I t d tiI t d tiIntroduction Introduction to to

M ti R I i (MRI) Ph iM ti R I i (MRI) Ph i

David C. Zhu, Ph.D.

Magnetic Resonance Imaging (MRI) PhysicsMagnetic Resonance Imaging (MRI) Physics

Cognitive Imaging Research CenterDepartments of Psychology and Radiology

Reading assignment for next three lectures:

(1) Read Chapters 1 5(1) Read Chapters 1-5.

(2) Watch “MRI-Made Easy” video.

~ 1937 Began the concept of magnetic resonance by Isidor Rabi

Nobel price in 1944

Felix Block and Edward Purcell discovered magnetic resonance

Nobel price in 1952~1945

Paul Lauterbur introduced spatial gradients~1972 Beginning of MRIspatial gradients to provide spatial information

g g

I t d ti fNobel price in 2003

~1976Introduction of echo-planar imaging (EPI)by Peter Mansfield

Fast MRI

First human-body 1.5T by GE1982 MRI technologyRapid growth

Discovery of BOLD contrastEarly 1990s Basis of fMRI

p g

GoalsGoalsGoalsGoals

1. Basic concepts of MRI2. Basic meanings of TE, TR, T1, T2, T2*, k space, EPI

An atom

Nucleusp+

e- p+

n

C l t d i MRICommon elements used in MRI:

1H, 13C, 23Na, 31P

Hydrogen

Nucleus

e- p+

( we have a lot of H2O)!

Spin Physics1H ( t ) classically:1H (proton)

Angular Momentum (spinspin)N

classically:

Magnetic dipole

Magnetic field B

S

Magnetic field B

Quantized to lower and higher energy states with a Boltzmann distribution: ~ 3 ppm/T excess in lower energy.

dM M B

Bloch Equation:

Bdt

M B

M = magnetization = net magnetic moment for all spins in a sample

= Larmor frequency= 42.58 MHz/T for proton

128 MHz at 3 TE = h , h = 6.626 x 10-34 J S

JT Bushberg, JA Seibert, EW Leidholdt Jr., and JM Boone. The Essential Physics of Medical Imaging

A happy volunteer after surviving a fMRI session

Magnet

Superconducting electromagnets

Magnet

Gradient coils -261C

RF coilsZero i t

Subject body

resistance

Coil for the static magnetic field

Gradient Coil

RF coils (Transmit and Receive)

surface coil volume coil phased-array coil

Magnetic Resonance Imaging Hardware Interface in Control RoomInterface in Control Room

fMRI stimulusfMRI stimulus presentation system

3T magnet Room

Equipment Room:Equipment Room:Gradient amplifiers

RF amplifierP l tPulse sequence generator

Image reconstruction

Spin-Lattice (T1) and Spin-Spin (T2) Relaxation Processes

(T2 becomes T2* if local field is inhomogeneous)

Z

M S i f t (dephasing)Z

M

Y

B0

Spins fan out (dephasing)

T2 decay

Longitudinal magnetization YInitial 90

XT1 recovery

re-growth

X

T deca and

T2 decay andT1 recovery

RF excitation

vector summation

Z

T2 decay andT1 recoverycontinueBack to

equilibrium state

1 ycontinue

TE = time of echo

TR = time of repetition

YRF

TE time of echo

X

T2* Decay and T1 Recovery Movie 1

http://www.stanford.edu/class/ee369b/Site/Movies.html

T2* Decay and T1 Recovery Movie 2

*2|)0(M||)(M| xyxyT

t

et

)1(M)(M 10z

Tt

et

*21 )1(0TTE

TTR

eekMS

Courtesy of Brian Hargreaves. http://www-mrsrl.stanford.edu/~brian/mri-movies/

TR = 3sGradient Echo

TR = 3s

TE = 6.9 ms TE = 45 ms

Spin Echo Techniques(Obtain the effect of T2 instead of T2* )

Spins fan out (dephasing) ZZ

M

Initial 90

p ( p g)

T2* decay

Y

180 RF excitation

TE/2

M

Y

B0

Initial 90RF excitation

X

TE/2

X

ZZ

YY

TE/2XX

Z

Y

X 128 MHzX

Z Z

128 MHz

Y Y

X X

127.9999 MHz 128.0001 MHz

Z

Y

X

Explanation of T2* decay

3.000 T 3.000 T

After 3 ms 3.000 T 3.000 T

Vectorsum

3.000 T 3.000 T 3.000 T 3.000 T

Af3+10-6 T 3.000 T

After 3 ms

Vectorsum3+10-6 T 3.000 T

3+2×10-6 T 3-10-6 T 3+2×10-6 T 3-10-6 T

Spin Echo Technique

Courtesy of Brian Hargreaves. http://www-mrsrl.stanford.edu/~brian/mri-movies/

Spin Echo

TE 13 TE 90

Proton density weighted

T2 weighted T1 weightedTE = 13 msTR 900TE = 13 ms TE = 90 ms

TR = 3 s

TR = 900 ms

TR 3 s21 )1(0

TTE

TTR

eekMS

Laboratory Frame

Courtesy of Brian Hargreaves. http://www-mrsrl.stanford.edu/~brian/mri-movies/

Rotating Frame

Courtesy of Brian Hargreaves. http://www-mrsrl.stanford.edu/~brian/mri-movies/

Long

T1

Relaxationtime

1

T2

Short

Molecular motion: slow intermediate fastllMolecular size:

Molecular interactions:

large intermediateintermediate

small

bound free

JT Bushberg, JA Seibert, EW Leidholdt Jr., and JM Boone. The Essential Physics of Medical Imaging

B

B B G Zz 0

Slice Selection

Z

- Z1

Z1B0

B G Zz0 1

2 1G Zz

0 G Zz

B G Zz0 1

Z

- Z1

Z10

0 1 G Zz

G Z

2 1G Zz

(a)

0 1 G Zz

(b)

RF coil

M

Gradient coils

RF with a narrow bandwidth Slice-select gradient

Y Magnet

B0ZX

Y

Excite a slice of tissue

B0

X

ZSpatial encoding using a gradient pulse

G

xYrot G X tx 1

Gx

0 G Xx

0 1 G Xx

Xrot

x 1

X

- X1

X1

0

G X

(b) At X1

Z 0 1 G XxZ

G X t(a)

Yrot

G X tx 1

Phase offset relative to rotating frame at 0Xrot

(c) At –X1

g 0

00 B

TR (time of repetition)

TE (time of echo)

Xgradient

( )

Gx

Gx tTx/2 Tx/2

Tx/2

Ygradient

t = 0

Gy Gradient Echo Sequence

Zgradient

Ty

TGz

Sequence

RF

g Tz

Tz/2

RF

DataAcquisitionAcquisition

Data acquisitionwindow

Acquire signal (Fourier Transform)

Frequency domain (k space)

Inverse Fourier Transform

Space domain

Dr. Seiji Ogawa

cycles/millimeter

millimeter

Transformation

Britney Spears on earth Britney Spears on Mars

ky (ky = 1/yfov) K space (Spatial Frequency Domain)

1st ky line

2nd ky line

(yres-1)/2

Xgradient

Gx

GTx/2 Tx/2

Tx/2

3rd ky linegradient

Y

Gx t

t = 0

x x

Gy

kx (k = 1/xfov)

-(xres-1)/2 (xres-1)/2Y

gradient

Ty

Gy

kx (kx 1/xfov)

ykixkixyxy

yxTt

eeeyxMtyxM 222)0,,(),,(

(kymax -1)th ky line

(kymax-2)th ky line

t

t

xx

dGk

dGk02

(kymax)th ky line-(yres-1)/2

dxdytyxMktS xy ),,()( 0

yy dGk02

http://www.revisemri.com/tutorials/what_is_k_space/

EPI Pulse Sequence

X Grad

Y Grad

Z GradZ Grad

RF

Time

Regular EPI Sequence

Xgradient gxep1 gxepdw

gxepw

g gxep1 gxepdw

gyep1

Ygradient gyepb

Zgradient

gzrf1

gz1

gzk

g

RF

gz1

Time

RF

EPI Pulse SequenceK space

Typical 64 64

KyTE

X Grad

Y Grad

63rd Ky line

Z Grad33rd Ky line

Kx

RF

Kx

Time

1st Ky line2nd Ky line

30 slices

Slice #30Sli #2Slice #1 Slice #3Slice #2

Slice #29

2 sec = TR

2 sec

Repeat many titimes

2 sec

Bimanual finger tapping motor study (P ≤ 10-7)(12 s resting and then 24 s finger tapping at 1 Hz, TR = 2 s)

2 sec

GoalsGoalsGoalsGoals

1. Basic concepts of MRI2. Basic meanings of TE, TR, T1, T2, T2*, k space, EPI

Artifacts due to back-and-forth trajectory in k space

Susceptibility artifacts

Image artifacts due to field variation

NormalNormal

Variation along X

Variation along Y

Variation l Zalong Z

Another common technique for fMRI: spiral imaging