Introduction to the Physics of NMR, MRI, BOLD fmri

Transcription

1 Pittsburgh, June 13-17, 2011 Introduction to the Physics of NMR, MRI, BOLD fmri (with an orientation toward the practical aspects of data acquisition) Pittsburgh, June 13-17, 2001 Functional MRI in Clinical Research Robert Savoy

2 MR physics and safety for functional MRI Lawrence L. Wald, Ph.D. Massachusetts General Hospital Athinoula A. Martinos Center

3 Outline: Part 1: Part 2: Part 3: MR signal MR contrast fmri contrast Image encoding (10 minute version) Imaging considerations for fmri MR Safety

4 Basics of Functional MRI Hemodynamics Roy and Sherrington History BOLD / Flow Instrumental Source of the Data NMR MRI Contrast Flexibility of Tool 8 Magnetic Fields and Relaxation Maximum Signal (minimal contrast) "Inject Signal" (90 saturation rf-pulse) Time No Signal (no contrast) Pittsburgh, June 13-17, 2001 Functional MRI in Clinical Research Robert Savoy

5 MRI in a Slide: MRI In a Slide 8 Magnetic Fields and Relaxation To Obtain the NMR Signal: Three Magnetic Fields µ The magnetic field of a nucleus with spin B0 The main magnetic field, used to align nuclei B1 The radio-frequency field, used to flip nuclei Relaxation: Two ways for the signal to go away T1 Longitudinal: The nuclei re-align with B0 T2 Transverse: The nuclei get out-of-phase To Select Slices and Make Images: Three More Fields G x, G y, G z The gradient fields Shim Fields To make better images Shielding Fields To protect us from all of the above! Pittsburgh, June 13-17, 2001 Functional MRI in Clinical Research Robert Savoy

6 Signal decays exponentially Maximum Signal Fading... Fading... Gone Singal Decays Expontntially Time "Inject Signal" (90 saturation rf-pulse) Pittsburgh, June 13-17, 2001 Functional MRI in Clinical Research Robert Savoy

7 Rate of decay varies across voxels Different Rates of Decay "Inject Signal" (90 saturation rf-pulse) Pittsburgh, June 13-17, 2001 Time Functional MRI in Clinical Research Robert Savoy

8 Image contrast varies with time Faces Contrast for fmri Maximum Signal (Little Contrast) Maximum Signal (minimal contrast) Intermediate Signals (Useful Contrasts) Minimum Signal (No Contrast) No Signal (no contrast) "Inject Signal" "Inject Signal" (90 saturation rf-pulse) (90 saturation rf-pulse) Pittsburgh, June 13-17, 2001 Time Time So, we must WAIT for dephasing to occur, in order to get T2 or T2* contrast. But while we are waiting, various bad things happen: signal decreases; imaging artifacts appear Functional MRI in Clinical Research Robert Savoy

9 Susceptibility in MR Gives us dropout (signal loss) (i.e., The Bad) Gives us BOLD (i.e., The Good) Gives us distortion (i.e., The Ugly)

10 MRI can yield many types of Contrast : Proton Density; T1-Weighted; T2-Weighted; MRA PD contrast enhanced; 95% T1 a c b d T2 MRA Pittsburgh, June 13-17, 2001 Functional MRI in Clinical Research Robert Savoy

11 What is NMR? NUCLEAR MAGNETIC RESONANCE A 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.

12 A Modern MRI; circa 2003 Figure from Huettel, et. alia (2004) Figure from Huettel, et. alia (2004) 12

13 B protons Earthʼs Field N W E compass S

14 Compass needles υ N Earthʼs Field z North Main Field Bo W E y S Freq = γ B MHz/T x

15 Gyroscopic motion Main Field Bo z North M y Proton has magnetic moment Proton has spin (angular momentum) >>gyroscopic precession Larmor precession freq. = MHz/T x υ = γ B o

16 EXCITATION : Displacing the spins from Equilibrium (North) Problem: It must be moving for us to detect it. Solution: knock out of equilibrium so it oscillates How? 1) Tilt the magnet or compass suddenly 2) Drive the magnetization (compass needle) with a periodic magnetic field

17 Excitation: Resonance Why does only one frequency efficiently tip protons? Resonant driving force. It s like pushing a child on a swing in time with the natural oscillating frequency.

18 z is "longitudinal" direction x-y is "transverse" plane z Static Field B0 y Applied RF Field M0 x The RF pulse rotates M0 the about applied field

19 The NMR Signal RF time Voltage (Signal) time υ υ o B o Mo z y z 90 y z y x υ o x V(t) x

20 Physical Foundations of MRI NMR: 60 year old phenomena that generates the signal from water that we detect. MRI: using NMR signal to generate an image Six magnetic fields (5 are generated by coils): 1) magnetic field of a nucleus, e.g., H1 on water 2) static magnetic field Bo 3) RF field that excites the spins B1 4-6) gradient fields that encode spatial info Gx, Gy, Gz

21 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).

22 Magnetization vector during the NMR experiment RF Voltage (Signal) encode time Mz Mxy

23 A bit more to temporal scale... FID: Free Induction Decay RF Voltage (Signal) TE encode T2* time Mz Mxy T2* Wald, fmri MR Physics

24 Three places in the process to make a measurement (image) 0) Equilibrium (magnetization points along Bo) 1) RF Excitation (tip magnetization away from equilibrium) proton density weighting 2) Precession induces signal, allow to dephase for time TE. 3) Return to equilibrium (timescale =T1). T2 or T2* weighting T1 Weighting

25 Contrast in MRI: proton density Form image immediately after excitation (creation of signal). Tissue with more protons per cc give more signal and is thus brighter on the image. No chance to dephase, thus no differences due to different tissue T2 or T2* values. Magnetization starts fully relaxed (full Mz), thus no T1 weighting.

26 Contrast in MRI: proton density Image immediately after excitation No time for relaxation! Signal proportional to # of spins in voxel All MRI images have proton density weighting underlying them CSF > gray > white Wald, fmri MR Physics

27 RF T1 T2 white matter voxel grey matter voxel TR Voltage (Signal) From Mxy Mz encode encode encode T1 T2 grey matter (long T1) (long T2*) white matter (short T1) (short T2*) time

28 RF PD Proton Density Weighting (not used in fmri) TR Voltage (Signal) From Mxy Mz encode encode encode T1 T2 grey matter (long T1) (long T2*) white matter (short T1) (short T2*) time

29 T2*-Dephasing Wait time TE after excitation before measuring M. Shorter T2* spins have dephased z z z y y y initially x at t= TE x vector sum x Is smaller

30 T2* Dephasing Just showing the tips of the vectors in the laboratory frame and in the rotating frame

31 1.0 T2* decay graphs Transverse Magnetization T2* = 200 Tissue #1 T2* = 60 Tissue # Time (milliseconds)

32 T2* Weighting... usually used for BOLD contrast RF TR: MUCH LONGER Voltage (Signal) From Mxy Mz encode encode T1 T2 grey matter (long T1) (long T2*) white matter (short T1) (short T2*) time

33 T2* Weighting Phantoms with four different T2* decay rates... There is no contrast difference immediately after excitation, must wait (but not too long!). Choose TE for maximum intensity difference.

34 Spin Echo (T2 contrast) Some dephasing can be refocused because its due to static fields. z 90 y z y 180 z y Echo! z y t = 0 x t = T x t = T (+) x t = 2T x Blue arrows precesses faster due to local field inhomogeneity than red arrow

35 Spin Echo 180 pulse only helps cancel static inhomogeneity The runners can have static speed distribution. If a runner trips, he will not make it back in phase with the others. TE TE/2 TE/2 Shown in Laboratory Frame Shown in Rotating Frame

36 T2 weighed spin echo image NMR Signal white gray Time to Echo, TE (ms) Wald, fmri MR Physics

37 T2 Weighting 90 RF 180 RF...usually used clinical anatomy, but may be used for BOLD, especially at higher fields. TR: MUCH LONGER Voltage (Signal) From Mxy Mz encode enco T1 T2 grey matter (long T1) (long T2*) white matter (short T1) (short T2*) time

38 T1-Weighting Signal white matter T1 = 600 grey matter T1 = 1000 CSF T1 = TR (milliseconds) 3000

39 T1 weighting in MRI......How is it possible?

40 RF PD Proton Density Weighting (not used in fmri) TR Voltage (Signal) From Mxy Mz encode encode encode T1 T2 grey matter (long T1) (long T2*) white matter (short T1) (short T2*) time

41 T2* Weighting... usually used for BOLD contrast RF TR: MUCH LONGER Voltage (Signal) From Mxy Mz encode encode T1 T2 grey matter (long T1) (long T2*) white matter (short T1) (short T2*) time

42 RF T1 T2 white matter voxel grey matter voxel T1 Weighting it possible? TR... How is Voltage (Signal) From Mxy Mz encode encode encode T1 T2 grey matter (long T1) (long T2*) white matter (short T1) (short T2*) time

43 Image contrast summary: TR, TE TR Long Short Proton Density T1 T2, T2* poor! Short TE Long

44 Basis of fmri: BOLD contrast Qualitative Changes During Activation Observation of Hemodynamic Changes!! Direct Flow effects!!! Blood oxygenation effects

45 Blood cell magnetization and Oxygen State B o M = 0 M = χb Oxygenated Red Cell de-oxygenated Red Cell

46 Addition of paramagnetic compound to blood: T2* effect B o Local field is heterogeneous Water is dephased T2* shortens, Signal goes down on EPI H 2 O

47 Deoxygenated blood attenuates signal in T 2* -weighted MR images O 2 MRI volume element Pittsburgh, June 13-17, 2001 Functional MRI in Clinical Research Figure from Rick Hoge Robert Savoy

48 Decrease of Venous Deoxyhemoglobin Concentration During Increased Perfusion O 2 Figure from Rick Hoge Pittsburgh, June 13-17, 2001 Functional MRI in Clinical Research Robert Savoy

49 Close up on a few hydrogen nuclei, the Larmor frequencies of each, and how they add up + = O 2 + = MRI volume element Pittsburgh, June 13-17, 2001 Functional MRI in Clinical Research Robert Savoy

50 Addition of paramagnetic compound to blood B o Signal from water is dephased T2* shortens, Signal goes down on T2* weighted image

51 Neuronal Activation... Produces local hemodynamic changes (Roy and Sherrington, 1890) Increases local blood flow Increases local blood volume BUT, relatively little change in oxygen consumption

52 Deoxyhemoglobin concentration goes down when flow goes up 1 sec 1 sec flow (4 balls/ sec.) 1 sec consumption = 3 balls/sec. Venous out 1 sec flow (6 balls/ sec.) consumption = 3 balls/sec. Venous out

53 Paramagnetic compound in blood: T2 also changes. B o H 2 O Water diffusion path Diffusion through local fields gives dynamic phase changes not refocused by spin echo T2 shortens, S goes down on spin echo EPI T2 effect increases with B o 2 10um

54 Why does T2 in extravascular water not change for large vessels? Field outside large magnetized venule is approx. constant on length scale of water mean path (~25um) B o θ Field is constant over water path, but magnitude depends on vessle orientation. Thus T2* effect only. 50um Water diffusion path

55 Extravascular T2 does not change for large vessels Field outside large magnetized venule is approx. constant on length scale of water mean path (~25um) θ venule capillary B o Water diffusion path B o 50um Wald, fmri MR Physics Water samples different fields while diffusing

56 MR pulse sequences to see BOLD Considerations: 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 hemodynamic changes (seconds) Requirement:! Fast, single shot imaging, image in 80ms, set of slices every 1-3 seconds.

57 Part II MR imaging methods for fmri

58 Magnetic field gradient: the key to image encoding Bo Gx x Bo + Gx x Uniform magnet z x Field from gradient coils Total field

59 Figures from Huettel, et. alia (2004) 59

60 A gradient causes a spread of frequencies y B o MR frequency of the protons in a given location is proportional to the local applied field. z v = γb TOT = γ(b o + G z z) B Field Bo B o + G z z z υ o υ # of spins υ

61 Step one: excite a slice y B o z While the grad. is on, excite only band of frequencies. B Field (w/ z gradient) B o B o + G z z z RF t Signal inten. G z t Δv v Why?

62 Step two: encode spatial info. in-plane B o along z y Frequency encoding x B B TOT = B o + G z x x Signal with gradient υ υ o υ without gradient

63 ʻPulse sequenceʼ so far RF slice select G z t t freq. encode (read-out) G x S(t) t Sample points t

64 Step 3: Phase encoding slice select phase encode RF G z G y t t t freq. encode (read-out) G x S(t) t t

65 Spin-warp encoding slice select RF G z t t k y phase enc G y t freq. enc (read-out) G x S(t) a 1 a 2 t t k x one excitation, one line of kspace...

66 Spin-warp encoding mathematics Keep track of the phase... Phase due to readout: θ(t) = ωo t + γ G x x t RF t Phase due to P.E. θ(t) = ωo t + γ G y y τ Δθ(t) = ωo t + γ G x x t + γ G y y τ G z G y G x S(t) a 1 a 2 t t t t

67 What s the difference? conventional MRI fast imaging slice select RF G z t RF G z t G y G y freq. enc (read-out) G x S(t) G x S(t) T2* k y etc... t k y k x k x

68 Susceptibility in MR Gives us BOLD (i.e., The Good) Gives us dropouts (i.e., The Bad) Gives us distortion (i.e., The Ugly)

69 What do we mean by susceptibility? In physics, it refers to a material s tendency to magnetize when placed in an external field. In MR, it refers to the effects of magnetized material on the image through its local distortion of the static magnetic field B o.

70 What is the source of susceptibility? 1) deoxyheme is paramagnetic 2) Water is diamagnetic (χ = ) 3) Air is paramagnetic (χ = 4x10-6 ) B o The magnet has a spatially uniform field but your head is magnetic Pattern of B field outside magnetic object in a uniform field

71 Ping-pong ball in water Susceptibility effects occur near magnetically dis-similar materials Field disturbance around air surrounded by water (e.g. sinuses) B o Field map (coronal image) 1.5T

72 B o map in head: itʼs the air tissue interface Sagittal Bo field maps at 3T

73 Susceptibility field (in Gauss) increases w/ B o Ping-pong ball in H 2 0: Field maps (ΔTE = 5ms), black lines spaced by 0.024G (0.8ppm at 3T) 1.5T 3T 7T

74 What is the effect of having a non-uniform field on the MR image? Sagittal B o field map at 3T Local field changes with position. To the extent the change is linear, = local suscept. field gradient. We expect uniform field and controllable external gradients

75 Local susceptibility gradients: two effects 1) Local dephasing of the signal (signal loss) within a voxel, mainly from thru-plane gradients 2) Local geometric distortions, (voxel location improperly reconstructed) mainly from local in-plane gradients.

76 1) Non-uniform Local Field Causes Local Dephasing Sagittal B o field map at 3T 5 water protons in different parts of the voxel z 90 z y slowest x T = 0 fastest T = TE

77 Thru-plane dephasing gets worse at longer TE 3T, TE = 21, 30, 40, 50, 60ms

78 Mitigation: thru-plane dephasing; easy to implement 1) Good shimming. (1st and 2nd order) 2) Use thinner slices, preferably with isotropic voxels. Drawback: takes more slices to cover the brain. 3) Use shorter TE. Drawback: BOLD contrast is optimized for TE = T2* local. Thus BOLD is only optimized for the poor susceptibility regions.

79 Problem #2 Susceptibility Causes Image Distortion in EPI Field near sinus y y To encode the image, we control phase evolution as a function of position with applied gradients. Local suscept. Gradient causes unwanted phase evolution. The phase encode error builds up with time. Δθ = γ B local Δt

80 Susceptibility Causes Image Distortion Field near sinus y y Conventional grad. echo, Δθ α encode time α 1/BW

81 Bandwidth is asymmetric in EPI Adjacent points in k x have short Δt = 5 us (high bandwidth) k y Adjacent points along ky are taken with long Δt (= 500us). (low bandwidth) The phase error (and thus distortions) are in the phase encode direction. k x

82 Susceptibility Causes Image Distortion Echoplanar Image, Δθ α encode time α 1/BW z Field near sinus 3T head gradients Encode time = 34, 26, 22, 17ms

83 Susceptibility in EPI can give either a compression or expansion Altering the direction kspace is transversed causes either local compression or expansion. choose your poison 3T whole body gradients

84 EPI needs second order shims EPI distortion is partially alleviated with second order shims Movie of EPI at 1.5T with and without second order shims

85 Coils 23-Channel Experimental 85

86 With fast gradients, add parallel imaging { Acquisition: SMASH Reduced k-space sampling SENSE Folded images in each receiver channel Reconstruction: Folded datasets + Coil sensitivity maps

87 GRAPPA for EPI susceptibility 3T Trio, MRI Devices Inc. 8 channel array b=1000 DWI images ipat (GRAPPA) = 0, 2x, 3x Fast gradients are the foundation, but EPI still suffers distortion

88 fmri w/ 8 channel phased array 1.5mm isotropic TE=30ms EPI 3T, 8ch array, GRAPPA =2

89

90 EPI Spirals Susceptibility: distortion, blurring, dephasing dephasing Eddy currents: ghosts blurring k = 0 is sampled: 1/2 through 1st Corners of kspace: yes no Gradient demands: very high pretty high

91 EPI and Spirals EPI at 3T Spirals at 3T (courtesy Stanford group)