MRI Basics BIC Seminar 2010 › uploads › Seminars › 2011-09-19...2011/09/19 · • Initial submission on MRI to Nature was rejected (later published 1973). • “You could

NOT FOR DISTRIBUTION

Bruce Pike

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•  NMR physics •  relaxation & contrast •  scanner hardware & safety •  image formation and reconstruction •  BOLD fMRI •  diffusion MRI


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•  Nuclear Magnetic Resonance – NMR –  Nobel Prize in Physics to Rabi in 1944 –  Nobel Prize in Physics to Bloch & Purcell in 1952 –  Nobel Prize in Chemistry to Ernst in 1991

•  NMR in radiological Imaging – MRI –  Nobel Prize in Medicine or Physiology to Lauterbur & Mansfield 2006 –  Will fMRI be recognized by a Nobel Prize ?

•  public anxiety over the word nuclear resulted in MRI

Felix Bloch (1905-1983)

Edward Purcell (1912-1997)

Paul Lauterbur (1929-2007)

Peter Mansfield (1933-)

Richard Ernst (1933-)

Isidor Rabi (1898-1988)

Rick Hoge 1999 Rabi Award



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•  nuclei with an odd number of nucleons have angular momentum

•  magnetic moment, or spin

•  In biological tissue: 1H, 23Na, and 31P

N

S NOT FOR DISTRIBUTION


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•  when placed in a magnetic field B0, a spin will rotate around the direction of B0 (i.e. precess or resonate) at Larmor frequency:

f0 = !B0

where ! is the gyromagnetic ratio ! = 42.58 MHz/T for 1H

=> @ B0 = 1.5 T, f0 ~ 64 MHz

Sir Joseph Larmor (1857-1942)

B0


NOT FOR DISTRIBUTION •  Tesla (T)

–  international (SI) unit of magnetic flux density (B) –  named after Serbian inventor Nikola Tesla

•  contemporary and adversary of Tomas Edison •  alternating current, AC motors, x-ray tubes, etc. •  was not awarded a Nobel prize (1915)

–  old unit was the “Gauss (G)” •  1 T = 10,000 G

–  earth’s magnetic field is approximately 50 µT (0.5 G)

Nikola Tesla (1856-1943) B Pike/MNI 6


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•  magnetic moments (spins) align to external magnetic •  net excess of spins in parallel state (lower energy)

B0

external field B0

M

no magnetic field

B0=0

net magnetization, vector M




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x

y

z

M Mz Longitudinal

Magnetization

Mx (real)

My

(imaginary) Mxy is Complex Magnitude (length)

Phase (angle)

Mxy is Transverse Magnetization

Mxy = Mx + i My



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rotating frame of reference

excitation

M0

x’

y’

z

B1

B0

evolution

x

y

z

B0

stationary (lab) frame of reference

f0 = ! B0"NOT FOR DISTRIBUTION


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evolution


Individual spins in blue, Mxy in yellow, Mz in red

rotating frame of reference

excitation

B1 in yellow, M in red



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x

y

z

f0


0 0.2 0.4 0.6 0.8 1 -1

-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

0.8

1

Time

Free Induction Decay (FID) detection

B0

Signal

Frequency

FT

30 90 120 150 0 0

10

20

30

40

50

60

NMR Spectrum for a homogenous H20 sample

f0

1H in H2O Signal

Faraday’s Law of induction



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evolution

x

y

z

B0


f0= ! B0"

T1 recovery T2 decay 0 1 2 3 4

0

0.2

0.4

0.6

0.8

1

Time (s)

Mz recovery: T1

PD(1- e-t/T1)

0 0.1 0.2 0.3 0.4 0

0.2

0.4

0.6

0.8

1

Time (s)

Mxy decay: T2, T2*

PDe-t/T2

PDe-t/T2

*

Mz

Mxy



•  T2* is the observed decay time constant without correction for static field inhomogeneities

•  Gradient Echo signal depends upon T2*

•  T2 is the decay time constant with correction for static field inhomogeneities

•  Spin Echo signal depends upon T2

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M

x’

y’

z

RF (B1) 90

B0

x’

y’

z

x’

y’

z

RF (B1) 180 a

b

x’

y’

z

a

b

x’

y’

z

b

a

90oy 180o

x

TE/2 TE

FID

Spin-Echo

e -t/T2 e -t/T2*

RF ... time

Signal

time

e -TE/T2 NOT FOR DISTRIBUTION


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0 1 2 3 4 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

Time (s)

T1 relaxation

WM

GM

CSF Mz

0 0.6 0.8 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

Time (s)

T2 relaxation

GM

WM

CSF

0.2 0.4

Mxy

0 150 200 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

1

Time (ms)

T2* relaxation

blood: 100 % O2 sat

50 100

Mxy

blood: 70 % O2 sat

GM: T1 = 950ms T2 = 100ms PD= 0.8 WM: T1 = 600ms T2 = 80ms PD = 0.7 CSF: T1 = 4500ms T2 = 2200ms PD= 1.0



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•  excitation –  apply a rotating magnetic field B1 (RF)

•  evolution –  let M0 precess freely and relax –  waiting (TE)

•  detection –  detect the signal

•  repeat (TR)

... TR

RF excite excite

A/D TE

... time

time

measure NOT FOR DISTRIBUTION


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T1W PDW T2W

contrast hyperintensity TE TR <<T2 >>T1 PDW high PD <<T2 ~ T1 T1W short T1 ~ T2 >>T1 T2W long T2 NOT FOR DISTRIBUTION


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main magnet (Tesla) gradient coils (mT/m)

RF coils (µT (Rx))

Gradient amps RF amp Receiver

Controller/ Computer

Display

X Y Z


NOT FOR DISTRIBUTION •  superconducting solenoid design

–  niobium-titanium alloy winding (many kilometers) –  liquid helium cooling (boils at -269° C - expensive) –  large DC current (100s of Amps - always on) –  0.5-12 Tesla (whole body design) –  very homogeneous (~1ppm over 50cm sphere)

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B0 B0 NOT FOR DISTRIBUTION


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•  No known biologically harmful effects of B0



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Head Coil B1 [µT] x

y

Main Magnet B0 [ T ] z

32 channel head wrist

breast flex

•  some Rx only, some Tx and Rx •  match coil size to object

–  high fill factor

•  multiple small coils can be combined –  parallel imaging



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•  RF heats subject –  SAR (specific absorption rate) –  FDA/HC regulated

•  3 W/kg averaged over the head for any 10 min period –  software and hardware limited on scanner –  can limit scan protocols

NOT FOR DISTRIBUTION •  key component required for imaging •  cause the magnetic field strength to vary linearly in x, y, or z •  switch on and off during scanning

B Pike/MNI 25 z gradient coil

B0 coil

y gradient coil

x gradient coil NOT FOR DISTRIBUTION


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NOT FOR DISTRIBUTION •  acoustic noise

–  can exceed 100-120 dB A –  must use ear protection

•  changing magnetic field can induce currents –  rate of change of magnetic field (dB/dt) –  same effect as used in TMS –  FDA/HC regulated –  if exceeded - peripheral nerve stimulation

•  “tingling” sensation and muscle “twitching” –  monitored and controlled by scanner –  can limit protocol parameters

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NOT FOR DISTRIBUTION •  the received signal in MRI is the sum of all Mxy

inside the sensitive volume of the RF coil

•  need to determine the signal from each voxel inside the volume

•  the key is the magnetic field gradients

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Paul Lauterbur (1929-2007)

•  Initial submission on MRI to Nature was rejected (later published 1973).

•  “You could write the entire history of science in the last 50 years in terms of papers rejected by Science or Nature”, Paul Lauterbur.

NOT FOR DISTRIBUTION •  Ray Damadian

–  proposed first MRI scanner –  founded company called FONAR –  did not share 2003 Nobel prize –  openly expressed anger at not being awarded the

Nobel Prize

Raymond Damadian (1936-)

Full page paid ads in NY Times and LA Times, October 9 & 10, 2003 B Pike/MNI 29



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measure of total Mxy in coil

x

y Mxy phase



kx

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t = 0

signal is k-space (0,0) value

ky

Gx

x B

Gy at t = 2


Gy y

B

Gx at t = 1


Gy at t = 1


Gx at t = 2


t = 0


x

y

Gx and Gy at t = 3


RF

Gx

x B



kx

ky

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•  Readout (aka Frequency Encode) along each line •  Each line is a new Phase Encode •  total scan time = TR x NPE



kx

ky

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Peter Mansfield (1933-)



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kx

ky

2D Inverse Fourier Transform



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kx

ky

+

+ + +

+ + +

= NOT FOR DISTRIBUTION


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kx

ky

x

y

2D IFT

raw data: magnitude reconstructed image: magnitude



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2D IFT

256x256

2D IFT

64x64

kx

ky

What happens if you only measure central area of k-space?

Extent of k-space sampled governs resolution.



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What if you only measure every second column in k-space?

kx

ky

2D IFT

256x256 128x256

2D IFT

Space between samples governs FoV.



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•  the behaviour of the magnetization vector M is phenomenologically described by the Bloch equation:

Felix Bloch (1905-1983)

d!Mdt

=!M ! "

!B #

Mxi + My j

T2#(Mz # M0)k

T1


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•  Signal equation (ignoring relaxation)

S(t) = M (r,t)drvol!

S(t) = Mz!

y!

x! (x, y, z,t)e" j# B0 te

" j# G(t ' )•rdt '

0

t

!dxdydz


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2D Fourier transform of M(x,y) is

therefore

where

•  Fourier interpretation of the signal equation (2D)

s(t) = M (x, y,t)y!

x! e" j2# [kx (t )x+ ky (t )y]dxdy

M(kx ,ky ) = M (x, y)y!

x! e" j2# (kx x+ ky y)dxdy

s(t) = M(kx (t),ky (t))

kx (t) =$2#

Gx (t' )

0

t

! dt '

ky (t) =$2#

Gy (t'

0

t

! )dt '

NOT FOR DISTRIBUTION •  Blood Oxygenation Level Dependent – BOLD

–  image rapidly in a movie-like mode –  sensitize acquisition to changes in deoxy-hemoglobin

concentration, [dHb], in the brain –  [dHb] depends on blood flow, blood volume and oxygen

consumption –  detect [dHb] changes that correlate with task or other

regions –  indirect measure of brain activity

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Seiji Ogawa (1934 - )


oxy-Hb !~ -0.3

longer T2, T2*

-  BOLD upon -  activation

deoxy-Hb ! ~ 1.6

shorter T2,T2*

BOLD at rest

oxy-RBC deoxy-RBC

Linus Pauling (1901-1994)

Nobel in Chemistry 1954 (Nobel Peace Prize 1962)

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O2!

at rest

O2!

ACTIVATED B Pike/MNI 44


NOT FOR DISTRIBUTION fMRI Example: finger movement task

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NOT FOR DISTRIBUTION •  sensitize acquisition to microscopic random

(Brownian) motion of water molecules –  use strong ‘diffusion encoding’ magnetic field gradients –  signal decrease is related to diffusion coefficient –  measure diffusion in multiple directions –  detect micro-structural changes –  detect principal direction of oriented fibres –  trace fibre pathways: tractography

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B. Pike, MNI 47

isotropic diffusion –  Brownian motion of water –  spherical Gaussian PDF –  scalar ADC

anisotropic diffusion –  motion restricted, hindered in vivo –  non-isotropic (elliptical) PDF –  tensor formulation

Beaulieu, 2002


NOT FOR DISTRIBUTION EPI

diffusion encoding gradients

" 48 B Pike/MNI



Fractional Anisotropy Mean Diffusivity

RGB plot: principal direction

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•  NMR physics: –  spins precess at a frequency proportional to the magnetic field –  upon excitation, net macroscopic magnetization vector M

relaxes through: •  longitudinal recovery (T1) •  transverse decay (T2 or T2*)

•  MR contrast: –  pulse sequence parameters control the amount of contrast

from each tissue parameters (PD,T1, T2, T2*) •  MR image formation:

–  spatial encoding via gradient application –  raw data acquired in spatial frequency domain (i.e. k-space) NOT FOR DISTRIBUTION

NOT FOR DISTRIBUTION •  students in my lab – past and present •  Luis Concha

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You’re more wired than you think.

Image: M

cConnell B

rain Imaging C

entre, MN

IC

oncept: CG

CO

M.C

OM

Exploring the mind-boggling potential of your brain is what the Montreal Neurological Institute and Hospital (The Neuro) is all about. Because today’s discoveriesbecome tomorrow’s treatments.

!!!"#$%&%'()"*)+th

e ne

uro

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Documents

MRI Basics BIC Seminar 2010 › uploads › Seminars › 2011-09-19...2011/09/19 · • Initial submission on MRI to Nature was rejected (later published 1973). • “You could