MR physics for fMRI Lawrence L. Wald, Ph.D. Massachusetts General Hospital Athinoula A.
Download ReportTranscript MR physics for fMRI Lawrence L. Wald, Ph.D. Massachusetts General Hospital Athinoula A.
MR physics for fMRI Lawrence L. Wald, Ph.D. Massachusetts General Hospital Athinoula A. Martinos Center Wald, fMRI MR Physics Outline: 1) Review: MR signal 2) Review: MR contrast 3) Image encoding Wald, fMRI MR Physics B protons Earth’s Field N E W S Wald, fMRI MR Physics compass Compass needles Earth’s Field u z Main Field Bo North N E W y S x Freq = g B Wald, fMRI MR Physics 42.58 MHz/T Gyroscopic motion Main Field Bo z North • Proton has magnetic moment M y • Proton has spin (angular momentum) >>gyroscopic precession x Larmor precession freq. = 42.58 MHz/T Wald, fMRI MR Physics u = g Bo 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 Wald, fMRI MR Physics 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. Wald, fMRI MR Physics z is "longitudinal" direction x-y is "transverse" plane Static Field z y Mo Applied RF Field x The RF pulse rotates Mo the about applied field Wald, fMRI MR Physics The NMR Signal RF time Voltage (Signal) time u uo Bo z z 90° z y Mo y y x x Wald, fMRI MR Physics uo V(t) x 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 Three magnetic fields (generated by 3 coils) 1) static magnetic field Bo 2) RF field that excites the spins B1 3) gradient fields that encode spatial info Gx, Gy, Gz Wald, fMRI MR Physics Three Steps in MR: 0) Equilibrium (magnetization points along Bo) 1) RF Excitation (tip magn. away from equil.) 2) Precession induces signal, dephasing (timescale = T2, T2*). 3) Return to equilibrium (timescale = T1). Wald, fMRI MR Physics Magnetization vector during MR RF encode time Voltage (Signal) Mz Mxy T2* Wald, fMRI MR Physics Three places in process to make a measurement (image) 0) Equilibrium (magnetization points along Bo) 1) RF Excitation (tip magn. away from equil.) 2) Precession induces signal, allow to dephase for time TE. 3) Return to equilibrium (timescale =T1). proton density weighting T2 or T2* weighting T1 Weighting Wald, fMRI MR Physics T2*-Dephasing Wait time TE after excitation before measuring M. Shorter T2* spins have dephased z z z y y y vector sum x initially Wald, fMRI MR Physics x at t= TE x T2* decay graphs Transverse Magnetization 1.0 T2* = 200 0.8 Tissue #1 0.6 T2* = 60 0.4 0.2 0.0 0 Wald, fMRI MR Physics Tissue #2 20 40 60 Time (milliseconds) 80 100 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 max. inten. difference. Wald, fMRI MR Physics T1 weighting in MRI TR RF encode encode encode Voltage (Signal) Mz grey matter (long T1) white matter (short T1) Wald, fMRI MR Physics time T1-Weighting 1.0 white matter T1 = 600 Signal 0.8 grey matter T1 = 1000 0.6 CSF T1 = 3000 0.4 0.2 0.0 0 1000 2000 TR (milliseconds) Wald, fMRI MR Physics 3000 Image contrast summary: TR, TE Long Proton Density T2 TR Short T1 poor! Short Wald, fMRI MR Physics Long TE Basis of fMRI: BOLD contrast Qualitative Changes during activation Observation of Hemodynamic Changes • Direct Flow effects • Blood oxygenation effects Wald, fMRI MR Physics Blood cell magnetization and Oxygen State Bo M= B=0 Red Cell Oxygenated Wald, fMRI MR Physics M = B de-Oxygenated Red Cell B Addition of paramagnetic compound to blood: T2* effect Bo Local field is heterogeneous • Water is dephased • T2* shortens, S goes down on EPI Wald, fMRI MR Physics H 2O Addition of paramagnetic compound to blood Bo Signal from water is dephased T2* shortens, S goes down on T2* weighted image Wald, fMRI MR Physics 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 Wald, fMRI MR Physics Deoxy. Heme Conc. goes down when flow goes up 1 sec 1 sec Venous out flow (4 balls/ sec.) consumption = 3 balls/sec. 1 sec 1 sec Venous out flow (6 balls/ sec.) Wald, fMRI MR Physics consumption = 3 balls/sec. Activation • Increases blood flow (F ) • Increases blood volume (V ) • Small increase in oxygen consumption So: venous O2 deoxy Hb concentration less magnetic stuff less dephasing MR signal increases on T2* weighted image Wald, fMRI MR Physics 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. Wald, fMRI MR Physics Magnetic field gradient: the key to image encoding Bo Gx x Uniform magnet Field from gradient coils Bo + Gx x Total field z x Wald, fMRI MR Physics Gx Bz x Gradient field for MR encoding B(z) The magnet’s field is homogeneous. Bo z A gradient coil is a spool of wire designed to provide a linear “trim” field. B(z) z 0 z=0 B(z) Gradient coil in magnet B0 Wald, fMRI MR Physics z=0 z A gradient causes a spread of frequencies Bo y MR frequency of the protons in a given location is proportional to the local applied field. Wald, fMRI MR Physics Bo + Gz z Bo # of spins uo u B Field v = gBTOT = g(Bo + Gz z) z z u Step one: excite a slice y Bo While the grad. is on, excite only band of frequencies. Bo + Gz z B z RF o t Signal inten. B Field (w/ z gradient) z Dv Wald, fMRI MR Physics Gz t v Why? Step two: encode spatial info. in-plane y “Frequency encoding” Bo along z x BTOT = Bo + Gz x B Signal x u with gradient Wald, fMRI MR Physics uo u without gradient ‘Pulse sequence’ so far RF t “slice select” Gz “freq. encode” (read-out) Gx t t S(t) Sample points Wald, fMRI MR Physics t “Phase encoding” RF “slice select” “phase encode” “freq. encode” (read-out) Gz Gy Gx t t t t S(t) t Wald, fMRI MR Physics How does blipping on a grad. encode spatial info? Bo y t Gy y2 z B Field (w/ z gradient) y1 all y locs process at same freq. B all y locs process at same freq. o y y1 y2 u(y) = g BTOT = g (Bo +Dy Gy) Dq (y) = Du(y) t = g Dy (Gy t) Wald, fMRI MR Physics spins in forehead precess faster... How does blipping on a grad. encode spatial info? Bo y y2 q(y) = u(y)t= gGy Dy t after RF z y1 After the blipped y gradient... z z z z 90° x uo y Wald, fMRI MR Physics x position y2 y x y x position 0 position y1 y How does blipping on a grad. encode spatial info? y The magnetization in the xy plane is wound into a helix directed along y axis. Phases are ‘locked in’ once the blip is over. q(y) = u(y)t= gGy Dy t Wald, fMRI MR Physics Big gradient blip area means tighter helix y small blip Wald, fMRI MR Physics medium blip q(y) = u(y)t = gGy Dy t gDy (Gy t) large blip Signal after the blip: Consider 2 samples: y uniform water y no signal observed Wald, fMRI MR Physics 1 cm signal is as big as if no gradient You’ve measured: intensity at a spatial frequency... ky 1/1.2mm = 1/Resolution y 1/2.5mm 10 mm 1/5mm 1/10 mm kx Wald, fMRI MR Physics Fourier transform ky 1 / Resx kx FOVx = matrix * Resx Wald, fMRI MR Physics 1 / FOVx Frequency encoding revisited RF t Gz Gx t t S(t) t Kspace, the movie... Wald, fMRI MR Physics “Spin-warp” encoding ky RF “slice select” t Gz t “phase enc” Gy “freq. enc” (read-out) Gx t a2 a1 kx t S(t) t one excitation, one line of kspace... Wald, fMRI MR Physics Image encoding strategies: FLASH One shot per readout line… ky RF Gz Gx Gy Sample Wald, fMRI MR Physics kx Image encoding strategies: FLASH TE One shot per readout line… ky RF Gz Gx Gy Sample Wald, fMRI MR Physics kx Image encoding strategies: FLASH TE One shot per readout line… ky RF Gz Gx Gy Sample Wald, fMRI MR Physics kx Image encoding strategies: FLASH TE One shot per readout line… ky RF Gz Gx Gy Sample Wald, fMRI MR Physics kx Image encoding strategies: FLASH TE One shot per readout line… ky RF Gz Gx Gy Sample Wald, fMRI MR Physics kx Image encoding strategies: FLASH TE One shot per readout line… ky RF Gz Gx Gy Sample Wald, fMRI MR Physics kx Image encoding strategies: FLASH TE One shot per readout line… ky RF Gz Gx Gy Sample Wald, fMRI MR Physics kx Image encoding strategies: FLASH One shot per readout line… TE RF Gz Gx Gy Sample Wald, fMRI MR Physics • High BW in readout. • new excitation every PE line (“reboot”). • Lenghty (~5 s per slice) for 2mm res, TR=50ms • Physiol. fluctuations/ motion modulate phase/amplitude across kspace. • Strong inflow effects. • All readouts same polarity. • All kspace treated equally. Fourier transform ky 1 / Resx kx FOVx = matrix * Resx Wald, fMRI MR Physics 1 / FOVx Fourier transform ky kx kspace (magnitude) Wald, fMRI MR Physics Image space (magnitude) Image encoding strategies: EPI All lines in one shot… ky RF Gz kx Gx Gy Sample Wald, fMRI MR Physics Image encoding strategies: EPI All lines in one shot… ky RF Gz esp kx Gx Gy Sample Wald, fMRI MR Physics Image encoding strategies: EPI All lines in one shot… ky RF Gz esp kx Gx Gy Sample Wald, fMRI MR Physics Image encoding strategies: EPI All lines in one shot… ky RF Gz esp kx Gx Gy Sample Wald, fMRI MR Physics Image encoding strategies: EPI All lines in one shot… ky RF Gz esp kx Gx Gy Sample Wald, fMRI MR Physics Image encoding strategies: EPI All lines in one shot… ky RF Gz esp kx Gx Gy Sample Wald, fMRI MR Physics Image encoding strategies: EPI Performance is parameterized by ESP for a given resolution BW in PE = 1/esp gives image distortion in mm. ESP esp Total readout length: gives image distortion in pixel units. Gx 3mm EPI: esp = 500 us for whole body grads, readout length = 32 ms esp = 270us for head gradients, readout length = 17 ms Wald, fMRI MR Physics Bandwidth is asymmetric in EPI (Distortion is 100x more in phase direction) ky The phase error (and thus distortions) are in the phase encode direction. u1 u2 j = Dut kx dt=0.5ms Wald, fMRI MR Physics dt=0.005ms Image encoding strategies: EPI Packing in the slices… fat sat TE start next slice 1/2 of EPI readout RF t Gz t t Gy bottom half Gx top half t 15ms 30ms 15ms 5ms Total = 65ms => 15 slices per second Wald, fMRI MR Physics Image encoding strategies: Spirals All kspace in one shot… TE ky RF Gz kx Gx Gy Sample “spiral out” Wald, fMRI MR Physics Image encoding strategies: Spiral All kspace in one shot… ky kx dt=0.005ms dt=0.5ms Wald, fMRI MR Physics • Fast (high BW ) in azimuthal k. • Slow (low BW) in radial k. • No “reboot”, phase error accumulates. • Fast (~10 slices per second) for 2mm res. • Physiological fluctuations modulate overall intensity • Readouts alternating polarity. • All kspace NOT treated equally. Image encoding strategies: Spirals TE Two problems: 1) deadtime. 2) kspace filtering RF Gz If TE = T2* (BOLD max) then signal down ~3 fold by first sample. Gx dead time Gy exp(-t/T2*) Wald, fMRI MR Physics High kspace is severely filtered. “Spin-warp” encoding mathematics Keep track of the phase... Phase due to readout: q(t) = wo t + g Gx x t RF t Gz Phase due to P.E. q(t) = wo t + g Gy y t Dq(t) = wo t + g Gx x t + g Gy y t Wald, fMRI MR Physics t Gy Gx t a2 a1 t S(t) t “Spin-warp” encoding mathematics Signal at time t from location (x,y) S(t) (x, y)e igGx xtig Gy yt The coil integrates over object: S(t) (x, y)e igG x xtigG y yt dxdy object Substituting kx = -g Gx t and kx = -g Gx t : S(kx , k y ) (x, y)e object Wald, fMRI MR Physics ik x xik y y dxdy “Spin-warp” encoding mathematics View signal as a matrix in kx, ky… S(kx , k y ) (x, y)e ik x xik y y dxdy object : Solve for (x,y,) (x, y) FT 1 S(k x ,k y ) (x, y) S(k x ,ky )e kspace Wald, fMRI MR Physics ik x x ik y y dk x dk y Drawbacks of Single Shot Imaging • Require high gradient performance to eliminate susceptibility induced distortions. • Susceptibility in the head is worse at 3T than 1.5T. Wald, fMRI MR Physics Enemy #1 of EPI: local susceptibility gradients Bo field maps in the head Wald, fMRI MR Physics Susceptibility in MR Gives us BOLD Gives us dropouts Gives us distortion. Wald, fMRI MR Physics 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 Bo. Wald, fMRI MR Physics What is the source of susceptibility? Bo 1) deoxyHeme is paramagnetic 2) Water is diamagnetic (= -10-5) 3) Air is paramagnetic (= 4x10-6) Pattern of B field outside magnetic object in a uniform field… The magnet has a spatially uniform field but your head is magnetic… Wald, fMRI MR Physics Ping-pong ball in water… Susceptibility effects occur near magnetically dis-similar materials Field disturbance around air surrounded by water (e.g. sinuses) Bo Field map (coronal image) 1.5T Wald, fMRI MR Physics Bo map in head: it’s the air tissue interface… Sagittal Bo field maps at 3T Wald, fMRI MR Physics Susceptibility field (in Gauss) increases w/ Bo Ping-pong ball in H20: Field maps (DTE = 5ms), black lines spaced by 0.024G (0.8ppm at 3T) 1.5T Wald, fMRI MR Physics 3T 7T What is the effect of having a non-uniform field on the MR image? Sagittal Bo 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… Wald, fMRI MR Physics 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 inplane gradients. Wald, fMRI MR Physics 1) Non-uniform Local Field Causes Local Dephasing 5 water protons in different parts of the voxel… Sagittal Bo field map at 3T z z 90° y slowest x Wald, fMRI MR Physics T=0 fastest T = TE Thru-plane dephasing gets worse at longer TE 3T, TE = 21, 30, 40, 50, 60ms Wald, fMRI MR Physics Local susceptibility gradients: thru-plane dephasing Bad for thick slice above frontal sinus… Wald, fMRI MR Physics Partial volume effects: w/ focal activation, less is more... 1.4mm x 1.4mm x 2mm EPI SNR is proportional to voxel volume but contrast? 1.5mm voxel 2.5mm N. Kanwisher face study Wald, fMRI MR Physics Mitigation: thru-plane dephasing; easy to implement 1) Good shimming. (first and second order) 2) Use thinner slices preferably w/ isotropic voxel. Drawback: takes more to cover brain. 3) Use shorter TE. Drawback: BOLD contrast is optimized for TE = T2*local. Thus BOLD is only optimized for the poor susceptibility regions. Wald, fMRI MR Physics Mitigation: thru-plane dephasing; harder to implement 1) Bo correction. 2) “Z-shimming” Repeat measurement several times with an applied z gradients that rewind the dephasing, Pick the right gradient afterward on a pixel by pixel basis. (Drawback: multi shot or longer encode). MRM 39 p402, 1998. 2) Use special RF pulse with built-in prephasing in just the right places. (Drawback: long RF pulse, pre-phasing differs from person to person.) Glover et al. Proceed. ISMRM p298, 1998. 3) The “mouth shim” diamagnetic material in roof of mouth. Wilson, Jenkinson, Jezzard, Proceed. ISMRM p205, 2002. Wald, fMRI MR Physics Problem #2 Susceptibility Causes Image Distortion in EPI y Field near sinus To encode the image, we control phase evolution as a function of position with applied gradients. Local suscept. Gradient causes unwanted phase evolution. y The phase encode error builds up with time. Dq = g Blocal Dt Wald, fMRI MR Physics Susceptibility Causes Image Distortion y Field near sinus y Conventional grad. echo, Dq a encode time a 1/BW Wald, fMRI MR Physics Bandwidth is asymmetric in EPI ky • Adjacent points in kx have short Dt = 5 us (high bandwidth) • Adjacent points along ky are taken with long Dt (= 500us). (low bandwidth) kx The phase error (and thus distortions) are in the phase encode direction. Wald, fMRI MR Physics Susceptibility Causes Image Distortion Echoplanar Image, Dq a encode time a 1/BW z 3T head gradients Field near sinus Wald, fMRI MR Physics Encode time = 34, 26, 22, 17ms Characterization of grad. performance length of readout train for given resolution or echo spacing (esp) or freq of readout… RF Gz Gy t t t Gx ‘echo spacing’ (esp) esp = 500 us for whole body grads, readout length = 32 ms Wald, fMRI MR Physics esp = 270us for 3T, readout length = 17 ms Parallel Imaging: speed up by 2x… FFT Folded, but many kspace, every other line (under-sampled) SMASH, GRAPPA FFT Wald, fMRI MR Physics SENSE 4 fold GRAPPA acceleration sub-millimeter, single shot SE-EPI: 23 channel array 23 Channel array at 1.5T With and without 4x Accel. Single shot EPI, 256x256, 230mm FOV TE = 78ms Wald, fMRI MR Physics 32ch fMRI 1mm isotropic TE=30ms EPI 3T, 8ch array, GRAPPA =2 6/8 part-Fourier Wald, fMRI MR Physics 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… Wald, fMRI MR Physics 3T whole body gradients Effect of Ear & Mouth Shim on EPI B0 From P. Jezzard, Oxford Wald, fMRI MR Physics ky EPI and Spirals ky kx kx Gx Gy Wald, fMRI MR Physics Gx Gy EPI Spirals Susceptibility: distortion, dephasing blurring, dephasing Eddy currents: ghosts blurring k = 0 is sampled: 1/2 through 1st Corners of kspace: yes no Gradient demands: very high pretty high Wald, fMRI MR Physics EPI and Spirals EPI at 3T Wald, fMRI MR Physics Spirals at 3T (courtesy Stanford group) Wald, fMRI MR Physics Dephasing: local field variations Near low deOxy Hb conc. T2* S(t) FT S(u) Du t u u o Near high deOxy Hb conc. . FT S(t) t Wald, fMRI MR Physics S(u) Du u u o z Contrast/Noise Ratio and Echo Time (TE) Sa = So exp(-Rat) DS So e R a t So e R b t Sb = So exp(-Rbt) R t (RaDR ) R DS So e t Ra= 1/T2a* Rb= 1/T2b* DR = Ra - Rb a So e bt DS So e R a t (1 e DRt ) DS S o eR a t DRt (DS) 0 t t 1/ Ra TE T Wald, fMRI MR Physics * 2a