Wald, fMRI MR Physics Massachusetts General Hospital Athinoula A. Martinos Center MR physics for fMRI Lawrence L. Wald, Ph.D.

Wald, fMRI MR Physics Outline: 1) Review: MR signal 2) Review: MR contrast 3) Image encoding

Wald, fMRI MR Physics B N S W E Earth’s Field protons compass

Wald, fMRI MR Physics Compass needles N S W E  x y z Main Field B o MHz/T Earth’s Field North Freq =  B

Wald, fMRI MR Physics Gyroscopic motion Main Field B o Larmor precession freq. = MHz/T x y z North Proton has magnetic moment Proton has spin (angular momentum) >>gyroscopic precession  =  B o M

Wald, fMRI MR Physics 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 x y z Static Field Applied RF Field z is "longitudinal" direction x-y is "transverse" plane The RF pulse rotates Mo the about applied field Mo

Wald, fMRI MR Physics The NMR Signal x y z RF time x y z Voltage (Signal) time oo  x y z oo 90° V(t) BoBo Mo

Wald, fMRI MR Physics 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 G x, G y, G z

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 Voltage (Signal) time encode 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 x y z x y z x y z vector sum initiallyat t= TE

Wald, fMRI MR Physics T2* = 200 T2* = Time (milliseconds) Transverse Magnetization T2* decay graphs Tissue #2 Tissue #1

Wald, fMRI MR Physics 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 RF Voltage (Signal) Mz time encode T1 weighting in MRI TR grey matter (long T1) white matter (short T1) encode

Wald, fMRI MR Physics white matter T1 = TR (milliseconds) Signal grey matter T1 = 1000 CSF T1 = 3000 T1-Weighting

Wald, fMRI MR Physics TR Long Short Long TE Proton Density T1 poor! Image contrast summary: TR, TE T2

Wald, fMRI MR Physics 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 Oxygenated Red Cell de-Oxygenated Red Cell BoBo

Wald, fMRI MR Physics Addition of paramagnetic compound to blood: T2* effect BoBo H2OH2O Local field is heterogeneous Water is dephased T2* shortens, S goes down on EPI

Wald, fMRI MR Physics Addition of paramagnetic compound to blood BoBo 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 Venous out flow (4 balls/ sec.) consumption = 3 balls/sec. Venous out flow (6 balls/ sec.) consumption = 3 balls/sec. Deoxy. Heme Conc. goes down when flow goes up 1 sec

Wald, fMRI MR Physics Activation So: venous O2 deoxy Hb concentration  less magnetic stuff less dephasing MR signal increases on T2* weighted image Increases blood flow (F  Increases blood volume (V ) Small increase in oxygen consumption   

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 Uniform magnet Field from gradient coils Total field B o G x x B o + G x x x z

Wald, fMRI MR Physics Gradient field for MR encoding The magnet’s field is homogeneous. A gradient coil is a spool of wire designed to provide a linear “trim” field. Gradient coil in magnet BoBo z B(z) 0 z B0B0 z = 0 z

Wald, fMRI MR Physics A gradient causes a spread of frequencies BoBo z y z B Field Bo B o + G z z # of spins oo  MR frequency of the protons in a given location is proportional to the local applied field. v =  B TOT =  (B o + G z z) 

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

Wald, fMRI MR Physics Step two: encode spatial info. in-plane x y x B B TOT = B o + G z x B o along z oo  with gradient “Frequency encoding” Signal  without gradient

Wald, fMRI MR Physics ‘Pulse sequence’ so far RF S(t) GzGz GxGx “slice select” “freq. encode” (read-out) Sample points t t t t

Wald, fMRI MR Physics “Phase encoding” RF t S(t) t GzGz t GyGy “slice select” “phase encode” GxGx t “freq. encode” (read-out) t

Wald, fMRI MR Physics How does blipping on a grad. encode spatial info? y B Field (w/ z gradient) BoBo BoBo GyGy  y1y1 y2y2 z y y1y1 y2y2 all y locs process at same freq. all y locs process at same freq. spins in forehead precess faster...  (y) =  B TOT =  (B o +  y G y )  (y) =  (y) t =   y (G y t)

Wald, fMRI MR Physics How does blipping on a grad. encode spatial info? yxyx z x y z oo 90° yx after RFAfter the blipped y gradient... position y 2 position 0 position y 1 z z z y y1y1 y2y2 BoBo  y  =  y  =  G y  y 

Wald, fMRI MR Physics How does blipping on a grad. encode spatial info? The magnetization in the xy plane is wound into a helix directed along y axis. Phases are ‘locked in’ once the blip is over. y  y  =  y  =  G y  y 

Wald, fMRI MR Physics Big gradient blip area means tighter helix y small blip medium blip large blip  y  =  y   =  G y  y   y  G y 

Wald, fMRI MR Physics Signal after the blip: Consider 2 samples: uniform water 1 cm no signal observed signal is as big as if no gradient yy

Wald, fMRI MR Physics 10 mm kxkx kyky 1/10 mm 1/5mm 1/2.5mm 1/1.2mm = 1/Resolution You’ve measured: intensity at a spatial frequency... y

Wald, fMRI MR Physics kxkx kyky 1 / Res x 1 / FOV x FOV x = matrix * Res x Fourier transform

Wald, fMRI MR Physics Frequency encoding revisited RF S(t) GzGz GxGx t t t t Kspace, the movie...

Wald, fMRI MR Physics “Spin-warp” encoding “slice select” “phase enc” “freq. enc” (read-out) kxkx kyky one excitation, one line of kspace... RF t S(t) t GzGz t GyGy GxGx t t a1a1 a2a2

Wald, fMRI MR Physics Image encoding strategies: FLASH kyky kxkx RF GzGz GxGx GyGy Sample One shot per readout line…

Wald, fMRI MR Physics Image encoding strategies: FLASH kyky kxkx RF GzGz GxGx GyGy Sample TE One shot per readout line…

Wald, fMRI MR Physics Image encoding strategies: FLASH kyky kxkx RF GzGz GxGx GyGy Sample TE One shot per readout line…

Wald, fMRI MR Physics Image encoding strategies: FLASH kyky kxkx RF GzGz GxGx GyGy Sample TE One shot per readout line…

Wald, fMRI MR Physics Image encoding strategies: FLASH kyky kxkx RF GzGz GxGx GyGy Sample TE One shot per readout line…

Wald, fMRI MR Physics Image encoding strategies: FLASH kyky kxkx RF GzGz GxGx GyGy Sample TE One shot per readout line…

Wald, fMRI MR Physics Image encoding strategies: FLASH kyky kxkx RF GzGz GxGx GyGy Sample TE One shot per readout line…

Wald, fMRI MR Physics Image encoding strategies: FLASH RF GzGz GxGx GyGy Sample TE 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. One shot per readout line…

Wald, fMRI MR Physics kxkx kyky 1 / Res x 1 / FOV x FOV x = matrix * Res x Fourier transform

Wald, fMRI MR Physics kspace (magnitude) Image space (magnitude) Fourier transform kxkx kyky

Wald, fMRI MR Physics Image encoding strategies: EPI kyky kxkx RF GzGz GxGx GyGy Sample All lines in one shot…

Wald, fMRI MR Physics Image encoding strategies: EPI kyky kxkx RF GzGz GxGx GyGy Sample All lines in one shot… esp

Wald, fMRI MR Physics Image encoding strategies: EPI kyky kxkx RF GzGz GxGx GyGy Sample All lines in one shot… esp

Wald, fMRI MR Physics Image encoding strategies: EPI kyky kxkx RF GzGz GxGx GyGy Sample All lines in one shot… esp

Wald, fMRI MR Physics Image encoding strategies: EPI kyky kxkx RF GzGz GxGx GyGy Sample All lines in one shot… esp

Wald, fMRI MR Physics Image encoding strategies: EPI kyky kxkx RF GzGz GxGx GyGy Sample All lines in one shot… esp

Wald, fMRI MR Physics Image encoding strategies: EPI Performance is parameterized by ESP for a given resolution GxGx esp ESP BW in PE = 1/esp gives image distortion in mm. Total readout length: gives image distortion in pixel units. 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) The phase error (and thus distortions) are in the phase encode direction.  =  kxkx kyky  t=0.005ms  t=0.5ms  

Wald, fMRI MR Physics Image encoding strategies: EPI Packing in the slices… RF t GzGz t GyGy GxGx t t TE bottom halftop half 1/2 of EPI readout fat sat start next slice 15ms30ms15ms 5ms Total = 65ms => 15 slices per second

Wald, fMRI MR Physics Image encoding strategies: Spirals kyky kxkx RF GzGz GxGx GyGy Sample All kspace in one shot… TE “spiral out”

Wald, fMRI MR Physics Image encoding strategies: Spiral All kspace in one shot… 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.  t=0.005ms  t=0.5ms kyky kxkx

Wald, fMRI MR Physics Image encoding strategies: Spirals RF GzGz GxGx GyGy TE If TE = T 2 * (BOLD max) then signal down ~3 fold by first sample. High kspace is severely filtered. dead time exp(-t/T 2 *) Two problems: 1) deadtime. 2) kspace filtering

Wald, fMRI MR Physics “Spin-warp” encoding mathematics Keep track of the phase... RF t S(t) t GzGz t GyGy GxGx t t a1a1 a2a2 Phase due to readout:  (t) =  o t +  G x x t Phase due to P.E.  (t) =  o t +  G y y   (t) =  o t +  G x x t +  G y y 

Wald, fMRI MR Physics “Spin-warp” encoding mathematics Signal at time t from location (x,y) The coil integrates over object: Substituting k x = -  G x t and k x = -  G x t :

Wald, fMRI MR Physics “Spin-warp” encoding mathematics View signal as a matrix in k x, k y … : Solve for  (x,y,)

Wald, fMRI MR Physics 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 B o 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 B o.

Wald, fMRI MR Physics What is the source of susceptibility? The magnet has a spatially uniform field but your head is magnetic… 1) deoxyHeme is paramagnetic 2) Water is diamagnetic (  = ) 3) Air is paramagnetic (  = 4x10 -6 ) Pattern of B field outside magnetic object in a uniform field… BoBo

Wald, fMRI MR Physics Susceptibility effects occur near magnetically dis-similar materials Field disturbance around air surrounded by water (e.g. sinuses) Field map (coronal image) 1.5T BoBo Ping-pong ball in water…

Wald, fMRI MR Physics B o 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/ B o 1.5T 3T 7T Ping-pong ball in H 2 0: Field maps (  TE = 5ms), black lines spaced by 0.024G (0.8ppm at 3T)

Wald, fMRI MR Physics 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…

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 in- plane gradients.

Wald, fMRI MR Physics 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 slowest fastest x y z 90° T = 0 T = TE

Wald, fMRI MR Physics 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 mm 1.5mm voxel 1.4mm x 1.4mm x 2mm EPI N. Kanwisher face study SNR is proportional to voxel volume but contrast?

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, ) 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, )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 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. The phase encode error builds up with time.  =  B local  t y y

Wald, fMRI MR Physics Susceptibility Causes Image Distortion Field near sinus y y Conventional grad. echo,   encode time  1/BW

Wald, fMRI MR Physics Bandwidth is asymmetric in EPI kxkx kyky Adjacent points in k x have short  t = 5 us (high bandwidth) Adjacent points along k y are taken with long  t (= 500us). (low bandwidth) The phase error (and thus distortions) are in the phase encode direction.

Wald, fMRI MR Physics Susceptibility Causes Image Distortion Field near sinus z Echoplanar Image,   encode time  1/BW Encode time = 34, 26, 22, 17ms 3T head gradients

Wald, fMRI MR Physics RF t GzGz t GyGy GxGx t ‘echo spacing’ (esp) esp = 500 us for whole body grads, readout length = 32 ms esp = 270us for 3T, readout length = 17 ms Characterization of grad. performance length of readout train for given resolution or echo spacing (esp) or freq of readout…

Wald, fMRI MR Physics Parallel Imaging: speed up by 2x… FFT kspace, every other line (under-sampled) Folded, but many SMASH, GRAPPA SENSE FFT

Wald, fMRI MR Physics 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… 3T whole body gradients

Wald, fMRI MR Physics Effect of Ear & Mouth Shim on EPI From P. Jezzard, Oxford B0B0

Wald, fMRI MR Physics EPI and Spirals kxkx kyky GxGx GyGy kxkx kyky GxGx GyGy

Wald, fMRI MR Physics EPISpirals Susceptibility:distortion,blurring,dephasing Eddy currents:ghostsblurring k = 0 is sampled:1/2 through1st Corners of kspace:yesno Gradient demands:very highpretty high

Wald, fMRI MR Physics EPI and Spirals EPI at 3T Spirals at 3T (courtesy Stanford group)

Wald, fMRI MR Physics

Dephasing: local field variations Near low deOxy Hb conc. z t S(t) oo  S(  )  Near high deOxy Hb conc.. t S(t) oo  S(  )  FT T2*

Wald, fMRI MR Physics Contrast/Noise Ratio and Echo Time (TE) t S a = S o exp(-R a t) S b = S o exp(-R b t) R a = 1/T 2a * R b = 1/T 2b *  R = R a - R b