Diffusion MRI. From Quantitative Measurement to In vivo Neuroanatomy

599 Pages·2014·103.319 MB·English

by  Heidi Johansen-Berg and Timothy E.J. Behrens (Eds.)

DIFFUSION MRI
From Quantitative Measurement
to Neuroanatomy
In-vivo
SECOND EDITION
Edited by
H J -B
EIDI OHANSEN ERG
AND
T E.J. B
IMOTHY EHRENS
CentreforFunctionalMagneticResonanceImagingoftheBrain(FMRIB)
NuffieldDepartmentofClinicalNeurosciences,UniversityofOxford,JohnRadcliffeHospital,Oxford,UK
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Foreword
If you want to know how an MP3 player works, the chart pathways that relate to abilities that are unique
first thing you need to establish is how it is wired up. to humans, such as language. Third, we can establish
Itisthesamewiththebrain.Yet,asCrickandJonescom- thebordersbetweenneighboringcytoarchitectonicareas
mented in Naturein 1993 (Crick and Jones, 1993) it was in the human brain, using the principle that each area
lamentable how little we knew at that time about the has a unique pattern of inputs and outputs. Finally, we
connections of the human brain. All we could do was canmakeuseoftheinvivonatureofthemeasurements
infer the connections indirectly from tracer studies in to examine how particular white matter connections
non-human primates. Yet it was only a year later that contributetoindividualvariabilityinbehavior,aresub-
Basseretal.(1994)(seeChapter1)showedthatonecould ject to experience-dependent plasticity,and areaffected
useMRItomeasurethediffusionofwateralongaxons, in different disease states.
andin this way to visualize themajorfiber tracts. Afterintroducing thekeymethodsunderlyingdiffu-
Anatomistswereskepticalthatmuchwouldcomeof sion imaging (Chapters 1 through 6), Section II of this
thenewmethods.Thereasonisthattheirconcerniswith bookfocusesonthislastpoint:Howcanwemakequan-
the fine details of the connections, rather than with the titativemeasurementsofwhitematterconnectionsinthe
lie of the tracts. These fine details can be demonstrated living brain, and use these measurements as a probe in
by using the transport of tracers, and the method has health and disease. In answering this question it is
been extensively used for the non-human primate clearly important to know how the diffusion signal
brain (see Chapter 17). We currently have data for 7009 relates to the underlying biophysical properties of the
sites in the macaque brain, with 36994 connections axonethe real quantities of interest in white matter.
detailed (http://cocomac.g-node.org). But, unfortu- Chapters 7 through 9 explore this issue in detail and
nately,thoughonecanuseMRItovisualizethetransport examine what biological inferences we can already
of tracers (Saleem et al., 2002), it is not ethical to inject makefromourdiffusiondata,andwhatnewinferences
tracers into the living brain. And so far, little progress wemaybeabletomakeinthenearfuture.Chapters10
has been made in using tracers in post-mortem brains. through15thenofferanessentialguidetoanyscientist
With current methods, dyes only diffuse at the rate of using these techniques to ask questions about white
about 5mmin 2 weeks (Kobbert etal., 2000). matter changes in health and disease. They start with
So to what extent can diffusion MRI provide similar a detailed and thorough guide to experimental design
informationforthehumanbrain?Fortunately,methods anddataanalysistechniques(Chapter10),andthenpro-
fortractographyaresteadilyincreasinginsophistication ceed with chapters giving key examples and highlight-
andalthoughchallengesremainitisnowpossibletoes- ing important results from diffusion imaging in
timate the probabilities of connections and to trace neurological and psychiatric disorders, in development
through regions of fiber complexity with some success and aging, and inbehavioral neuroscience.
(Chapter19).Confidenceintheexactsiteoftermination Thefirsttwosectionsofthisbookarethereforeessen-
will increase as the spatial resolution of MRI increases tial reading for scientists using diffusion imaging in
and it is possible to measure anisotropy within the their quantitative investigations, for those developing
gray matter. There are already hopeful signs. By use of new methodologies for diffusion imaging, and for any
a specialized coil array it has been possible to visualize clinicians and systems neuroscientists with an interest
thalamocortical fibers as they penetrate perpendicular in white matter.
to the pial surfaceand terminate in layer IVof occipital But there is an overarching reason why we need to
cortex(Jaermannetal.,2008).Andithasevenbeenpos- know about the underlying architecture of connections
sible to measurelaminar profilesof activityusing fMRI inthehumanbrain.Theaimofneuroscienceistounder-
(Ress et al., 2007). standhowthebrainworksasawhole,andtheoutstand-
Giventhesetools,whatcanweusethemfor?First,we ingadvantageofimagingmethods(fMRI,EEG,MEG)is
can check whether our inferences about connections that they are whole-brain methods. Of course, we need
from non-human primates are correct. Second, we can to understand how each area performs its specific
ix
x
FOREWORD
function,andforthiswewillneedtoresorttorecording Bartsch et al. (Chapter 23). In the next chapter,
the electrical activity of cells, whether singly or in sub- Rushworth et al. compare the frontal and parietal lobe
populations.Buttasksarenotperformedbysingleareas connections in the macaque and human brain (Chapter
butbysystems.Andthismeansthatwehavetounder- 24). The last chapter (Chapter 25) is called “Imaging
stand the interactions between areas within those sys- structure and function.” That surely is the aim of all of
tems. In imaging, measures of effective connectivity, those who use imaging to understand the workings of
whether structural equation modeling or dynamic the human brain.
causalmodeling(Pennyetal.,2004),requirethespecifi-
cationofaprioranatomicalmodelforthatsystem.This Richard Passingham
modelneednotincludeeverysynapticstageinacircuit, ProfessorofCognitive Neuroscience,Department of
but we do needto beconfidentthat it holds for thehu- Experimental Psychology,University ofOxford,UK
man brain. Diffusion MRI promises to provide that
model. This means that everyone who uses functional
brain imaging needs to consult this book. In it they
References
willfind everything they need.
The last section providesan extensive account of the
Basser,P.J.,Mattiello,J.,LeBihan,D.,1994.Estimationoftheeffective
uses of diffusion MRI for neuroanatomy, and it is this
self-diffusiontensorfromtheNMRspinecho.J.Magn.Reson.B.
section that those engaged in fMRI and MEG will need 103,247e254.
toconsult.Itstartswithanoverviewoftheemergingsci- Crick, F., Jones, E., 1993. Backwardness of human neuroanatomy.
ence of connectomics by Van Essen et al. and Sporns Nature361,109e110.
(Chapters16and18)andanaccountoftherelatedclas- Jaermann, T., De Zanche, N., Staempfli, P., Pruessmann, K.P.,
Valavanis, A., Boesiger, P., Kollias, S.S., 2008.Preliminary experi-
sical methods for tract tracing in animals by Morecraft
ence with visualization of intracortical fibers by focused high-
and colleagues (Chapter 17). In Chapter 19, Behrens
resolutiondiffusiontensorimaging.AJNRAm.J.Neuroradiol.29,
and colleagues give an introduction to probabilistic 146e150.
methods for tractography. In Chapter 20 Hubbard and Kobbert,C.,Apps,R.,Bechmann,I.,Lanciego,J.L.,Mey,J.,Thanos,S.,
Parker review the ways in which tractography has 2000. Current concepts in neuroanatomical tracing. Prog. Neuro-
biol.62,327e351.
been validated. Klein et al. (Chapter 21) introduce the
Penny,W.D.,Stephan,K.E.,Mechelli,A.,Friston,K.J.,2004.Modelling
notion of connectional fingerprints (see also Chapter
functional integration: a comparison of structural equation and
19), and demonstrate that the pattern of connections dynamiccausalmodels.NeuroImage23(Suppl.1),S264eS274.
can be used to distinguish between neighboring Ress,D.,Glover,G.H.,Liu,J.,Wandell,B., 2007.Laminarprofiles of
cytoarchitectonic areas. In Chapter 22, Catani and functionalactivityinthehumanbrain.NeuroImage34,74e84.
(cid:1) Saleem, K.S., Pauls, J.M., Augath, M., Trinath, T., Prause, B.A.,
Budisavljevicdescribethelanguagepathwaysinthehu-
Hashikawa,T., Logothetis, N.K., 2002.Magneticresonanceimag-
man brain,andthischapter isfollowedby adiscussion
ingof neuronalconnections in themacaquemonkey. Neuron 34,
oftheuseoftractographyinneurosurgicalplanningby 685e700.
Contributors
Daniel C. Alexander Department of Computer Science, Uni- Olga Ciccarelli NMR Unit, Queen Square MS Centre, UCL
versity CollegeLondon,UK Instituteof Neurology,London, UK
Jesper L.R. Andersson Centre for Functional Magnetic Reso- Tim Coalson Department of Anatomy and Neurobiology,
nance Imaging of the Brain (FMRIB), Nuffield Department Washington University School of Medicine, St. Louis, MO,
ofClinical Neurosciences,University of Oxford, JohnRad- USA
cliffe Hospital, Oxford, UK Yoram Cohen School of Chemistry, Raymond and Beverly
Yaniv Assaf Department of Neurobiology, George S. Wise Sackler Faculty of Exact Sciences, Tel Aviv University, Tel
FacultyofLifeSciences,TelAvivUniversity,TelAviv,Israel Aviv,Israel
Gareth Ball Centre for the Developing Brain, Department Serena J. Counsell Centre for the Developing Brain, Depart-
of Perinatal Imaging, Division of Imaging Sciences & ment of Perinatal Imaging, Division of Imaging Sciences
Biomedical Engineering, St Thomas’ Hospital, Kings Col- & Biomedical Engineering, St Thomas’ Hospital, Kings
legeLondon, London,UK CollegeLondon,London, UK
AndreasJ.BartschDepartmentofNeuroradiology,University Krikor Dikranian Department of Anatomy and Neurobiol-
ofHeidelberg,Heidelberg,Germany;CentreforFunctional ogy, Washington University School of Medicine, St. Louis,
Magnetic Resonance Imaging of the Brain (FMRIB), MO,USA
Nuffield Department of Clinical Neurosciences, University JuliaM.EdgarInstituteofInfection,ImmunityandInflamma-
ofOxford,John Radcliffe Hospital, Oxford,UK tion, College of Medical, Veterinary and Life Sciences,
PeterJ.BasserSectiononTissueBiophysicsandBiomimetics, University of Glasgow, Glasgow, UK; Department of Neu-
PPITS, NICHD, National Institutes of Health, Bethesda, rogenetics,MaxPlanckInstituteofExperimentalMedicine,
MD,USA Goettingen,Germany
Christian Beaulieu Department of Biomedical Engineering, A. David Edwards Centre for the Developing Brain, Depart-
Faculty of Medicine and Dentistry, University of Alberta, ment of Perinatal Imaging, Division of Imaging Sciences
Edmonton,Alberta, Canada & Biomedical Engineering, St Thomas’ Hospital, Kings
Timothy E.J. Behrens Centre for Functional Magnetic Reso- CollegeLondon,London, UK
nance Imaging of the Brain (FMRIB), Nuffield Department Matthew F. Glasser Department ofAnatomy and Neurobiol-
ofClinical Neurosciences,University of Oxford, JohnRad- ogy, Washington University School of Medicine, St. Louis,
cliffe Hospital, Oxford, UK; Department of Experimental MO,USA
Psychology,University ofOxford,Oxford,UK Ian R. Griffiths Institute of Infection, Immunity and Inflam-
Armin Biller Department of Neuroradiology, University of mation, College of Medical, Veterinary and Life Sciences,
Heidelberg, Heidelberg,Germany University ofGlasgow,Glasgow,UK
BenedettaBodiniCentrederecherchedel’institutducerveau John Harwell Department of Anatomy and Neurobiology,
et de la moelle e´pinie`re, Universite´ Pierre & Marie Curie, Washington University School of Medicine, St. Louis, MO,
Hoˆpital Pitie´ Salpeˆtrie`re,Paris,France USA
Erie D. Boorman Department of Experimental Psychology, Gyo¨rgy A. Homola Department of Neuroradiology, Univer-
University of Oxford and Centre for Functional Magnetic sityofWu¨rzburg,Wu¨rzburg, Germany
ResonanceImagingoftheBrain(FMRIB),NuffieldDepart- PennyL.HubbardCentre for Imaging Sciences & Biomed-
mentofClinicalNeurosciences,UniversityofOxford,John
ical Imaging Institute, University of Manchester, Man-
Radcliffe Hospital, Oxford,UK
chester Academic Health Science Centre, Manchester,
SanjaBudisavljevi(cid:1)cNatbrainlab,DepartmentofForensicand UK
NeurodevelopmentalScience,InstituteofPsychiatry,King’s SaadJbabdiCentreforFunctionalMagneticResonanceImag-
CollegeLondon,London, UK
ing of the Brain (FMRIB), Nuffield Department of Clinical
MarcoCataniNatbrainlab,DepartmentofForensicandNeuro- Neurosciences,UniversityofOxford,JohnRadcliffeHospi-
developmental Science, Institute of Psychiatry, King’s tal,Oxford,UK
CollegeLondon,London,UK Heidi Johansen-Berg Centre for Functional Magnetic Reso-
Charles Chen Department of Anatomy and Neurobiology, nance Imaging of the Brain (FMRIB), Nuffield Department
Washington University School of Medicine, St. Louis, MO, ofClinical Neurosciences, University of Oxford, JohnRad-
USA cliffe Hospital, Oxford, UK
xi
xii
CONTRIBUTORS
Derek K. Jones Cardiff University Brain Research Imaging Matthew F.S. Rushworth Department of Experimental Psy-
Centre(CUBRIC),SchoolofPsychology,CardiffUniversity, chology, University of Oxford and Centre for Functional
UK Magnetic Resonance Imaging of the Brain (FMRIB), Nuf-
Gordon Kindlmann Department of Computer Science, field Department of Clinical Neurosciences, University of
Oxford, JohnRadcliffeHospital, Oxford,UK
University ofChicago,Chicago, IL,USA
Johannes C. Klein Department of Neurology, Goethe- DavidH.SalatAthinoulaA.MartinosCenterforBiomedical
Imaging, Charlestown, MA, USA; Massachusetts General
University of Frankfurt, Frankfurt am Main, Germany;
Hospital Department of Radiology, Boston, MA, USA;
Centre for Functional Magnetic Resonance Imaging of the
Boston VA Healthcare System, NeuroimagingResearchfor
Brain (FMRIB), Nuffield Department of Clinical Neurosci-
Veterans Center,Boston, MA,USA
ences, University of Oxford, John Radcliffe Hospital,
Oxford,UK Je´roˆme Sallet Department of Experimental Psychology,
M. Kubicki Psychiatry Neuroimaging Laboratory, Depart- University of Oxford and Centre for Functional Magnetic
ResonanceImagingoftheBrain(FMRIB),NuffieldDepart-
ment of Psychiatry, Brigham and Women’s Hospital,
mentofClinicalNeurosciences,UniversityofOxford,John
HarvardMedical School, Boston,MA, USA
Radcliffe Hospital, Oxford, UK
Jose´ L.LanciegoCenterforAppliedMedicalResearch(CIMA
JanScholzHospitalforSickChildren,Toronto,Ontario,Canada
and CIBERNED), Neurosciences Division, University of
Navarra MedicalCollege, Pamplona Navarra, Spain Kiran K. Seunarine Department of Computer Science,
Rogier B. Mars Department of Experimental Psychology, University CollegeLondon, UK
University of Oxford and Centre for Functional Magnetic M.E. Shenton Psychiatry Neuroimaging Laboratory, Depart-
ResonanceImagingoftheBrain(FMRIB),NuffieldDepart- ment of Psychiatry, Brigham and Women’s Hospital,
mentofClinicalNeurosciences,UniversityofOxford,John Harvard Medical School, Boston, MA, USA; VA Boston
Radcliffe Hospital, Oxford,UK HealthcareSystem, Brockton, MA,USA
Karla L. Miller Centre for Functional Magnetic Resonance StephenM.SmithCentreforFunctionalMagneticResonance
Imaging of the Brain (FMRIB), Nuffield Department of Imaging of the Brain (FMRIB), Nuffield Department
Clinical Neurosciences, University of Oxford, John Rad- of Clinical Neurosciences, University of Oxford, John
cliffeHospital, Oxford,UK Radcliffe Hospital, Oxford, UK
RobertJ.MorecraftDivisionofBasicBiomedicalSciences,Lab- Stamatios N. Sotiropoulos Centre for Functional Magnetic
oratoryofNeurologicalSciences,UniversityofSouthDakota, Resonance Imaging of the Brain (FMRIB), Nuffield
SanfordSchoolofMedicine,Vermillion,SouthDakota,USA Department of Clinical Neurosciences, University of
Evren O¨zarslan Section on Tissue Biophysics and Biomi- Oxford, JohnRadcliffeHospital, Oxford,UK
metics, PPITS, NICHD, National Institutes of Health, OlafSpornsDepartmentofPsychologicalandBrainSciences,
Bethesda, MD,USA IndianaUniversity,Bloomington, IN,USA
Anand Pandit Centre for the Developing Brain, Department Valentina Tomassini Institute of Psychological Medicine
of Perinatal Imaging, Division of Imaging Sciences & Bio- and Clinical Neurosciences, Cardiff University School of
medical Engineering, St Thomas’ Hospital, Kings College Medicine, University Hospital of Wales, Heath Park,
London,London, UK Cardiff,UK
Deepak N. Pandya Department of Anatomy and Neurobiol- Gabriella Ugolini Neurobiologie et Developement, UPR3294
ogy, Department of Neurology, Boston University School CNRS, Institut de Neurobiologie Alfred Fessard, Gif-
ofMedicine, Boston, MA,USA sur-Yvette, France
GeoffreyJ.M.ParkerCentreforImagingSciences&Biomed- DavidC.VanEssenDepartmentofAnatomyandNeurobiol-
ical Imaging Institute, University of Manchester, Manches- ogy, Washington University School of Medicine, St. Louis,
terAcademic Health ScienceCentre,Manchester,UK MO, USA
O. Pasternak Psychiatry Neuroimaging Laboratory, Depart- C-F. Westin Laboratory of Mathematics in Imaging,
ment of Psychiatry, Brigham and Women’s Hospital, DepartmentofRadiology,BrighannandWomen’sHospital,
Harvard Medical School, Boston, MA, USA; Laboratory of HarvardMedical School, Boston, MA,USA
MathematicsinImaging,DepartmentofRadiology,Brigham FlorisG.WouterloodDepartmentofAnatomyandNeurosci-
and Women’s Hospital, Harvard Medical School, Boston, ences, Vrije Universiteit Medical Center, Neuroscience
MA,USA
CampusAmsterdam,Amsterdam, The Netherlands
Jim Pipe KellerCenterfor Imaging Innovation, Barrow Neu-
rological Institute, Phoenix, Arizona,USA
C H A P T E R
1
Introduction to Diffusion MR
¨
Peter J. Basser, Evren Ozarslan
Section on Tissue Biophysics and Biomimetics, PPITS, NICHD,
National Institutes of Health, Bethesda, MD, USA
O U T L I N E
1.1 What isDiffusion? 3 1.4 ConcludingRemarks 8
1.2 Magnetic Resonance andDiffusion 5 Acknowledgments 9
1.2.1 From the MRSignal Attenuation to the
References 9
Average Propagator 7
1.3 Diffusion inNeural Tissue 7
1.1 WHAT IS DIFFUSION? particles flow from regions of high concentration to
thoseoflowconcentration(hencethe“(cid:2)”signinequa-
Diffusion is a mass transport process arising in na- tion1.1),justasheatflowsfromregionsofhightemper-
ture, which results in molecular or particle mixing ature to low temperature, as described in the earlier
without requiring bulk motion. Diffusion should not Fourier’slawofheatingonwhichFick’slawwasbased.
be confused with convection or dispersiondother In the case of diffusion, the flux is proportional to the
transportmechanismsthatrequirebulkmotiontocarry concentration gradient as well as the diffusion coeffi-
particlesfrom one place to another. cient. Unlike the flux vector or the concentration, the
The excellent book by Howard Berg (1983) Random diffusion coefficient is an intrinsic property of the me-
Walks in Biology describes a helpful Gedanken experi- dium, and its value is determined by the size of the
mentthatillustratesthediffusionphenomenon.Imagine diffusing molecules and the temperature and micro-
carefully introducing a drop of colored fluorescent dye structural features of the environment. The sensitivity
into a jar of water. Initially, the dye appears to remain of the diffusion coefficient on the local microstructure
concentrated at the point of release, but over time it
spreads radially, in a spherically symmetric profile. J
Thismixingprocesstakesplacewithoutstirringorother
bulk fluid motion. The physical law that explains this
phenomenon is called Fick’s first law (Fick, 1855a,
1855b),whichrelatesthediffusivefluxtoanyconcentra-
tion difference throughthe relationship
J ¼ (cid:2)DVC; (1.1)
whereJisthenetparticleflux(vector),Cistheparticle
FIGURE 1.1 According to Fick’s first law, when the specimen
concentration,andtheconstantofproportionality,D,is
containsdifferentregionswithdifferentconcentrationsofmolecules,
called the “diffusion coefficient.” As illustrated in
theparticleswill,onaverage,tendtomovefromhighconcentration
Figure 1.1, Fick’s first law embodies the notion that regionstolowconcentrationregionsleadingtoanetflux(J).
DiffusionMRI
http://dx.doi.org/10.1016/B978-0-12-396460-1.00001-9 3 Copyright(cid:1)2014ElsevierInc.Allrightsreserved.
4
1. INTRODUCTIONTODIFFUSIONMR
enablesitsuseasaprobeofphysicalpropertiesofbio- of particles undergoing diffusion, which led to a
logical tissue. coherentdescriptionofdiffusion,reconcilingtheFickian
On a molecular level, diffusive mixing results solely and Brownian pictures. He introduced the “displace-
fromcollisionsbetweenatomsormoleculesintheliquid ment distribution” for this purpose, which quantifies
or gas state. Another interesting feature of diffusion is the fraction of particles that will traverse a certain dis-
that it occurs even in thermodynamic equilibrium, for tance within a particular timeframe, or equivalently,
example,inajarofwaterkeptataconstanttemperature the likelihood that a single given particle will undergo
andpressure.Thisisquiteremarkablebecausetheclas- that displacement. For example, in free diffusion the
sical picture of diffusion, as expressed above in Fick’s displacementdistributionisaGaussianfunctionwhose
first law, implies that when the temperature or concen- widthisdeterminedbythediffusioncoefficient,asillus-
tration gradients vanish, there is no net flux. There tratedinFigure1.3.Gaussiandiffusionwillbetreatedin
were many who held that diffusive mixing or energy moredetailinChapter5,whereasthemoregeneralcase
transfer stopped at this point. We now know that of non-Gaussianitywillbetackled in Chapters6 and 9.
althoughthenetfluxvanishes,therearestillmicroscopic Usingthedisplacementdistributionconcept,Einstein
motions of molecules that persist; it is just that on was able to derive an explicit relationship between the
average, thereis nonetmolecular flux in equilibrium. mean-squareddisplacementoftheensemble,character-
A framework that explains this phenomenon has its izingitsBrownianmotion,andtheclassicaldiffusionco-
origins in the observations of Robert Brown, who is efficient, D, appearing in Fick’s law (Einstein, 1905,
credited with being the first to report the random mo- 1926), given by
(cid:1) (cid:3)
tionsofpollengrainswhilestudyingthemunderthemi-
x2 ¼ 2DD; (1.2)
croscope(Brown,1828)(Figure1.2).Brownreportedthat
particlesmovedrandomly,withoutanyapparentcause. where hx2i is the mean-squared displacement of parti-
He initially believed that there was some life force that cles during a diffusion time D and D is the diffusion
was causing these motions, but disabused himself of coefficient.
this notion when he observed the same fluctuations At around the same time as Einstein, Smoluchowski
whenstudying dust andother inorganicmatter. (1906) was able to reach the same conclusions using
Intheearlypartofthetwentiethcentury,AlbertEin- different means. Langevin improved upon Einstein’s
stein, who was unaware of Brown’s observation and description of diffusion for ultra-short timescales in
seeking evidence that would undoubtedly imply the which there are few molecular collisions, but we are
existence of atoms, came to the conclusion that “bodies not able to probe this regime using MR diffusion mea-
of microscopically visible size suspended in a liquid surements in water. Since a particle experiences about
will perform movements of such magnitude that they 1021 collisions every second in typical proton-rich sol-
can be easily observed in a microscope” (Einstein, vents like water (Chandrasekhar, 1943), we generally
1905;Fu¨rthandCowper,1956).Einsteinusedaprobabi- do not concern ourselves with this correction in diffu-
listic framework to describe the motion of an ensemble sion MR.
FIGURE 1.3 The Gaussian displacement distribution plotted for
FIGURE1.2 RobertBrown,abotanistworkingonthemechanisms variousvaluesofthediffusioncoefficientwhenthediffusiontimewas
of fertilization in flowering plants, noticed the perpetual motion of taken to be 40ms. Larger diffusion coefficients lead to broader
pollengrainssuspendedinwaterin1827. displacementprobabilities,suggestingincreaseddiffusionalmobility.
I. INTRODUCTIONTODIFFUSIONMRI
5
1.2.MAGNETICRESONANCEANDDIFFUSION
1.2 MAGNETIC RESONANCE inspace,enabletheacquisitionofMRimages.MRsignal
AND DIFFUSION andimageacquisitionisdiscussedindetailinChapter2.
The sensitivity of the spin echo MR signal on molec-
Magneticresonanceprovidesauniqueopportunityto ular diffusion was recognized by Hahn. He reported a
quantifythediffusionalcharacteristicsofawiderangeof reduction of signal of the spin echo and explained it in
specimens.Becausediffusionalprocessesareinfluenced terms of the dephasing of spinscaused by translational
bythegeometricalstructureoftheenvironment,MRcan diffusion within an inhomogeneous magnetic field
be used to probe the structural environment non- (Hahn, 1950). While he proposed that one could mea-
invasively.Thisisparticularlyimportantinstudiesthat sure the diffusion coefficient of a solution containing
involve biological samples in which the characteristic spin-labeled molecules, he did not propose a direct
length of the boundaries influencing diffusion are typi- method fordoing so.
cally so small that they cannot be resolved by conven- Afewyearslater,CarrandPurcell(1954)proposeda
tionalmagneticresonanceimaging(MRI)techniques. complete mathematical and physical framework for
A typical nuclear magnetic resonance (NMR) scan such a measurement using Hahn’s NMR spin echo
starts with the excitation of the nuclei with a 90(cid:3) sequence. They realized that the echo magnitude could
radiofrequency (RF) pulse that tilts the magnetization be sensitized solely to the effects of random molecular
vector into the plane whose normal is along the main spreading caused by diffusion in a way that permits a
magnetic field. The spins subsequently start to precess direct measurement. The idea they employed is not
around the magnetic fieldda phenomenon called very different from what is utilized in most current
Larmor precession. The angular frequency of this pre- studies using diffusion-weighted imaging (DWI).
cession isgiven by Because a spin’s precession frequency is determined
by the local magnetic field as implied by equation
u ¼ gB; (1.3)
(1.3), if a “magnetic field gradient” is applied, spins
whereBisthemagneticfieldthatthespinisexposedto, that are at different locations experience different mag-
and g is the gyromagnetic ratioda constant specific to neticfieldsdhencetheyprecessatdifferentangularfre-
the nucleus under examination. In water, the hydrogen quencies.Afteracertaintime,thespinsacquiredifferent
nucleus (i.e. the proton) has a gyromagnetic ratio of phaseshiftsdependingontheirlocation.Strongergradi-
approximately 2.68(cid:4)108rads(cid:2)1T(cid:2)1. Spins that are entswillleadtosharperphasechangesacrossthespec-
initially coherent dephase due to factors such as mag- imen, yielding a higher sensitivity to diffusion. In most
netic field inhomogeneities and dipolar interactions current clinical applications, a quantity called the
(Abragam 1961), leading to a decay of the voltage “b-value” that is proportional to the square of the
(signal) induced inthe receiver. gradient strength is used to characterize the level of
As proposed by Edwin Hahn (1950), and illustrated the induced sensitivity ondiffusion.
inFigure1.4,thedephasingduetomagneticfieldinho- IntheschemeconsideredbyCarrandPurcell,acon-
mogeneities can be reversed through a subsequent stant magnetic field gradient is applied throughout the
(cid:3)
application of a 180 RF pulse, and the signal is repro- entire Hahn spin echo experiment as shown in
duced.Inthis“spinecho”experiment,thetimebetween Figure 1.5. Such an acquisition can be performed either
thefirstRFpulseandformationoftheechoiscalledTE in a spatially linear main field, or using another coil
and it is twice the time between the two RF pulses, that is capable of creating a linear magnetic field on
which is denoted by s. The generated echo is detected topofthehomogeneousfieldofthescanner(B0).Intheir
by a receiver antenna (MR coil) and is used to produce description, at a particular time t, a particle situated at
spectra.CarefullydevisedsequencesofRFpulsesalong
1800
withexternalmagneticfieldgradientslinearlychanging
900
RF
1800
900
Gradient
RF
Signal
Signal FIGURE 1.5 A schematic of the spin echo experiment in the
presence of a constant field gradient discussed by Carr and Purcell
FIGURE 1.4 Aschematicofthespinechomethodintroducedby (1954). Diffusion taking place in the resulting inhomogeneous field
Hahn. givesrisetoadecreasedMRsignalintensity.
I. INTRODUCTIONTODIFFUSIONMRI
6
1. INTRODUCTIONTODIFFUSIONMR
position x experiences a magnetic field of B þGx(t). If “narrow pulse” regime, the net phase change induced
0
the particle is assumed to spend a short time, s0, at this by the first gradientpulse is given simply by
point before moving to another location, it suffers a
f ¼ (cid:2)qx ; (1.5)
phase shiftgiven by 1 1
fðxðtÞÞ ¼ (cid:2)uðxðtÞÞs0 ¼ (cid:2)gðB þGxðtÞÞs0 (1.4) wherex1isthepositionoftheparticleduringtheappli-
0 cationofthefirstpulseandweignorethephasechange
asaresultoftheLarmorprecessionatthefieldmodified duetotheB0field,whichisconstantforallspinsinthe
bytheconstantgradient.Here,theminussignisneces- ensemble. In the above expression all experimental pa-
saryforprotonswhoseprecessionisintheclockwisedi- rameterswerecombinedinthequantityq¼gdG,where
rectionontheplaneperpendiculartothemainmagnetic d and G are the duration and the magnitude of the
field. Therefore, the net phase shift that influences the gradient pulses, respectively. Similarly, if the particle is
MR signal at t¼2s is related to the motional history of situatedatpositionx2duringtheapplicationofthesec-
theparticlesintheensemble.Byexploitingthisphenom- ondpulse,thenetphasechangeduetothesecondpulse
enon,CarrandPurcellproposedMRsequencestosensi- isgiven by
tize the MR spin echo to the effects of diffusion, and f ¼ (cid:2)qx : (1.6)
developed a rigorous mathematical framework to mea- 2 2
(cid:3)
sure the diffusion coefficient from such sequences. The180 RFpulseappliedinbetweenreversesthephase
This elevated NMR to being a “gold standard” for change that occurs prior to it (i.e. that induced by the
measuring molecular diffusion. An alternative mathe- first gradient pulse). Therefore, the net phase change
matical formulation of the problem was introduced by that the particlesuffersisgiven by
Torrey (1956), who generalized the phenomenological f (cid:2)f ¼ (cid:2)qðx (cid:2)x Þ: (1.7)
Bloch equations (Bloch, 1946) to include the effects of 2 1 2 1
diffusion. Clearly, if particles remained stationary (i.e. x ¼x ),
1 2
Afteraboutadecade,StejskalandTanner(1965)intro-
thenetphaseshiftwouldvanish.Inthiscase,andinthe
duced many innovations that made modern diffusion
caseinwhichallspinsaredisplacedbythesameconstant
measurements by NMR and MRI possible. First, they
amount, the magnitude of the echo will be unchanged
introduced the pulsed gradient spin echo (PGSE)
(except for the T1 and T2 decay that is occurring
sequence, which replaced Carr and Purcell’s constant
throughout the sequence). However, if particles were
magnetic field with short-duration gradient pulses as
diffusing randomly throughout the excited volume,
illustratedinFigure1.6.Thisallowedacleardistinction
thephase incrementtheygained during thefirstperiod
between the encoding time (pulse duration, d) and the
does not generally cancel the phase decrement experi-
diffusion time (separation of the two pulses, D). A
encedduringthesecondperiod.Thisincompletecancel-
particularly interesting case of this pulse sequence that
lationresultsinphasedispersionoraspreadingofphases
makestheproblemconsiderablysimplerfromatheoret-
amongtherandomlymovingpopulationofspins.There-
ical point ofview isobtained when thediffusiongradi-
fore,theoverallsignal,givenbythesumofthemagnetic
ents are so short that diffusion taking place during the
momentsofallspins,isattenuatedduetotheincoherence
application of these pulses can be neglected. In this
intheorientationsofindividualmagneticmoments.
Rather than dealing with the MR signal itself, it has
proven convenient to introduce a new quantity, E(q),
1800 called the MR signal attenuation, which is obtained
900 by dividing the diffusion-attenuated signal, S(q), by
the signal in the absence of any gradients, S ¼S(0)
0
RF (i.e.E(q)¼S(q)/S ).Sincerelaxation-relatedsignalatten-
0
uation is approximately independent of the applied
G
diffusion gradients, dividing S(q) by S eliminates the
0
Gradient
effects of relaxation, and the q-dependence of E(q) can
beattributedsolelytodiffusion.TheMRsignalattenua-
tion isthen given by (Stejskal, 1965)
Signal
Z Z
MFIRGUteRchEniq1u.6e inAtrosdchuecmedatbicyoSftethjsekaplualsneddTfiaenldnegrra(1d9i6e5n)t.sTphine eticmhoe EðqÞ ¼ rðx1Þ Pðx1;x2;DÞe(cid:2)iqðx2(cid:2)x1Þdx2dx1; (1.8)
between the application of the two gradient pulses, D, may be any-
where between 10ms and a few hundreds of milliseconds. The
where we employed two new quantities. The first of
gradientpulseduration,d,canvarybetweenafewmillisecondstoD,
where when d¼D, the pulse sequence becomes the same as that in these,r(x1),isthespindensityatthetimeofapplication
Figure1.5. of thefirstpulse quantifying thelikelihood of findinga
I. INTRODUCTIONTODIFFUSIONMRI