principles of (n)mr imaging - ucsf radiology · from nmr to mri •1946: nmr phenomenon first...
TRANSCRIPT
Principlesof(N)MRImaging
Peder Larson,Ph.D.UniversityofCalifornia– SanFrancisco,Departmentof
RadiologyandBiomedicalImagingExperimentalNMRConference,EducationalPresentation,
Asilomar,PacificGrove,CAMarch28,2017
https://radiology.ucsf.edu/research/labs/larson/educational-materials(Google:Peder LarsonLab,EducationalMaterialslinkonsidebar)
Overview
1. MRISystems– Magneticfieldgradients
2. ImagingPrinciples– Slice-selectiveRFPulses– ImageFormation
3. MRspectroscopicimaging(MRSI)– Spectroscopicimageformation– Spectral-SpatialRFpulses
FromNMRtoMRI
• 1946:NMRphenomenonfirstdiscoveredbyFelixBlochandEdwardPurcell(PhysicsNobelPrizein1952)
• 1973:FirstdescriptionofNMRImaging(MedicineNobelPrizetoPaulLauterbur andPeterMansfieldin2003)
• 1982:Clinicalmagneticresonanceimaging(MRI)systems(“NuclearwasassociatedwithbombsandwarsandGodknowswhat”– JohnMallard)
MRIhascomealongway…
The key factors were the development of fast imagingtechniques, particularly gradient echo, and phasedarray coil technology. The 1990s also saw the coming ofage of earlier developments, namely cardiac MRI andEcho Planar Imaging (EPI). EPI, which is the fastest and
one of the most cutting edge methods, was actually oneof the first imaging methods to be proposed, by Sir PeterMansfield. EPI is now extensively used in neurologicalimaging through functional MRI (fMRI) and diffusionimaging.
1.3 How to use this book
Everyone starts MRI with the same basic problem: it’slike nothing else they’ve learnt in the past. All thatknowledge you have about radioactive isotopes and
MR: What’s the attraction?
4
Figure 1.3 First ever human head image using MRI at 0.1 T
from EMI Central Research Laboratories. For this image CT
type “back projection” was used. Courtesy of Ian Young.
The early history of NMR‘Nuclear induction’, as it was first described, was dis-covered in 1945, soon after the close of World War II,by Bloch and independently by Purcell and Pound. Itis said that the development of radio communica-tions in the war effort, to which Purcell had con-tributed scientifically, was one of the factorsunderpinning this important scientific discovery.Another important factor, as in the development ofatomic physics, was the expulsion or fleeing ofEuropean physicists from the Nazi regime, an exodusthat included Bloch and Bloembergen. What didthese MR pioneers discover? That you can detect asignal (a voltage in a coil) when you place a sample ina magnetic field and irradiate it with radiofrequency(RF) energy of a certain frequency, the resonant orLarmor frequency. The signal is produced by theinteraction of the sample nuclei with the magneticfield. The spin echo was ‘stumbled upon’ by Hahn in1949. He discovered that you could get a repeat of theNMR signal at a delayed time by adding a secondburst of RF energy. That’s all you need to know fornow. So what were NMR researchers doing betweenthe forties and the seventies – that’s a long time incultural and scientific terms. The answer: they weredoing chemistry, including Lauterbur, a professor ofchemistry at the same institution as Damadian,albeit on different campuses. NMR developed into alaboratory spectroscopic technique capable ofexamining the molecular structure of compounds,until Damadian’s ground-breaking discovery in 1971.
Figure 1.4 0.15T resistive magnet used by Philips in the
early development of MRI. Courtesy of Philips Medical
Systems.
FirsthumanheadMRI(published1978) 2010
SiemensPET/MRI
Siemens7TMRI
MRISystemComponents
Q:Whatmakesthisanimagingsystem?A:Magneticfieldgradientcoils,the“gradients”
http://www.magnet.fsu.edu/education/tutorials/magnetacademy/mri/
(RF)
GradientEncoding
Position (z)
Magnetic Field/Frequency
Magneticfieldgradient
B0
ω0
GZ • Appliedmagneticfieldgradients(G)addorsubtracttothemainmagneticfield(B0)
• Thischangestheresonancefrequencyasafunctionofposition:ω=γB =γ(B0 +GZz)
x
y
Mxy NetMagnetizationVectors(RotatingFrameatω0)
B0
GradientEncoding
Position (x)
Magneticfieldgradient
B0
GX
Magnetic Field/Frequency
• Gradientsincludedforallthreeaxes(x,y,z),andcanbemodulatedindependently
• Createimagebyseparatingsignalsatdifferentfrequencies
ω0B0
Mxy NetMagnetizationVectors(RotatingFrameatω0)
x
y
BlochEquation– GradientFields
• Gradientcoilscreatechangesinthemagneticfieldversusposition
• Changesprecessionfrequencytobeafunctionofposition(enablingimageformation):
�G(t) = [GX(t), GY (t), GZ(t)]
~B(~r, t) =
2
400
B0 + ~G(t) · ~r
3
5
!0 = �(B0 + ~G(t) · ~r)
d ~M(t)
dt= � ~M(t)⇥ ~B(t) +
2
4�1/T2 0 0
0 �1/T2 00 0 �1/T1
3
5 ~M(t) +
2
400
M0/T1
3
5
MagneticFieldsinMRI
z
x y
Fieldcomponent Notation Direction ApproximateStrength
Mainfield±inhomogeneity
B0 ± ΔB0 z 104 ± 10-2 G
Chemicalshift σ z 10-2 - 10-1G
MagneticSusceptibility
χ z 10-2 - 10-1G
Gradients GX,GY,GZ z 5G/cmè101- 102 G
Radiofrequency(RF) B1 x,y 10-1 G
B0 • Chemicalshiftandmagneticsusceptibilityareinherentinthebodyandaresourcesof“off-resonance”
• GradientsandRFarecontrolledfieldsandmanipulatedtocreateimages
FrequencyEncoding
• NoGradientsapplied• DifferentpositionsnotdistinguishableinMRsignal
Position
Frequency
G=0FourierTransform
ω0
t
f/x
Reference(ω0)
0
s(t)
FrequencyEncoding– 1Dimaging
• Gradientfieldapplied• Differentpositions
distinguishableinMRsignalbaseduponfrequency
Position
Frequency
G>0FourierTransform
f/x
ω0
t
Reference(ω0)
0
s(t)
Typical2DMRIPulseSequence
1. RFExcitation2. SpatialEncoding3. DataAcquisition
TE=EchoTime
”FrequencyEncoding”
”PhaseEncoding”
PhaseEncoding
x
y
tGX
tGY
Mxy ofNetMagnetizationVectors(afterRFexcitation)
TR#1:constantencodingpatterniny
PhaseEncoding
x
y
tGX
tGY
Mxy NetMagnetizationVectorsTR#2:lowfrequencyencodingpatterniny
PhaseEncoding
x
y
tGX
tGY
Mxy NetMagnetizationVectorsTR#3:highfrequencyencodingpatterniny
MRSignal
x
y
Mxy(r)
x
y
x
y
s(t)
Gy >0
DecodingPosition
• GeneralbehaviorofMxy inthepresenceofgradients
• Defining“k-space”as• Andneglectingrelaxation• Resultsin
General case: time varying gradients on x,y,z
Proportional to phase of Mxy
( ) ( ) ttpg dGtk
t
ò=0
2
Demodulate received signal at Larmor (rotating frame) frequency for s(t)
Looking like a Fourier Transform...
FourierTransformSignalRelationship
• MRSignalistheFourierTransformoftheobjectnetmagnetization
• k-spacelocation(definedbygradients)determineswhereinFTspacethesignaliscomingfrom
Assume T2 large relative to t, then
Received signal is the spatial Fourier Transform of the transverse (xy) net magnetization! Evaluated at k-space location that depends on gradients
Example : consider signal from three locations - x= 0, x1, x2 - with magnetic field gradient on
Signal is sum of different locations, which have different frequencies with gradient
Or we can model our object with delta functions and use the Fourier transform
( ) ( ) ttpg dGtk
t
ò=0
2
K-space
kx
ky
Frequency space(k-space), M(kx,ky)
x
y
FourierTransform
Image space, m(x,y)
GX
GY
periodic variation in signal spatial distribution or imagebrightness, measured not as line-pairs per centimetrebut as ‘cycles per centimetre’ (which are very similar).
Applying the theory of Fourier, any image (not justMRI) may be decomposed into a spectrum of periodic(sinusoidal) brightness variations or spatial frequen-cies. In a digital image with a matrix of 256!256 pixelsthere are 256!256 possible spatial frequencies, allow-ing for positive and negative values. If we know thespatial frequencies we can calculate an image of theobject that formed them. The purpose of MR localiza-tion by gradients is to manipulate the MR signal so thatit gives all the spatial frequencies necessary to form animage. Each point of data or k-space is a spatial fre-quency component.
Figure 7.10 shows an image and its constituent spatialfrequencies (k-space). If we remove the high spatial fre-quencies we are left with an image which has the rightbrightness but no detail. Removing the low spatial fre-quencies leaves the image with details of edges andsharp features but low intensity elsewhere. So bigobjects have low spatial frequencies. Small objects orsharp edges have high spatial frequencies.
7.5.2 Totally fazed: phase encoding
Most people find phase encoding the hardest part ofMR image formation to understand, but gaining a con-ceptual grasp of it will pay dividends in terms of youroverall understanding. Consider the following in
Spaced out: spatial encoding
120
Figure 7.10 Images and their 2D spectra (k-space) showing: (a) reconstruction from all spatial frequencies, (b) low spatial
frequencies, i.e. the centre of k-space only and (c) high spatial frequencies, i.e. the edges of k-space only.
(a) (b) (c)
k-space(freq
uencydo
main)
Image-space(re
aldom
ain)
FourierTransform
Low-frequencyonly High-frequencyonly
McRobbie etal.MRI:FromPicturetoProton
K-space
kx
ky
Frequency space(k-space)
FourierTransform
Image space
K-space
Image space
x
yM(k1)
Spatialfrequencypatternsweightedbyk-spacevalue
EncodingGradients
kx
ky
tGX
tGY
( ) ( ) ttpg dGtk
t
ò=0
2s(t) = M(kx(t),ky(t))
M(kx,ky)
EncodingGradients
kx
ky
tGX
tGY
( ) ( ) ttpg dGtk
t
ò=0
2s(t) = M(kx(t),ky(t))
M(kx,ky)
EncodingGradients
kx
ky
tGX
tGY
( ) ( ) ttpg dGtk
t
ò=0
2s(t) = M(kx(t),ky(t))
M(kx,ky)
EncodingGradients
kx
ky
tGX
tGY
( ) ( ) ttpg dGtk
t
ò=0
2s(t) = M(kx(t),ky(t))
M(kx,ky)
“2DFT”PulseSequence
”FrequencyEncoding”
”PhaseEncoding”
Reconstructdataviaa2DFourierTransform
CoveringK-space
kx
ky
tGX
tGY
Gradients(GX,GY,GZ)spatiallyencodespins
Acquirefrequency-encodeddataink-space (frequencyspace)
MoreTrajectories
GX
DAQ
GY
a b
kx
ky
kx
ky
kx
ky
kx
ky
kx
ky
c d e
2DFT Echo-planarImaging(EPI)
RadialorProjection
reconstruction
PROPELLER(formotioncorrection)
Spiral
CartesianEncoding:FOVandresolution
kx
ky
1FOVy
k-space(sampling pattern)
Image space(point spread function)FourierTransform
x
y
FOVy
1/resx
resx
resy
1/resy
SelectiveExcitation
• EveryRFpulseisselectiveinfrequency• (ApproximateFourierTransformrelationshipbetweenRFpulseshapeandMagnetizationprofile)
• Profilecharacterizedbythe“Bandwidth”
γΔBZ(resonance frequency)
|MXY|
FourierTransform
0
(γB0)
�f
�f
ExcitationProfiles
Frequency
MXY
FourierTransform
Time
RF
Slice-selectiveExcitation
Frequency
Position
GZ
MXYSlope = γGZ
Frequency
�f
�z = �f�/2⇥·Gz
SpatiallySelectiveRFExcitation
Position
Flip Angle
FourierTransform
Slice thickness
• RFpulsewithappliedGradientpulseexcitesonlyalimitedregionofspins
• ReceivedRFsignalwillonlycomefromthisregion• (ApproximateFourierTransformrelationship,validfor
“small”tipangles,<60°)
MRS(FID)AcquisitionK-space
Gf t
RF t
DAQ t
kf = tOff-resonanceisidenticaltoaconstantgradient
kf f
FourierTransform
MRSpectroscopicImaging(MRSI)
GZ
DAQ
GZ
kz
kf
kz
kf
DAQ
PhaseEncoding
Echo-planarspectroscopicimaging(EPSI)
Spectral-SpatialSampling
• Echo-planarspectroscopicimaging(EPSI)
• FourierTransform–basedreconstructionfromkz-kfspacetoz-fspace
kz
kf
Gf t
GZ t
MRSISamplingRequirements
kz
kf
kz
kf1/resz
1/FOVf =1/bandwidth
1/resz
1/FOVf =1/bandwidth
• FastAcquisition• ReducedSNR
efficiency• Tradeoffbetween
spatialresolutionandbandwidth
PhaseEncoding
Echo-planarspectroscopicimaging(EPSI)
0 2 4 6 8 10
-1-0.5
00.5
1-1
-0.5
0
0.5
1
Ky
(cm
-1)
time (ms)Kx (cm-1)
EPSI(EchoPlanarSpectroscopicImaging)
-1 -0.5 0 0.5 1-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
Kx (cm-1)
Ky (c
m-1
)
SpiralSpectroscopicImaging
0 10 20 30 40 50-1
-0.5
0
0.5
1-1
-0.5
0
0.5
1
time(ms)
Kx(cm-1)
Ky(cm
-1)
-1 -0.5 0 0.5 1-1
-0.8
-0.4
0
0.4
0.8
1
Kx(cm-1)
Ky(cm
-1)
ConcentricRingsTrajectory
Tradeoffs• Speed• SNRefficiency• Robustnessto
hardwareimperfections
• Bandwidth• Resolution
ComparisonofAcceleratedMRSIStrategies
0.4 0.5 0.6 0.7 0.8 0.9 10
500
1000
1500
2000
2500
3000Spectral Bandwidth
Resolution (cm)
SB
W (
Hz)
Concentric Rings
Symmetric EPSI
Flyback EPSI
Spiral
0.4 0.5 0.6 0.7 0.8 0.9 10
1
2
3
4
5
6
7
8
9Acquisition Time
Resolution (cm)
Acq
uis
ito
n T
ime
(s)
Concentric Rings
Symmetric EPSI
Flyback EPSI
Spiral
0.4 0.5 0.6 0.7 0.8 0.9 10
500
1000
1500
2000
2500
3000Spectral Bandwidth with Interleaves
Resolution (cm)
SB
W (
Hz)
Concentric Rings
Symmetric EPSI
Flyback EPSI
Spiral
0.4 0.5 0.6 0.7 0.8 0.9 10.65
0.7
0.75
0.8
0.85
0.9
0.95
1SNR Efficiency
Resolution (cm)
SN
R E
ffic
ien
cy
Concentric Rings
Symmetric EPSI
Flyback EPSI
Spiral
FlybackEPSI
SymmetricEPSI
ConcentricRings
Spiral
Speed - - + ++SNR - ++ + ++Robustness ++ - ++ --
JiangW,etal,MRM2014.
Spectral-spatialRFpulses• Designedwithspectralk-space(kf =t)inmind• Spectrallyandspatiallyselective• Typicallyuseecho-planargradientduringRFpulse
Meyeretal.MRM15:287-304(1990)
ExcitationSpectralk-space
Gf t
RF t
GZ t
kZ = 0 kf = t
Frequencyshifts(e.g.chemicalshift)isidenticaltoaconstantgradient
kz
kf
Spectral-spatialProfile
b(kf, kZ)
MXY(f,z)kz
kf
2DFourierTransform(small-tip)
ChemicalShiftslicemisregistration
2DSLR(anytip)
Spectral-SpatialDesignSpectralPulse(envelope)
SpatialPulses(subpulses)
2DFT(approximately)
Spectral-SpatialDesign
1. Designspectralpulse2. Designspatialpulseand
sliceselectgradient3. Usemultiplespatialpulses
andgradients– Weightspatialpulseswith
spectral pulseenvelope– Alternatesignofgradient
(EP)oraddrewinder(flyback)
z
f
z
f
z
f
Spectral-SpatialDesign
SpectralProfile
SpatialProfile
1)SpectralPulse
2)SpatialPulse
DT
1/DT
Spectral-SpatialRFExample
A.Schricker etal.MRM46:1079-10872001
• Replace spin echo 180 pulses with spectral spatial pulses in PRESS
• Design such that NAA/Cr/Cho only within passband and water/fat are in stopband
• No need for CHESS (Spectrally-selective water suppression pulses)
RecommendedMRIResources• Nishimura.PrinciplesofMagneticResonanceImaging.Availablefromlulu.com:Paperback or
Hardcover– CompleteandcoherentdescriptionofMRI,targetedtowardsengineersandphysicists
• McRobbie,Moore,Graves,andPrince.MRIFromPicturetoProton(2nd edition).CambridgeUniversityPress.– ComprehensivedescriptionofMRI,targetedtowardsalesstechnicalaudience– Manyusefulimagingexamplesandpracticaltips
• Schröder,Faber. InVivoNMRImaging.Spinger.http://link.springer.com/book/10.1007/978-1-61779-219-9/page/1– Usefulchaptersonimageformation,specialcontrastinMRI,andapplications– Verydetaileddescriptions
• Bernstein,King,Zhou.HandbookofMRIPulseSequences.AcademicPress.http://www.sciencedirect.com/science/book/9780120928613– DetaileddescriptionsofspecializedMRItopics– AssumesintroductoryknowledgeofMRI– EssentialforMRIscientists
• DanishResearchCentreforMagneticResonance.EducationalMaterials:http://www.drcmr.dk/educations/education-material– IntroductiontoMRInotes,targetedtowardsphysicistsandengineers– Blochequationand“compassMR”simulationsforteaching– Videosexplainingsimulations