Pittsburgh, June 13-17, 2001 Robert SavoyFunctional MRI in Clinical Research
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 HospitalAthinoula A. Martinos Center
MR physics and safety for functional MRI
Lawrence L. Wald, Ph.D.
Wald, Savoy, fMRI MR Physics
Outline:
Part 1:MR signalMR contrastfMRI contrast
Part 3:MR Safety
Part 2:Image encoding (10 minute version)Imaging considerations for fMRI
Pittsburgh, June 13-17, 2001 Robert SavoyFunctional MRI in Clinical Research
Basics of Functional MRI•Hemodynamics
•Roy and Sherrington•History•BOLD / Flow
•Instrumental Source of the Data•NMR•MRI•Contrast•Flexibility of Tool
"Inject Signal" (90° saturation rf-pulse)
Maximum Signal(minimal contrast)
Time
No Signal(no contrast)
8 Magnetic Fields and Relaxation
Pittsburgh, June 13-17, 2001 Robert SavoyFunctional MRI in Clinical Research
MRI In a SlideMRI in a Slide:
8 Magnetic Fields and Relaxation
01
x y z
12
■ To Obtain the NMR Signal: Three Magnetic Fields µ The magnetic field of a nucleus with spin B The main magnetic field, used to align nuclei B The radio-frequency field, used to flip nuclei
■ Relaxation: Two ways for the signal to go away T Longitudinal: The nuclei re-align with B T Transverse: The nuclei get out-of-phase
■ To Select Slices and Make Images: Three More Fields G , G , G The gradient fields
■ Shim Fields To make better images■ Shielding Fields To protect us from all of the above!
0
Pittsburgh, June 13-17, 2001 Robert SavoyFunctional MRI in Clinical Research
Singal Decays Expontntially
Signal decays exponentially
MaximumSignal Fading... Fading... Gone
"Inject Signal" (90° saturation rf-pulse)
Time
Pittsburgh, June 13-17, 2001 Robert SavoyFunctional MRI in Clinical Research
Different Rates of Decay
"Inject Signal" Time
Rate of decay varies across voxels
(90° saturation rf-pulse)
Pittsburgh, June 13-17, 2001 Robert SavoyFunctional MRI in Clinical Research
Faces Contrast for fMRIImage contrast varies with time
"Inject Signal" (90° saturation rf-pulse)
Maximum Signal(minimal contrast)
Time
No Signal(no contrast)
MaximumSignal
Time
(Little Contrast)
"Inject Signal"
(90° saturation rf-pulse)
MinimumSignal
(No Contrast)
IntermediateSignals
(Useful Contrasts)
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
Wald, Savoy, fMRI MR Physics
Susceptibility in MR
Gives us BOLD(i.e., The Good)
Gives us “dropout” (signal loss)(i.e., The Bad)
Gives us distortion(i.e., The Ugly)
Pittsburgh, June 13-17, 2001 Robert SavoyFunctional MRI in Clinical Research
MRI can yield many types of “Contrast”:Proton Density; T1-Weighted;
T2-Weighted; MRA
contrast enhanced; 95%
dc
a b
PD T1
T2 MRA
Wald, Savoy, fMRI MR Physics
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.
Wald, Savoy, fMRI MR Physics
A Modern MRI; circa 2003
12Figure from Huettel, et. alia (2004)
Figure from Huettel, et. alia (2004)
Wald, Savoy, fMRI MR Physics
B
N
S
W E
EarthʼsField
protons
compass
Wald, Savoy, fMRI MR Physics
Compass needles
N
S
W E
υ
x
y
zMainField Bo
42.58 MHz/T
EarthʼsField North
Freq = γ B
Wald, Savoy, fMRI MR Physics
Gyroscopic motion
MainField Bo
Larmor precession freq. = 42.58 MHz/Tx
y
z North • Proton has magnetic moment
• Proton has spin (angular momentum)
>>gyroscopic precession
υ = γ Bo
M
Wald, Savoy, fMRI MR Physics
EXCITATION : Displacing the spinsfrom 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, Savoy, 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, Savoy, fMRI MR Physics
x
y
z
StaticField
Applied RFField
z is "longitudinal" directionx-y is "transverse" plane
The RF pulse rotates M0 the about applied field
B0
M0
Wald, Savoy, fMRI MR Physics
The NMR Signal
x
y
z
RF
time
x
y
z
Voltage(Signal)
time
υo
υ
V(t)
Bo
Mo
x
y
z
υo
90°
Wald, Savoy, 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
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
Wald, 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 the NMR experiment
RF
Voltage(Signal)
timeencode
Mz
Mxy
Wald, fMRI MR Physics
A bit more to temporal scale...
RF
Voltage(Signal)
timeencode
Mz
MxyT2*
T2*
TE
FID: Free Induction Decay
Wald, Savoy, fMRI MR Physics
Three places in the process to make a measurement (image)
0) Equilibrium (magnetization points along Bo)
1) RF Excitation (tip magnetization away from equilibrium)
2) Precession induces signal, allow to dephase for time TE.
3) Return to equilibrium (timescale =T1).
protondensityweighting
T2 or T2*weighting
T1 Weighting
Wald, Savoy, fMRI MR Physics
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.
Wald, fMRI MR Physics
Contrast in MRI: proton density
No time for relaxation!
Signal proportional to # of spins in voxel
Image immediately after excitation
CSF > gray > whiteAll MRI images have proton density weighting underlying them…
RF
Mz
time
TR
grey matter (long T1) (long T2*)white matter (short T1) (short T2*)
Voltage(Signal)From Mxy
encodeencode encode
white mattervoxel
grey matter voxel
T1 T2
T1 T2
RF
Mz
time
TR
grey matter (long T1) (long T2*)white matter (short T1) (short T2*)
Voltage(Signal)From Mxy
encodeencode encode
T1 T2
PD Proton Density Weighting (not used in fMRI)
Wald, Savoy, 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
initially at t= TE
vectorsum
Is smaller…
Wald, Savoy, fMRI MR Physics
T2* Dephasing
Just showing the tips of the vectors…
in the laboratory frame … and in the rotating frame
Wald, Savoy, fMRI MR Physics
T2* = 200
T2* = 60
1008060402000.0
0.2
0.4
0.6
0.8
1.0
Time (milliseconds)
Tran
sver
se M
agne
tizat
ion
T2* decay graphs
Tissue #2
Tissue #1
RF
Mz
time
TR: MUCH LONGER
Voltage(Signal)From Mxy
encode encode
grey matter (long T1) (long T2*)white matter (short T1) (short T2*)
T1 T2
T2* Weighting ... usually used for BOLD contrast
Wald, Savoy, fMRI MR Physics
T2* Weighting
Phantoms withfour different T2* decay rates...
There is no contrast difference immediately after excitation, must wait (but not too long!).
Choose TE for maximum intensity difference.
Wald, Savoy, fMRI MR Physics
Spin Echo (T2 contrast)
Some dephasing can be refocused because its due to static fields.
t = 0x
y
z90°
t = T
Blue arrows precesses faster due to localfield inhomogeneity than red arrow
x
y
z
t = T (+) t = 2T
Echo!
x
y
z
x
y
z
180°
Wald, Savoy, fMRI MR Physics
Spin Echo180° 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.
Shown in
Laboratory Frame
Shown in
Rotating Frame
TE
TE/2TE/2
Wald, fMRI MR Physics
T2 weighed spin echo image
gray
white
Time to Echo , TE (ms)
NM
R S
igna
l
90°RF
Mz
time
TR: MUCH LONGER
Voltage(Signal)From Mxy
180°RF
encode encode
grey matter (long T1) (long T2*)white matter (short T1) (short T2*)
T1 T2
T2 Weighting ...usually used clinical anatomy, but may be used for BOLD, especially at higher fields.
Wald, Savoy, fMRI MR Physics
white matterT1 = 600
30002000100000.0
0.2
0.4
0.6
0.8
1.0
TR (milliseconds)
Sign
al
grey matterT1 = 1000
CSFT1 = 3000
T1-Weighting
Wald, Savoy, fMRI MR Physics
T1 weighting in MRI...
...How is it possible?
RF
Mz
time
TR
grey matter (long T1) (long T2*)white matter (short T1) (short T2*)
Voltage(Signal)From Mxy
encodeencode encode
T1 T2
PD Proton Density Weighting (not used in fMRI)
RF
Mz
time
TR: MUCH LONGER
Voltage(Signal)From Mxy
encode encode
grey matter (long T1) (long T2*)white matter (short T1) (short T2*)
T1 T2
T2* Weighting ... usually used for BOLD contrast
RF
Mz
time
TR
grey matter (long T1) (long T2*)white matter (short T1) (short T2*)
Voltage(Signal)From Mxy
encodeencode encode
white mattervoxel
grey matter voxel
T1 T2
T1 T2
T1 Weighting ... How is it possible?
Wald, Savoy, fMRI MR Physics
TR
Long
Short
Short LongTE
ProtonDensity
T1 poor!
Image contrast summary: TR, TE
T2, T2*
Wald, Savoy, fMRI MR Physics
Basis of fMRI: BOLD contrast
Qualitative Changes During Activation
Observation of Hemodynamic Changes
! ! • Direct Flow effects!!
! ! • Blood oxygenation effects
Wald, Savoy, fMRI MR Physics
Blood cell magnetization and Oxygen State
Oxygenated Red Cell de-Oxygenated Red Cell
Bo
B=0
M = 0
B
M = χB
Wald, Savoy, fMRI MR Physics
Addition of paramagnetic compoundto blood: T2* effect
Bo
H2OLocal field is heterogeneous• Water is dephased• T2* shortens, Signal goes down on EPI
Pittsburgh, June 13-17, 2001 Robert SavoyFunctional MRI in Clinical Research
Deoxygenated blood attenuates signalin T2
*-weighted MR images
MRI volume element
O2
Figure from Rick Hoge
Pittsburgh, June 13-17, 2001 Robert SavoyFunctional MRI in Clinical Research
Decrease of Venous DeoxyhemoglobinConcentration During Increased Perfusion
O2
Figure from Rick Hoge
Pittsburgh, June 13-17, 2001 Robert SavoyFunctional MRI in Clinical Research
Close up on a few hydrogen nuclei, the Larmor frequencies of each, and how they add up
MRI volume element
O2
+ =
+ =
Wald, Savoy, fMRI MR Physics
Addition of paramagnetic compoundto blood
Bo
Signal from water is dephased
T2* shortens, Signal goes down on T2* weighted image
Wald, Savoy, 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, Savoy, fMRI MR Physics
Venous outflow (4 balls/ sec.)
consumption = 3 balls/sec.
Venous outflow (6 balls/ sec.)
consumption = 3 balls/sec.
Deoxyhemoglobin concentration goes down when flow goes up
1 sec1 sec
1 sec1 sec
Wald, Savoy, fMRI MR Physics
Paramagnetic compound in blood: T2 also changes.
Bo
H2O
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 Bo2
10um
Water diffusion path
Wald, Savoy, fMRI MR Physics
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)
50umWater diffusion path
Field is constant over water path, but magnitude depends on vessle orientation. Thus T2* effect only.
Bo
θ
Wald, fMRI MR Physics
Extravascular T2 does not change for large vessels
Field outside large “magnetized” venule is approx. constant on length scale of water mean path (~25um)
50um
Water diffusionpath
Bo
θ
Bo
venule capillary
Water samples different fields while diffusing
Wald, Savoy, 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, Savoy, fMRI MR Physics
Part IIMR imaging methods for fMRI
Wald, Savoy, fMRI MR Physics
Magnetic field gradient: the key to image encoding
Uniform magnet Field from gradient coils Total field
Bo Gx x Bo + Gx x
x
z
Wald, Savoy, fMRI MR Physics 59
Figures from Huettel, et. alia (2004)
Wald, Savoy, fMRI MR Physics
A gradient causes a spread of frequencies
Bo
z
y
z
B
Fie
ld Bo
Bo + Gz z
# of
spin
s
υo
υ
MR frequency of the protons in a given location is proportional tothe local applied field.
v = γBTOT = γ(Bo + Gz z)
υ
Wald, Savoy, fMRI MR Physics
Step one: excite a slice
z
y
z
B
Fie
ld(w
/ z g
radi
ent)
Bo
Bo + Gz z
v
Sign
al in
ten.
Bo
Δv
While the grad. is on,excite only band of frequencies.
Gz
t
RF
t
Why?
Wald, Savoy, fMRI MR Physics
Step two: encode spatial info. in-plane
x
y
x
B BTOT = Bo + Gz x
Bo along z
υo
υ
with gradient
“Frequency encoding”
Sign
al
υwithout gradient
Wald, Savoy, fMRI MR Physics
ʻPulse sequenceʼ so far
RF
S(t)
Gz
Gx
“slice select”
“freq. encode” (read-out)
Sample points t
t
t
t
Wald, Savoy, fMRI MR Physics
Step 3: “Phase encoding”
RF
t
S(t)
tGz t
Gy
“slice select”
“phase encode”
Gx t“freq. encode” (read-out)
t
Wald, Savoy, fMRI MR Physics
“Spin-warp” encoding
“slice select”
“phase enc”
“freq. enc” (read-out)
kx
ky
one excitation, one line of kspace...
RF
tS(t)
tGz tGy
Gx t
t
a1
a2
Wald, Savoy, fMRI MR Physics
“Spin-warp” encoding mathematics
Keep track of the phase...
RF
tS(t)
tGz tGy
Gx t
t
a1
a2
Phase due to readout:
θ(t) = ωo t + γ Gx x t
Phase due to P.E.
θ(t) = ωo t + γ Gy y τ
Δθ(t) = ωo t + γ Gx x t + γ Gy y τ
Wald, Savoy, fMRI MR Physics
What’s the difference?
S(t)
“slice select”
“freq. enc” (read-out)
RFtGz
Gy
Gx
kx
ky
RF
tS(t)
tGz
Gy
Gx etc...T2*
conventional MRI
kx
ky
“fast” imaging
Wald, Savoy, fMRI MR Physics
Susceptibility in MR
Gives us BOLD
(i.e., The Good)
Gives us dropouts
(i.e., The Bad)
Gives us distortion
(i.e., The Ugly)
Wald, Savoy, 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, Savoy, fMRI MR Physics
What is the source of susceptibility?
The magnet has a spatially uniform field but your head is magnetic…
1) deoxyHeme is paramagnetic2) Water is diamagnetic (χ = -10-5)
3) Air is paramagnetic (χ = 4x10-6)
Pattern of B field outside magnetic object in a
uniform field…
Bo
Wald, Savoy, 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
Bo
Ping-pong ball in water…
Wald, Savoy, fMRI MR Physics
Bo map in head: itʼs the air tissue interface…
Sagittal Bo field maps at 3T
Wald, Savoy, fMRI MR Physics
Susceptibility field (in Gauss) increases w/ Bo
1.5T 3T 7T
Ping-pong ball in H20:Field maps (ΔTE = 5ms), black lines spaced by 0.024G (0.8ppm at 3T)
Wald, Savoy, fMRI MR Physics
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, Savoy, 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, Savoy, fMRI MR Physics
1) Non-uniform Local Field Causes Local Dephasing
Sagittal Bo field map at 3T 5 water protons in different parts of the voxel…
z
slowest
fastestx
y
z90°
T = 0 T = TE
Wald, Savoy, fMRI MR Physics
Thru-plane dephasing gets worse at longer TE
3T, TE = 21, 30, 40, 50, 60ms
Wald, Savoy, fMRI MR Physics
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.
Wald, Savoy, 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. Δθ = γ Blocal Δt
y
y
Wald, Savoy, fMRI MR Physics
Susceptibility Causes Image Distortion
Field near sinus
y
y
Conventional grad. echo, Δθ α encode time α 1/BW
Wald, Savoy, fMRI MR Physics
Bandwidth is asymmetric in EPI
kx
ky• Adjacent points in kx have short Δt = 5 us (high bandwidth)
• Adjacent points along ky are takenwith long Δt (= 500us). (low bandwidth)
The phase error (and thus distortions) are in the phase encode direction.
Wald, Savoy, fMRI MR Physics
Susceptibility Causes Image Distortion
Field near sinus
z
Echoplanar Image, Δθ α encode time α 1/BW
Encode time = 34, 26, 22, 17ms
3T head gradients
Wald, Savoy, 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, Savoy, fMRI MR Physics
EPI needs second order shims
• EPI distortion ispartially alleviated withsecond order shims
Movie of EPI at 1.5T with and without second order shims
Wald, Savoy, fMRI MR Physics 8523-Channel Experimental
Coils
Wald, Savoy, fMRI MR Physics
With fast gradients, add parallel imaging
Acquisition: SMA
SH
SENSE
Reconstruction:
Folded datasets+
Coil sensitivity maps
Reduced k-space sampling
{
Folded images ineach receiver channel
Wald, Savoy, fMRI MR Physics
GRAPPA for EPI susceptibility
Fast gradients are the foundation, but EPI still suffers distortion
3T Trio, MRI Devices Inc. 8 channel arrayb=1000 DWI images
iPAT (GRAPPA) = 0, 2x, 3x
Wald, Savoy, fMRI MR Physics
fMRI w/ 8 channel phased array
1.5mm isotropic TE=30ms EPI3T, 8ch array,GRAPPA =2
Wald, Savoy, fMRI MR Physics
Wald, Savoy, fMRI MR Physics
EPI SpiralsSusceptibility: 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
Wald, Savoy, fMRI MR Physics
EPI and Spirals
EPI at 3T Spirals at 3T(courtesy Stanford group)