introduction to the physics of nmr, mri, bold fmri · wald, savoy, fmri mr physics physical...

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.


Outline:

Part 1:MR signalMR contrastfMRI contrast

Part 3:MR Safety

Part 2:Image encoding (10 minute version)Imaging considerations for fMRI


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


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


Singal Decays Expontntially

Signal decays exponentially

MaximumSignal Fading... Fading... Gone


Time


Different Rates of Decay

"Inject Signal" Time

Rate of decay varies across voxels

(90° saturation rf-pulse)


Faces Contrast for fMRIImage contrast varies with time


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


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)


MRI can yield many types of “Contrast”:Proton Density; T1-Weighted;

T2-Weighted; MRA

contrast enhanced; 95%

dc

a b

PD T1

T2 MRA


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.


A Modern MRI; circa 2003

12Figure from Huettel, et. alia (2004)

Figure from Huettel, et. alia (2004)


B

N

S

W E

EarthʼsField

protons

compass


Compass needles

N

S

W E

υ

x

y

zMainField Bo

42.58 MHz/T

EarthʼsField North

Freq = γ B


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


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


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.


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


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°


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


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).


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


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


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.


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



encodeencode encode

T1 T2

PD Proton Density Weighting (not used in fMRI)


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…


T2* Dephasing

Just showing the tips of the vectors…

in the laboratory frame … and in the rotating frame


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


encode encode


T1 T2

T2* Weighting ... usually used for BOLD contrast


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.


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°


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


T2 weighed spin echo image

gray

white

Time to Echo , TE (ms)

NM

R S

igna

l

90°RF

Mz

time

TR: MUCH LONGER


180°RF

encode encode


T1 T2

T2 Weighting ...usually used clinical anatomy, but may be used for BOLD, especially at higher fields.


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


T1 weighting in MRI...

...How is it possible?

RF

Mz

time

TR



encodeencode encode

T1 T2

PD Proton Density Weighting (not used in fMRI)

RF

Mz

time

TR: MUCH LONGER


encode encode


T1 T2

T2* Weighting ... usually used for BOLD contrast

RF

Mz

time

TR



encodeencode encode

white mattervoxel

grey matter voxel

T1 T2

T1 T2

T1 Weighting ... How is it possible?


TR

Long

Short

Short LongTE

ProtonDensity

T1 poor!

Image contrast summary: TR, TE

T2, T2*


Basis of fMRI: BOLD contrast

Qualitative Changes During Activation

Observation of Hemodynamic Changes

! ! • Direct Flow effects!!

! ! • Blood oxygenation effects


Blood cell magnetization and Oxygen State

Oxygenated Red Cell de-Oxygenated Red Cell

Bo

B=0

M = 0

B

M = χB


Addition of paramagnetic compoundto blood: T2* effect

Bo

H2OLocal field is heterogeneous• Water is dephased• T2* shortens, Signal goes down on EPI


Deoxygenated blood attenuates signalin T2

*-weighted MR images

MRI volume element

O2

Figure from Rick Hoge


Decrease of Venous DeoxyhemoglobinConcentration During Increased Perfusion

O2

Figure from Rick Hoge


Close up on a few hydrogen nuclei, the Larmor frequencies of each, and how they add up

MRI volume element

O2

+ =

+ =


Addition of paramagnetic compoundto blood

Bo

Signal from water is dephased

T2* shortens, Signal goes down on T2* weighted image


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


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


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


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


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


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.


Part IIMR imaging methods for fMRI


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)


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


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?


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


ʻPulse sequenceʼ so far

RF

S(t)

Gz

Gx

“slice select”

“freq. encode” (read-out)

Sample points t

t

t

t


Step 3: “Phase encoding”

RF

t

S(t)

tGz t

Gy

“slice select”

“phase encode”

Gx t“freq. encode” (read-out)

t


“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


“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


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


Susceptibility in MR

Gives us BOLD

(i.e., The Good)

Gives us dropouts

(i.e., The Bad)

Gives us distortion

(i.e., The Ugly)


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.


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


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…


Bo map in head: itʼs the air tissue interface…

Sagittal Bo field maps at 3T


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)


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…


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.


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


Thru-plane dephasing gets worse at longer TE

3T, TE = 21, 30, 40, 50, 60ms


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.


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


Susceptibility Causes Image Distortion

Field near sinus

y

y

Conventional grad. echo, Δθ α encode time α 1/BW


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.


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


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


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


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


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


fMRI w/ 8 channel phased array

1.5mm isotropic TE=30ms EPI3T, 8ch array,GRAPPA =2


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


EPI and Spirals

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

introduction to the physics of nmr, mri, bold fmri · wald, savoy, fmri mr physics physical...

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