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