Introduction To The Physics Of NMR, MRI, BOLD FMRI
Pittsburgh, June 13-17, 2011Introduction to the Physics ofNMR, MRI, BOLD fMRI(with an orientation toward the practicalaspects of data acquisition)Pittsburgh, June 13-17, 2001Functional MRI in Clinical ResearchRobert Savoy
MR physics and safetyfor functional MRILawrence L. Wald, Ph.D.Massachusetts General HospitalAthinoula A. Martinos CenterWald, Savoy, fMRI MR Physics
Outline:Part 1:MR signalMR contrastfMRI contrastPart 2:Image encoding (10 minute version)Imaging considerations for fMRIPart 3:MR SafetyWald, Savoy, fMRI MR Physics
Basics of Functional MRI Hemodynamics Roy and Sherrington History BOLD / Flow Instrumental Source of the Data NMR8MagneticFieldsandRelaxation MRI Contrast Flexibility of ToolMaximum Signal(minimal contrast)"Inject Signal"(90 saturation rf-pulse)Pittsburgh, June 13-17, 2001No Signal(no contrast)TimeFunctional MRI in Clinical ResearchRobert Savoy
MRI in a Slide:MRIInaSlide8 Magnetic Fields and Relaxation To Obtain the NMR Signal: Three Magnetic Fields µThe magnetic field of a nucleus with spin B 0 The main magnetic field, used to align nuclei B1 The radio-frequency field, used to flip nucleiRelaxation: Two ways for the signal to go away T1Longitudinal: The nuclei re-align with B0 T2 Transverse: The nuclei get out-of-phaseTo Select Slices and Make Images: Three More Fields G , G , GThe gradient fieldsx y zShim FieldsTo make better imagesShielding Fields To protect us from all of the above!Pittsburgh, June 13-17, 2001Functional MRI in Clinical ResearchRobert Savoy
Signal decays exponentiallyMaximumSignalFading.Fading.GoneSingal Decays ExpontntiallyTime"Inject Signal"(90 saturation rf-pulse)Pittsburgh, June 13-17, 2001Functional MRI in Clinical ResearchRobert Savoy
Rate of decay varies across voxelsDifferent Rates of Decay"Inject Signal"(90 saturation rf-pulse)Pittsburgh, June 13-17, 2001TimeFunctional MRI in Clinical ResearchRobert Savoy
ImagecontrastvarieswithtimeFaces Contrast for fMRIMaximumSignal(Little Contrast)IntermediateSignals(Useful Contrasts)Maximum Signal(minimal contrast)(90 saturation rf-pulse)(90 saturation rf-pulse)Pittsburgh, June 13-17, 2001(No Contrast)No Signal(no contrast)"Inject Signal""Inject Signal"MinimumSignalTimeTimeSo, we must WAIT for dephasing to occur, in orderto get T2 or T2* contrast.But while we are waiting, various bad thingshappen: signal decreases; imaging artifacts appearFunctional MRI in Clinical ResearchRobert Savoy
Susceptibility in MRGives us “dropout” (signal loss)(i.e., The Bad)Gives us BOLD(i.e., The Good)Gives us distortion(i.e., The Ugly)Wald, Savoy, fMRI MR Physics
MRI can yield many types of “Contrast”:Proton Density; T1-Weighted;T2-Weighted; MRAPDcontrast enhanced; 95%abcdMRAT2Pittsburgh, June 13-17, 2001T1Functional MRI in Clinical ResearchRobert Savoy
What is NMR?NUCLEARMAGNETICRESONANCEA magnet, a glass of water,and a radio wave source and detector .Almost every idea in MRI is easy.but the combined collection is complicated.Wald, Savoy, fMRI MR Physics
A Modern MRI; circa 2003Figure from Huettel, et. alia (2004)FigureWald, Savoy, fMRI MR Physicsfrom Huettel, et. alia (2004)12
BprotonsEarthʼsFieldNEWSWald, Savoy, fMRI MR Physicscompass
Compass needlesEarthʼsFieldυzMainFieldBoNorthNEWySxFreq γ BWald, Savoy, fMRI MR Physics42.58 MHz/T
Gyroscopic motionMainFieldBozNorth Proton has magnetic momentMy Proton has spin(angular momentum) gyroscopic precessionxLarmor precession freq. 42.58 MHz/TWald, Savoy, fMRI MR Physicsυ γ Bo
EXCITATION : Displacing the spinsfrom Equilibrium (North)Problem: It must be moving for us to detect it.Solution: knock out of equilibrium so it oscillatesHow? 1) Tilt the magnet or compass suddenly2) Drive the magnetization (compass needle)with a periodic magnetic fieldWald, Savoy, fMRI MR Physics
Excitation: ResonanceWhy does only one frequency efficiently tipprotons?Resonant driving force.It’s like pushing a child on a swing in time withthe natural oscillating frequency.Wald, Savoy, fMRI MR Physics
z is "longitudinal" directionx-y is "transverse" planeStaticFieldzB0yM0Applied RFFieldxThe RF pulse rotates M0 the about applied fieldWald, Savoy, fMRI MR Physics
The NMR SignalRFtimeVoltage(Signal)timeυυozBoz90 zMoyyyxxWald, Savoy, fMRI MR PhysicsυoV(t)x
Physical Foundations of MRINMR: 60 year old phenomena that generates thesignal from water that we detect.MRI: using NMR signal to generate an imageSix magnetic fields (5 are generated by coils):1) magnetic field of a nucleus, e.g., H1 on water2) static magnetic field Bo3) RF field that excites the spins B14-6) gradient fields that encode spatial infoGx, Gy, GzWald, Savoy, fMRI MR Physics
Three Steps in MR:0) Equilibrium (magnetization points along B0)1) RF Excitation (tip magn. away from equil.)2) Precession induces signal,dephasing (timescale T2, T2*).3) Return to equilibrium (timescale T1).Wald, Savoy, fMRI MR Physics
Magnetization vector during theNMR experimentRFencodetimeVoltage(Signal)MzMxyWald, Savoy, fMRI MR Physics
A bit more to temporal scale.FID:Free Induction DecayTERFencodeT2*Voltage(Signal)MzMxyT2*Wald, fMRI MR Physicstime
Three places in the process tomake a measurement (image)0) Equilibrium (magnetization points along Bo)1) RF Excitation (tip magnetization away fromequilibrium)protondensityweighting2) Precession induces signal, allow to dephasefor time TE.T2 or T2*weighting3) Return to equilibrium (timescale T1).T1 WeightingWald, Savoy, fMRI MR Physics
Contrast in MRI: proton densityForm image immediately afterexcitation (creation of signal).Tissue with more protons per cc givemore signal and is thus brighter on theimage.No chance to dephase, thus nodifferences due to different tissue T2 orT2* values.Magnetization starts fully relaxed (fullMz), thus no T1 weighting.Wald, Savoy, fMRI MR Physics
Contrast in MRI: proton densityImage immediately after excitationNo time for relaxation!Signal proportional to# of spins in voxelAll MRI images have proton densityweighting underlying them Wald, fMRI MR PhysicsCSF gray white
nal)From MxyMzT1encodeT2encodeencodegrey matter (long T1) (long T2*)white matter (short T1) (short T2*)time
PDProton Density Weighting(not used in fMRI)TRRFVoltage(Signal)From MxyMzT1encodeT2encodeencodegrey matter (long T1) (long T2*)white matter (short T1) (short T2*)time
T2*-DephasingWait time TE after excitation before measuring M.Shorter T2* spins have dephasedzzzyyyvectorsumxinitiallyWald, Savoy, fMRI MR Physicsat t TExxIs smaller
T2* DephasingJust showing the tips of the vectors in the laboratory frame and in the rotating frameWald, Savoy, fMRI MR Physics
T2* decay graphsTransverse Magnetization1.0T2* 2000.8Tissue #10.6T2* 600.40.20.00Wald, Savoy, fMRI MR PhysicsTissue #2204060Time (milliseconds)80100
T2* Weighting. usually used for BOLD contrastTR: MUCH LONGERRFVoltage(Signal)From MxyMzT1encodeT2encodegrey matter (long T1) (long T2*)white matter (short T1) (short T2*)time
T2* WeightingPhantoms withfour different T2* decay rates.There is no contrast differenceimmediately after excitation, mustwait (but not too long!).Choose TE for maximum intensitydifference.Wald, Savoy, fMRI MR Physics
Spin Echo (T2 contrast)Some dephasing can be refocused because its due tostatic fields.180 z90 yt 0xzt TEcho!zzyyyxxxt T ( )Blue arrows precesses faster due to localfield inhomogeneity than red arrowWald, Savoy, fMRI MR Physicst 2T
Spin Echo180 pulse only helps cancel static inhomogeneityThe “runners” can have static speed distribution.If a runner trips, he will not make it back in phase with the others.TETE/2Wald, Savoy, fMRI MR PhysicsTE/2Shown inShown inLaboratory FrameRotating Frame
NMR SignalT2 weighed spin echo imagegraywhiteTime to Echo , TE (ms)Wald, fMRI MR Physics
T2 Weighting90 RF180 RF.usually used clinical anatomy, but may beused for BOLD, especially at higher fields.TR: MUCH LONGERVoltage(Signal)From MxyMzT1encodeT2grey matter (long T1) (long T2*)white matter (short T1) (short T2*)encotime
T1-Weighting1.0white matterT1 600Signal0.8grey matterT1 10000.6CSFT1 30000.40.20.0010002000TR (milliseconds)Wald, Savoy, fMRI MR Physics3000
T1 weighting in MRI.How is it possible?Wald, Savoy, fMRI MR Physics
PDProton Density Weighting(not used in fMRI)TRRFVoltage(Signal)From MxyMzT1encodeT2encodeencodegrey matter (long T1) (long T2*)white matter (short T1) (short T2*)time
T2* Weighting. usually used for BOLD contrastTR: MUCH LONGERRFVoltage(Signal)From MxyMzT1encodeT2encodegrey matter (long T1) (long T2*)white matter (short T1) (short T2*)time
T1T2whitemattervoxelRFgreymattervoxelT1 Weightingit possible?. How isTRVoltage(Signal)From MxyMzT1encodeT2encodeencodegrey matter (long T1) (long T2*)white matter (short T1) (short T2*)time
Image contrast summary: TR, TELongProtonDensityT2, T2*TRShortT1poor!ShortWald, Savoy, fMRI MR PhysicsLongTE
Basis of fMRI: BOLD contrastQualitative Changes During ActivationObservation of Hemodynamic Changes! ! Direct Flow effects!!! ! Blood oxygenation effectsWald, Savoy, fMRI MR Physics
Blood cell magnetizationand Oxygen StateBoM 0OxygenatedB 0 Red CellWald, Savoy, fMRI MR PhysicsM χBde-Oxygenated Red CellB
Addition of paramagnetic compoundto blood: T2* effectBoLocal field is heterogeneous Water is dephased T2* shortens,Signal goes down on EPIWald, Savoy, fMRI MR PhysicsH 2O
Deoxygenated blood attenuates signalin T2*-weighted MR imagesO2Figure from Rick HogeMRI volume elementPittsburgh, June 13-17, 2001Functional MRI in Clinical ResearchRobert Savoy
Decrease of Venous DeoxyhemoglobinConcentration During Increased PerfusionO2Figure from Rick HogePittsburgh, June 13-17, 2001Functional MRI in Clinical ResearchRobert Savoy
Close up on a few hydrogen nuclei, the Larmorfrequencies of each, and how they add up O2 MRI volume elementPittsburgh, June 13-17, 2001Functional MRI in Clinical ResearchRobert Savoy
Addition of paramagnetic compoundto bloodBoSignal from water is dephasedT2* shortens, Signal goesdown on T2* weighted imageWald, Savoy, fMRI MR Physics
Neuronal Activation . . .Produces local hemodynamic changes(Roy and Sherrington, 1890)Increases local blood flowIncreases local blood volumeBUT, relatively little change in oxygen consumptionWald, Savoy, fMRI MR Physics
Deoxyhemoglobin concentration goes downwhen flow goes up1 sec1 secVenous outflow (4 balls/ sec.)1 secconsumption 3 balls/sec.1 secVenous outflow (6 balls/ sec.)Wald, Savoy, fMRI MR Physicsconsumption 3 balls/sec.
Paramagnetic compound in blood: T2also changes.BoWater diffusion pathH 2O10umDiffusion through local fields gives dynamic phase changesnot refocused by spin echo T2 shortens, S goes down on spin echo EPI T2 effect increases with Bo2Wald, Savoy, fMRI MR Physics
Why does T2 in extravascular waternot change for large vessels?Field outside large “magnetized” venule is approx.constant on length scale of water mean path ( 25um)θBoField is constant over waterpath, but magnitudedepends on vessleorientation. Thus T2* effectonly.Water diffusion path50umWald, Savoy, fMRI MR Physics
Extravascular T2 does not changefor large vesselsField outside large “magnetized” venule is approx.constant on length scale of water mean path ( 25um)θBovenuleWater diffusionpath50umWald, fMRI MR PhysicscapillaryBoWater samples different fieldswhile diffusing
MR pulse sequences to see BOLDConsiderations:Signal increase 0 to 5% (small)Motion artifact on conventional image is 0.5% - 3% need to “freeze motion”Need to see changes on timescale of hemodynamicchanges (seconds)Requirement:!Fast, “single shot” imaging, imagein 80ms, set of slices every 1-3 seconds.Wald, Savoy, fMRI MR Physics
Part IIMR imaging methods for fMRIWald, Savoy, fMRI MR Physics
Magnetic field gradient:the key to image encodingBoGx xUniform magnetzxWald, Savoy, fMRI MR PhysicsField fromgradient coilsBo Gx xTotal field
Figures from Huettel, et. alia (2004)Wald, Savoy, fMRI MR Physics59
A gradient causes a spread of frequenciesBoyMR frequency of the protons ina given location is proportional tothe local applied field.υoWald, Savoy, fMRI MR PhysicsBo# of spinsυBo Gz zB Fieldv γBTOT γ(Bo Gz z)zzυ
Step one: excite a sliceBoyWhile the grad. is on,excite only band offrequencies.Bo Gz zzBRFotSignal inten.B Field(w/ z gradient)zGztΔvWald, Savoy, fMRI MR PhysicsvWhy?
Step two:encode spatial info. in-planey“Frequency encoding”Bo along zxBTOT Bo Gz xBSignalxυυwith gradientWald, Savoy, fMRI MR Physicsυowithout gradient
ʻPulse sequenceʼ so farRFt“slice select”Gz“freq. encode”(read-out)GxttS(t)Sample pointsWald, Savoy, fMRI MR Physicst
Step 3: “Phase encoding”RF“slice select”Gz“phase encode”Gy“freq. encode”(read-out)GxttttS(t)tWald, Savoy, fMRI MR Physics
“Spin-warp” encodingkyRF“slice select”Gz“phase enc”Gy“freq. enc”(read-out)Gxttta1a2kxtS(t)tone excitation, one line of kspace.Wald, Savoy, fMRI MR Physics
“Spin-warp” encoding mathematicsKeep track of the phase.Phase due to readout:θ(t) ωo t γ Gx x tPhase due to P.E.θ(t) ωo t γ Gy y τΔθ(t) ωo t γ Gx x t γ Gy y τWald, Savoy, fMRI MR PhysicsRFtGztGyGxta1a2tS(t)t
What’s the difference?“fast” imagingconventional MRIRF“slice select”“freq. xWald, Savoy, fMRI MR PhysicstGzkx
Susceptibility in MRGives usBOLD(i.e., The Good)Gives usdropouts(i.e., The Bad)Gives usdistortion(i.e., The Ugly)Wald, Savoy, fMRI MR Physics
What do we mean by“susceptibility”?In physics, it refers to a material’s tendency tomagnetize when placed in an external field.In MR, it refers to the effects of magnetized materialon the image through its local distortion of thestatic magnetic field Bo.Wald, Savoy, fMRI MR Physics
What is the source of susceptibility?Bo1) deoxyHeme is paramagnetic2) Water is diamagnetic (χ -10-5)3) Air is paramagnetic (χ 4x10-6)Pattern of B field outsidemagnetic object in auniform field The magnet has a spatially uniform fieldbut your head is magnetic Wald, Savoy, fMRI MR Physics
Ping-pong ball in water Susceptibility effects occur nearmagnetically dis-similar materialsField disturbance around airsurrounded by water (e.g. sinuses)BoField map(coronal image) 1.5TWald, Savoy, fMRI MR Physics
Bo map in head: itʼs the air tissueinterface Sagittal Bo field maps at 3TWald, Savoy, fMRI MR Physics
Susceptibility field (in Gauss)increases w/ BoPing-pong ball in H20:Field maps (ΔTE 5ms), black lines spacedby 0.024G (0.8ppm at 3T)1.5TWald, Savoy, fMRI MR Physics3T7T
What is the effect of having a non-uniform fieldon the MR image?Sagittal Bo field map at 3TLocal field changes with position.To the extent the change is linear, local suscept. field gradient.We expect uniform field andcontrollable externalgradients Wald, Savoy, fMRI MR Physics
Local susceptibility gradients:two effects1) Local dephasing of the signal (signal loss) within avoxel, mainly from thru-plane gradients2) Local geometric distortions, (voxel locationimproperly reconstructed) mainly from local in-planegradients.Wald, Savoy, fMRI MR Physics
1) Non-uniform Local FieldCauses Local Dephasing5 waterprotons indifferent partsof the voxel Sagittal Bo field map at 3Tzz90 yslowestxT 0Wald, Savoy, fMRI MR PhysicsfastestT TE
Thru-plane dephasing gets worseat longer TE3T, TE 21, 30, 40, 50, 60msWald, Savoy, fMRI MR Physics
Mitigation: thru-planedephasing; easy to implement1) Good shimming. (1st and 2nd order)2) Use thinner slices,preferably with isotropic voxels.Drawback: takes more slicesto cover the brain.3) Use shorter TE.Drawback: BOLD contrast is optimizedfor TE T2*local. Thus BOLD isonly optimized for the poorsusceptibility regions.Wald, Savoy, fMRI MR Physics
Problem #2 Susceptibility CausesImage Distortion in EPIField nearsinusyTo encode the image, we controlphase evolution as a function ofposition with applied gradients.Local suscept. Gradient causesunwanted phase evolution.yWald, Savoy, fMRI MR PhysicsThe phase encode error builds upwith time. Δθ γ Blocal Δt
Susceptibility CausesImage DistortionyField nearsinusyConventional grad. echo,Δθ α encode time α 1/BWWald, Savoy, fMRI MR Physics
Bandwidth is asymmetric in EPI Adjacent points in kx haveshort Δt 5 us (high bandwidth)ky Adjacent points along ky are takenwith long Δt ( 500us). (lowbandwidth)The phase error (and thus distortions)are in the phase encode direction.Wald, Savoy, fMRI MR Physicskx
Susceptibility Causes Image DistortionEchoplanar Image,Δθ α encode time α 1/BWz3T head gradientsField near sinusWald, Savoy, fMRI MR PhysicsEncode time 34, 26, 22, 17ms
Susceptibility in EPI can give eithera compression or expansionAltering the direction kspace istransversed causes either localcompression or expansion.choose your poison Wald, Savoy, fMRI MR Physics3T whole body gradients
EPI needs second order shims EPI distortion ispartially alleviated withsecond order shimsMovie of EPI at 1.5Twith and withoutsecond order shimsWald, Savoy, fMRI MR Physics
Coils23-Channel ExperimentalWald, Savoy, fMRI MR Physics85
With fast gradients, add parallel imaging{Acquisition:Folded datasets Coil sensitivitymapsWald, Savoy, fMRI MR PhysicsSENSESMASHReconstruction:Reduced k-spacesamplingFolded images ineach receiver channel
GRAPPA for EPI susceptibility3T Trio, MRI Devices Inc. 8 channel arrayb 1000 DWI imagesiPAT (GRAPPA) 0, 2x, 3xFast gradients are the foundation, but EPI stillsuffers distortionWald, Savoy, fMRI MR Physics
fMRI w/8 channelphased array1.5mm isotropicTE 30ms EPI3T, 8ch array,GRAPPA 2Wald, Savoy, fMRI MR Physics
Wald, Savoy, fMRI MR Physics
ing,dephasingEddy currents:ghostsblurringk 0 is sampled:1/2 through1stCorners of kspace:yesnoGradient demands:very highpretty highWald, Savoy, fMRI MR Physics
EPI and SpiralsEPI at 3TWald, Savoy, fMRI MR PhysicsSpirals at 3T(courtesy Stanford group)
Introduction to the Physics of NMR, MRI, BOLD fMRI (with an orientation toward the practical aspects of data acquisition) Pittsburgh, June 13-17, 2011. Wald, Savoy, fMRI MR Physics Massachusetts General Hospital Athinoula A. Martinos Center MR physics and safety for functional MRI Lawrence L. Wald, Ph.D. Wald, Savoy, fMRI MR Physics
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