricted diffusion in the SI direction, is facilitated in the RL direction,and has mixed pattern in the AP direction. Combined image (A) minimizes the anisotropy effects of the individualimages.

Basic Concepts of MRI 13

minimize motion artifacts, as well as parallelimaging and optimized application of diffusiongradient schemes to improve signal-to-noise ratioand reduce artifacts.

Themain sequence parameters are summarizedas follows.

Choice of sensitizing directions and combined

image The number of sensitizing directions andorientation used depends on the kind of informa-tion needed and the isotropic/anisotropic behaviorof the structure being studied.

If the goal is to identify areas of altered diffusionin a structure that is normally isotropic, andconsidering the altered area is also isotropic, onedirection would be enough. In this case, the totalacquisition time is reduced to a single acquisitionper b-value.

A more complex scenario is presented if theobject of study and/or the expected altered areaof interest are anisotropic. It is important toremember that the diffusion sensitization gradientwill affect spins moving along its direction only.Organs such as the brain, kidneys, and muscleshave important anisotropy, as others havea more isotropic behavior. This scenario isexemplified in Fig. 21: the splenium of the corpuscallosum shows restricted diffusion in the SI (supe-rior-inferior) direction (see Fig. 21B) and is facili-tated in the RL (right-left) direction (see Fig. 21C),because of the orientation of the fibers thatinduces strong directional diffusion dependence.Notice the low-bright pattern in the AP (anterior-posterior) as the inverted “V” disposition of thefibers. In this instance, acquiring diffusion imaging,sensitized in the 3 directions, and averaging them

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into one combined image is the most usedstrategy (see Fig. 21A).

b-Value The b-value provides diffusion weightingfor DWI images as TE provides T2 weighting forT2 images.The higher the b-value, the more diffusion-

weighted the image will be at the cost of signal-to-noise ratio (SNR). As b-value is increased,a structure of lower ADC loses signal faster thanstructures of higher ADC, and the contrast isincreased. If the lower ADC regions have the signaldecreased from a certain threshold, the combinedimage may exhibit increased signal from restrictedwater motion, due to anisotropy. An example isgiven in Fig. 22.If the b-value is high enough, only structures with

very low ADC will show up and higher ADC struc-tures will fade into the noise floor; this approachcan be used as “background suppression” andincrease sensitivity. As the minimum TE isincreased with the b-value, relatively short T2tissues such as liver and muscle may be sup-pressedbecause of T2 effects rather thandiffusion,and this should be taken in account regardingchoice of diffusion sequence parameters.Low b-values have intrinsically high SNR;

however, IVIM effects become important andshould be taken into consideration. An interestingproperty is that flow is suppressed, and “black-blood “imaging can be performed (Fig. 23).

Receiver bandwidth Receiver bandwidth (rBW)controls the number of frequencies that aredetected. The higher the rBW, the shorter the

Fig. 22. From right to left the sensitization directions areTE 5 88 ms; Row (B) b 5 2500 s/mm2, TE 5 104 ms.

“flat-top” or readout time, and the fewer the distor-tions present (Fig. 24). Therefore, higher rBW ispreferable for EPI-DWI studies.

Frequency direction Echo-planar acquisitions aresensitive to water off-resonance spins in the areasof soft tissue/air/bone interface. With a properchoice of frequency direction, the distortion ismore symmetric (Fig. 25). Axial plane is the mostcommonly used acquisition plane with EPI andfrequency RL direction.

Fat suppression Due to the large chemical shift, allEPI-DWI acquisitions should be fat-suppressed orfat-saturated. The choice of the method to be em-ployed depends more on the region to be studied.Spectral spatial excitation excites only the waterspins on a slice-by-slice basis, instead of thewhole volume. Chemical shift selective appliesa spectral saturation pulse over the fat spins, butit may be less effective than spectral spatial exci-tation once the fat saturation pulse is appliedover the entire volume. STIR is a good option fora large field of view (FOV), off-center acquisitions,or areas where the other techniques may fail, suchas brachial plexus.12

Number of measurements The data are acquiredseveral times and averaged into one image, thenused to build more SNR, allowing the acquisitionof thinner slices and longer b-values at theexpense of acquisition time. If motion is presentas free-breathing scans in abdomen and chest,some degree of blurring is expected, as the struc-tures are not in the same position in each acquisi-tion and are averaged out. Small structures and

: combined, SI, RL, and AP. Row (A) b 5 1000 s/mm2,

Fig. 23. Diffusion is inherently a black-blood image. Image (A) b 5 0 s/mm2, usually named “T2 image,” andImage (B), usually named “diffusion image,” have b 5 90 s/mm2.

Fig. 24. (A) High rBW 5 �250 kHz, (B) Low rBW 5 �62 kHz; both at 3 T field strength. Distortion is reduced usinghigh bandwidth. The unit of the receiver bandwidth can change between vendors, as peak to peak or Hz/pixel,and lead to mistakes if protocol parameters are copied without proper adjustment.

Fig. 25. Frequency direction (A) RL and (B) AP. (A) is more symmetric. Both images were acquired at 3 T fieldstrength.

Basic Concepts of MRI 15

de Figueiredo et al16

motion-ghosting artifacts may not show up in thefinal image as well, due to averaging.The use of one single acquisition may require

adjustment of other parameters, as increased slicethickness or lower acquisition matrix to compen-sate for the reduced SNR.

Repetition time The number of slices availableand acquisition time are proportional to the TR. ATR of 3000 ms is enough to minimize T1 effectsand can be as long as needed to accommodateall slices required in one acquisition, typically5000 ms. Reduced TR acquisition with reducednumber of slices can be used to shorten breath-hold time in expiration, but multiple acquisitionsare necessary to cover the entire volume, andeach group of slices may not be perfectly aligned.

Echo time The TE should be as short as possibleand should increase with the b-value. Reducedfrequency matrix and the use of parallel imagingdecrease the echo spacing, and therefore theminimum TE.In cases where multiple b-value acquisitions and

ADC quantification are needed, it is suggested touse the TE corresponding to the highest usedb-value and keep it constant in all other acquisi-tions of b-values.

Respiratory/cardiac trigger Respiratory triggersynchronizes the acquisition with the respiratorymovement, by acquiring data in the expirationphase, reducing movement artifacts, and allowingthe use of more measurements with less or noblurring, besides improving lesion detection ascompared with breath-hold.13 It is mostly usedfor imaging the chest and upper abdomen. Totalacquisition time is increased, as only part of therespiration/cardiac cycle is used. The effectiveTR depends on the respiratory frequency andcan be increased using more respiration cycles,to accommodate the number of slices. Cardiacmotion is a known source of artifacts (Fig. 26)

Fig. 26. Respiratory-triggered DWI, but not cardiac trigg(A) b 5 150 s/mm2 and TE 5 54 ms; (B) b 5 600 s/mm2

and can be minimized with cardiac triggering andappropriate trigger delay,14 but again at theexpense of time.

Parallel imaging Parallel imaging plays an impor-tant role in EPI-DWI, as the distortion and short T2blurring are reduced at the expense of SNR. Thisfeat is accomplished by omitting lines of the K-space and increasing the distance between them,just like reduced-phase FOV, but eliminating wrap-around artifacts that use special algorithms andneed some K-space reference lines. As such thiscould be either a separate mask acquisition ora built one, and rely on different coil element sensi-tivity. Because susceptibility effects are enhancedat higher field strengths, parallel imaging isroutinely used at 3 T, in combination with EPIsequences, and could be considered optional,but is recommended at 1.5 T. Other benefits ofparallel imaging are increased number of slicesfor the same TR and reduction of acquisition time.

ADC measurement and ADC mapsThe diffusion images have a T2 weighting contam-ination, and long T2 regions may present anartificial signal enhancement, such as the T2shine-through artifact. This sign can be removedusing exponential images (Fig. 27C) that aresimply the diffusion image (see Fig. 27B) dividedby b 5 0 image (see Fig. 27A), or by using para-metric images where the contrast reflects thecalculated ADC (see Fig. 27D). Gray scale is nor-mally used on ADC parametric images: dark repre-senting low ADC values and bright representinghigh ADC values. Color scale can be used withlow ADC in red and high ADC in blue asa mnemonic for free water, using different colorsbetween the 2 extreme thresholds. However, thereis no standard for the use of color scale, and it maybe confusing if not properly explained.In general, ADC (or D depending on the defini-

tion) is calculated using b 5 0 and another b that

ered. White arrows indicate cardiac motion artifact.and TE 5 68 ms.

Fig. 27. Example of T2 shine-through effect and correction using exponential and parametric ADC maps: Whitearrow indicates bright signal on T2 image (A), isointense signal on diffusion image (B). The exponential map (C)has the T2 shine-through artifact removed and the expected low signal of facilitated diffusion is present. Theparametric ADC map (D) demonstrates high ADC value as a bright region and enables quantification of ADC.

Basic Concepts of MRI 17

can vary, depending on the organ studied, usuallybetween 600 s/mm2 and 1000 s/mm2.

Keeping the TR and TE the same and changingonly the b-value, ADC can be calculated using theequation (4):

ADC5 lnðS1=S0Þ=ðb1 � b0Þ (4)

where S0 is the signal intensity with the b-value5 0and S1, the signal intensity with b-value 5 b. Amonoexponential behavior is assumed.

In the context of research or clinical trial, a moreprecise estimation can be made using multipleb-values, and in this case, a more complex anal-ysis is necessary because of the microcirculationinfluence.9,10,15

A plot of a multi b-value acquisition in a liver isexemplified in Fig. 28: respiratory trigger andb-values of 0 to 1000 s/mm2. Notice the fast decayin the first part of thecurve (b-values0e100s/mm2),due to increased effects of microcirculation and

Fig. 28. Signal intensity versus b-value plot froma multieb-value study on a liver. The signal decaysfaster between b 5 0 and 100 s/mm2.

a slower decay in the second part (b-values200e1000 s/mm2), due to increased effects ofdiffusion.

The low range of b-values from 10 to 200 s/mm2

maybeused to study fast diffusion and is character-ized by perfusion parameters D* (or ADCfast) and f(fraction of volume of water flowing in capillaries).High b-values between 200 and 1000 s/mm2, orhigher, are used to study slow diffusion parametersD (or ADCslow). The term global diffusion is usedwhenb5 0 andb>200 s/mm2, and is characterizedas ADCglobal.

The quantification of ADC in moving organs or inthe path of its influence is challenging, and the useof free breathing, respiratory triggering, or breath-hold may lead to different results and are underinvestigation.16,17

In summary, diffusion is used as a source ofcontrast for many different applications in thebody, and gives insights on the pathologies byvisual inspection. Also, there is a growing numberof investigations using quantification; the totalprocess is not completely understood, and a stan-dardization of the acquisition and quantification isyet to be established.

Another aspect of diffusion, the anisotropy, isthe study object of diffusion tensor imaging (DTI),which is now discussed.

DIFFUSION TENSOR IMAGING

DTI18 is based on diffusion-weighted images thatinvestigate the fiber architecture of several regionsin the human body as for example of the brainwhite matter or muscle fibers of the heart. Incontrast to DWI, a diffusion tensor D (a 3 � 3matrix) is calculated for each voxel, instead ofonly one numerical value (such as the ADC), andit enables the possibility to investigate anisotropic

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diffusion. Anisotropic diffusion means that thewater molecules are moving in a specific directionat a specific rate, whereas isotropic diffusionmeans that the molecules move at equal rates inall directions. This tensor is able to fully describethe molecular mobility along each direction andthe correlation between these directions.18 Toachieve this directional information, additionaldiffusion-weighted images along several gradientdirections, using diffusion-sensitized MR imagingpulse sequences, have to be collected. After thepostprocessing of the raw diffusion-weightedimages, the fractional anisotropy (FA) maps,mean diffusivity (MD), eigenvectors, radial diffu-sivity, and so forth are calculated, derived fromthe diffusion tensor.

Physical Basics and Definitions

DWI and DTI use the mathematical model of freediffusion, which is described in physics by the“first Fick’s law of diffusion.” It can be written as:

J 5 � DVc (5)

where J is the flux density, Vc the concentrationgradient, and D the diffusion coefficient.When diffusion occurs in the imaged volume,

there will be attenuation, A, on the MR signal,which depends on D and on the “b-factor,” whichcharacterizes the gradient pulses used in the MRimaging sequence:

A5 expð�bDÞ (6)

In anisotropic media, the diffusion coefficientdepends on the direction of diffusion. LeavingDWI and going to DTI, the diffusion coefficient Dhas to be substituted through a diffusion tensorD (a 3 � 3 matrix).

D 5

0@Dxx Dxy Dxz

Dyx Dyy Dyz

Dzx Dzy Dzz

1A (7)

To determine the diffusion tensor one must, asmentioned before, acquire diffusion-weightedimages in several gradient directions. In a nextstep, it is necessary to estimate the entries of thematrix D from the set of diffusion-weightedimages. As the tensor is symmetric, only 6 differentgradient directions are necessary togetherwith one acquisition with no diffusion weighting(b 5 0) resulting in a total of 7 acquisition. Usingmore diffusion directions, it is not necessary, butof advantage, to cover the space more uniformlyalong many directions, especially for fiber orienta-tion mapping.

Eigenvectors and eigenvalues, mean diffusivity,fractional anisotropy, radial diffusivity, andaxial diffusivityThe entries of the tensor reflect average diffusionand degree of anisotropy in each voxel. It is impor-tant todetermine themaindirectionsof diffusivities,called eigenvectors, in each voxel, and thediffusionvalues, called eigenvalues, associated with thesedirections. The eigenvalues represent the diffusioncoefficients in the main directions of diffusivities ofthe medium (Fig. 29). Most common parameters,such as MD, FA, radial diffusivity, and axial diffu-sivity can be derived from them.The MD gives an overall measure of the diffusion

in a voxel or region. It can be calculated from thetrace of the diffusion tensor:

MD 5Tr�D��

35�Dxx1Dyy1Dzz

��3 (8)

In the literature, the eigenvalues Dxx,Dyy, andDzz

are often called l1, l2, and l3.The FA is a measure of the degree of the diffu-

sion anisotropy. The FA values range from 1(anisotropic diffusion 5 “directed”) to 0 (isotropicdiffusion 5 “not directed”).It can be calculated from:

FA5

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi�Dxx � Dyy

�21�Dyy � Dzz

�21ðDzz � Dxx Þ2

qffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi2�D2

xx1D2yy1D2

zz

�r

(9)

The diffusivity along the main axis, Dxx , is alsocalled axial diffusivity (or parallel diffusivity).The average diffusivity ðDyy1DzzÞ=2 of the 2

minor axes is called radial diffusivity.

Visualization of the Tensor Model: theEllipsoid Model

As the tensor data cannot be simply displayed inone image through gray-scale information or colorcoding, the diffusion ellipsoid approach has beenpresented.19 The ellipsoid is a tridimensionalrepresentation of the diffusion distance in space,which the water molecules can reach. In the ellip-soid the x, y, and z axes represent the main diffu-sion direction in the voxel, corresponding to thedirection of the fibers. The eccentricity of the ellip-soid provides information about the degree ofanisotropy. This way, an anisotropic diffusion inany direction would be represented as a poleand an isotropic diffusion as a sphere (see Fig. 29).

Besides those representations, it is common tovisualize FA and MD values in a gray scale or ona direction-coded color map (Fig. 30). Their valuescan be directly measured on these maps with

Fig. 29. (Left) The ellipsoid model overlaid on a conventional T1 image. (Right) The ellipsoid becomes a sphere inareas where no main diffusion directions exist: isotropic diffusion; and the ellipsoid becomes a pole with onemain direction where the diffusion is anisotropic.

Basic Concepts of MRI 19

region of interest (ROI) tools provided by the soft-ware manufacturers.

Interpretation

In the brain, the mobility of the water moleculescan be limited through obstacles, for example,the cellular membrane. Especially in the nervefibers, the molecules can only move freely alongthe length of the axons and can only move shortdistances perpendicularly across the length.When interpreting diffusion tensor data, the basic

Fig. 30. (Left) Gray scale FA map, where the intensity valuemean intensity value of the ROI of 831 corresponds to an Ftion is color-coded.

idea is that the direction of the highest diffusioncoefficient represents the course of the nerve fiber.

Tractography

The reconstruction of nerve fiber tracts of DTI datais called tractography. This technique is based onconnecting voxels in order to build a whole fiber toinvestigate the fiber architecture in the brain. Thereare 2 major approaches in tractography: determin-istic and probabilistic tractography. With deter-ministic tractography, the reconstructed fibers

divided by 1000 corresponds to the FA value. Example:A of 0.831 in this ROI. (Right) FA map where the direc-

de Figueiredo et al20

result from the most likely directions in each voxel,whereas probabilistic fiber-tracking methods useprobability distributions to draw several sets ofdifferent directions, this way repeating the stream-lining process multiple times.

High Angular Resolution Diffusion Imaging

The diffusion-tensor model describes the behaviorof diffusion in a voxel correctly only when the diffu-sion has one main direction. When nerve fiberscross with others or have ramifications, this modelis limited. As a result, over the past few yearsapproaches have been developed that aim touse more gradient directions, in order to gaina better insight into the complex behavior of diffu-sion. These techniques are called high angularresolution diffusion imaging or HARDI.

Number of diffusion directionsAs mentioned before, at least 6 diffusion directionsare necessary to determine the elements of thediffusion tensor. But what is the impact of usingmore directions and the relevance for clinicalapplication? For a robust estimation (using a b-value of 1000 s/mm2) of the FA, which was shownusing a Monte Carlo technique, a minimum of 20unique sampling directions should be used and30 directions, at least, in the case of MD.20

Fig. 31. After choosing a seed point the streaming ofthe fibers can be realized.

Postprocessing and Evaluation of Diffusion-Weighted Images and Diffusion TensorImaging

Evaluation with manufacturers’ softwareMostMRmanufacturers offer their own software toreconstruct the parametric maps for the diffusionparameters, such as ADC (in the case of DWI) andFA, MD, eigenvalues, and trace (in the case ofDTI), that are most relevant for the radiologist.The reconstruction is normally performed in anin-line process, whereby the generations of thosemaps are performed automatically, immediatelyafter running the sequence. In this way a rapid eval-uation by the radiologist is possible.Within the manufacturers’ software, in general

ROI-based analysis tools are available, enablingthe radiologist to draw the ROI directly, such asfor example the FA map, providing ROI parame-ters as the mean value, standard deviation, area,and minimum and maximum value. To obtaina “real” value for the diffusion parameters, some-times a scaling factor has to be applied.Region-of-interest based analysis is a common

way to analyze, for example, differences in injuredtissue with normal tissue (see Fig. 30).

Deterministic tractography (streamlinetractography)To reconstruct the trajectories of fibers, first atleast one stream particle (seed point) has to bechosen (Fig. 31). Then the voxels are connectedusing pre-chosen calculation criteria for the tract,for example, angular threshold that determinesthe maximum orientation that a fiber can achieveand FA threshold that determines when the FAvalue falls below this threshold. Calculation forthis tract can then be realized.

Advanced evaluation by third-party softwareInstead of or in addition to the use of the softwareoffered by the manufactures, or in addition to it, itis possible to realize advanced evaluation of thediffusion data with third-party software, aftertransferring the image volume to anotherworkstation.Especially for the brain, these software

programs often offer additional tools that can beuseful for analysis, as the image quality potentiallycan be improved. For instance, it is possible toapply eddy current correction algorithms in theEPI images, which take care of distortion artifacts.Also, distortions of the diffusion-weighted imagescaused by motion can be corrected. Especiallyfor tractography, when one is interested in quanti-fying brain connectivity it may be interesting to usesuch software programs, because they canperform probabilistic tractography instead ofmore qualitative deterministic tractographyoffered by most MR manufacturers.Another interesting option for institutions that

are interested in clinical research is the possibilitythat comes with third-party software, namely theability to carry out intersubject group analysis.The software includes tools for brain registration

Fig. 32. Tract-based spatial statistical analysis (TBSS; FSL, Oxford, UK). In green: the main tracts (skeleton) wherestatistical analysis was performed. Overlaid in yellow-red: significant areas of reduction of FA, P<.05.

Basic Concepts of MRI 21

to a pre-chosen target, which may be a mean FAimage of the subjects under analysis,21 to performvoxel-based analysis of the whole brain, usingbrain atlases as a reference (Fig. 32).

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