Chapter 3
Principles of Nuclear Magnetic
Resonance and MRI
Many thanks to those that share their MRI slides online

Physical Science
Technology
Physics
Engineering
Computer
Science
Methodology
Statistics
Cognitive
Science
Physiology
Neuroscience
Medicine
Interpretation Applications
Peter Bandettini NIH

Even subdivisions below have multiple layers of complexity
Physics … Engineering … Technology … Applications … Interpretation …
…

• 1940s – Bloch & Purcell: Nuclear Magnetic
Resonance
• 1973 - Lauterbur: gradients for spatial localization of images
• 1977 – Mansfield: first image of human anatomy, first echo planar image (a fast imaging technique)
• 1990s - Discovery that MRI can be used to distinguish oxygenated blood from deoxygenated blood. Leads to Functional Magnetic Resonance imaging (fMRI)
• Paul Lauterbur and Peter Mansfield won the Nobel
Prize in Physiology/Medicine ( 2003 ) for their pioneering work in MRI

Venography
Fiber Track Imaging
Angiography
Perfusion
Peter Bandettini NIH
Anatomy

fMRI
P
R
Peter Bandettini NIH

• All magnetic fields are the result of charge in motion
• Nucleus of an atom has a magnetic moment when it has an odd number of protons (or neutrons). Single proton in Hydrogen yields strongest magnetic effect.
Model of spin as motion
• Why does neutron have magnetic properties?
• What about electron(s) magnetic properties?

• The orientation of nuclear magnetic moments are affected by an external magnetic field (that not due to the local nuclear magnetic moments).
No external magnetic field. Orientation is random.
External magnetic field
B
0
. Orientation follows direction of external magnetic field.

• Nuclei line up with magnetic moments either in a parallel or anti-parallel configuration.
• In body tissues more line up in parallel creating a small additional magnetization M in the direction of B
0
.
Nuclei spin axis not parallel to B
0 field direction.
Nuclear magnetic moments precess about B
0
.

M
.
.
N
U
= 1,000,000 5
.
.
.
N
U
= 1,000,000
ΔE
1.5T
ΔE
3.0T
= 2*ΔE
1.5T
...
N
L
~ 1,000,000 + 10
...
N
L
~ 1,000,000 + 15
1.5 T
M
N
L
N
U
= # /volume in low energy state
= # /volume high energy state
3.0 T M
M

(N
L
- N
U
)
Lowering temperature increases M
– Any volunteers?

• Frequency of precession of magnetic moments given by Larmor relationship f = g x B
0 f = Larmor frequency (mHz) g
= Gyromagnetic ratio (mHz/Tesla)
B
0
= Magnetic field strength (Tesla) g
~ 43 mHz/Tesla
Larmor frequencies of RICs MRIs
3T ~ 130 mHZ
7T ~ 300 mHz
11.7T ~ 500 mHz

able
 Body 1 H content is high due to water (>67%)
 Hydrogen protons in mobile water are primary source of signals in fMRI and aMRI

•
M is parallel to B
0 since transverse components of magnetic moments are randomly oriented.
• The difference between the numbers of protons in the parallel (up here) and antiparallel states leads to the net magnetization ( M ).
• Proton density relates to the number of parallel states per unit volume.
• Signal producing capability depends on proton density.
B
0

• 6.023x10
23 molecules in 18 gm of H
2
O
• 3.35x10
22 molecules in 1 gm (1 cc ~ cm 3 )
• 3.35x10
19 molecules in 1 mg (1 mm 3 )
• 7.70x10
19 hydrogen atoms/mm 3
• 7.70x10
14 signal producing protons/mm 3
So the approximately 1 in 10 5 signal producing protons is still a lot.
Note: The number of protons contributing to signal will depend on volume from which the signal arises (voxel size).

• Radio Frequency (RF)
•
B
1
(f) is magnetic field rotating at frequency = f
• Resonance Condition: f = Larmor frequency
NOTE: coordinate system
B
1 is rotating magnetic field associated with the RF pulse.
Rotating B1 from RF pulse?
RF at Larmor frequency will cause M to rotate about B
1 in rotating frame of reference.

Frequency of rotation of M about B
1 determined by the magnitude (strength) of B
1
.
Basic RF Pulse Concepts
RF Pulse strength duration
RF pulse duration and strength determine flip angle

M
M o
B o
B o
: magnetic field
B
1
: generated by the RF coil
α
: flip angle
M
0
: depends on proton density
α
B
1 y’
RF coil x’
When α = 90 ° then M xy
When α = 180 ° then M xy
= M
0 and
= 0 and
M
M z
= 0 z = M
0
Sample

FID = Free Induction Decay
• 90 °
RF pulse rotates M into transverse (x-y) plane
• Rotation of M within transverse plane induces signal in receiver coil at Larmor frequency.
• Magnitude signal dependent on
M xy
.
FID magnitude decays in an exponential manner with a time constant T2. Decay due to ‘spin-spin’ relaxation.
S ( t )

S
0 e

T t
2
 sin( 2
 ft )

•
FID also diminishes due to local static magnetic field inhomogeneity
•
Some spins precess faster and some slower than those due to B
0
90
°
• 180 ° RF pulse reverses dephasing at TE (echo time)
• Residual decay due to T2
180 °
Spin Echo Signal

TR (repetition time) = time between RF excitation pulses
90 o 90 o 180 o
FID Spin Echo
TE/2 TE/2
TE = time from 90 o pulse to center of spin echo

• A helium-cooled superconducting magnet generates the static field.
– Always on: only quench field in emergency.
– niobium titanium wire.
• Coils allow us to
– Make static field homogenous (shims: solenoid coils)
– Briefly adjust magnetic field (gradients: solenoid coils)
– Transmit, record RF signal (RF coils: antennas)

Necessary Equipment
Magnet
3T magnet gradient coils
(inside)
RF Coil
Gradient Coils RF Coil

Sounds generated during imaging due to mechanical stress within gradient coils.

• RF Coils can transmit and receive RF signals
(i.e. apply B
1 and monitor M xy
)
• A typical coil is a tuned LC circuit and may be considered a near-field antenna

www.fmrib.ox.ac.uk/~karla/
• The MRI antenna is called a coil.
• Use different coils for different body parts.
• For brains, the most common antenna is the head coil
(surrounds the volume of interest)
• S coils: better signal for a small region near the coil.
Head coil Surface coil Volume coil Surface coil

Comprehensive Receiving coils

7 standard configuration ：
QD head coil QD Neck Coil QD Body Coil
QD Extremity Coil Flat Spine Coil Breast Coil

• In theory:
– Signal increases with square of field strength
– Noise increases linearly with field strength
– A 3T scanner should have twice
SNR of 1.5T scanner; 7T should have ~4.7 times SNR of 1.5T.
• Unfortunately, physiological artifacts also increase, so advantage is less in practice.
• Benefits: speed, resolution
• Costs: Artifacts, RF heating, wavelength effects, auditory noise, $

• Uniform magnetic field to set the stage (Main
Magnet)
• Gradient coils for positional information
• RF transceiver (excite and receive)
• Digitizer (convert received analog to digital)
• Pulse sequencer (controls timing of gradients,
RF, and digitizer)
• Computer (FFT to form images, store pulse sequences, display results, archive, etc.)

• Coils that produce magnetic field gradients along x-,y-,and z-directions to encode spatial information
• Selective excitation: ( during RF ) excite those spins within a thin “slice” of the subject
• Frequency encoding: ( during readout ) make the signal’s frequency depend on position
• Phase encoding: ( between excitation and readout ) make the signal’s phase depend on position

z
• Field Characteristics
• Gradient field direction parallel to B
0
• Created by Maxwell Pair
— currents are anti-parallel (opposite direction)
B
G
Coil 1
Coil 2

• Total Field
• Sum of Main Magnet and Gradient Fields
• In practice a “shim” field is also used to “flatten” the field.
B
0
= B
M
+ B
G
D
B
0
~ 1mT
Gradient field decreases total
Gradient field increases total


• Field varies (almost) linearly
• Field magnitude changes with z here
• Frequency changes with z
• Delta B
0 system
= 0 at z = 0 for balanced
• Gradient units (T/m)
D
B
0 f


G g 
B
0 z
 z
 D
B
0

D
B= 0.001 T
D z = 0.25 m
D
B/
D z = 0.004 T/m
~ 172 kHz/m

During RF excitation, a linear gradient is applied. Only a “slice” of the sample is excited.
f f= g
( B
0
+ G s s)
Slice Location center of RF frequency range s
Thickness
TH = BW
RF
/ g
G s

• RF Coils
 Transmit RF Field ( B
1
)
— Transmitter at frequency
D f f
0 with bandwidth
 Receive signal from M xy
— Receiver tuned to frequency f
0
Body
Transmitter/
Receiver f o
Head
Transmitter/
Receiver f o
D f = 1/ t t FT

During signal readout, a gradient is applied in one direction:
B(x) = B
0
+ G x x f(x) = g
{ B
0
+ G x x}
D f(x) = g
G x x
M xy f(x)
The precession frequency of the net magnetization M x-direction.
xy depends on x-location. A
Fourier transform of the time signal can determine where the nuclei are along the

Between excitation and readout a gradient is applied in one direction. This is done in small increments (once per TR) such that the summed effect is similar to frequency encoding.
B(y) = B
0 f(y) = g
{ B
0
+ G y y
+ G y y}
D f (y) = g
G y y
M xy f (y)
The phase difference depends on y-location. When phase encoding is complete a Fourier transform of the signal tells us where the nuclei are along the y-direction.

RF Excitation
Select slice ( G s
)
Phase Encode ( G p
)
Frequency encode ( G f
)
Readout
Repeat this many times with G p changed each time
Slice Select for Brain Orientation: G x
– sagittal; G y
– coronal; G z
- axial

k-space k y
Image space y
FT -1 k x
FT x
Acquired Data
MRI task is to acquire k-space image then transform to a spatial-domain image. kx is sampled (read out) in real time to give N samples. ky is adjusted before each readout.
Final Image
MR image is the magnitude of the Fourier transform of the k-space image

Equations that govern 2D k-space trajectory kx = g
0 t G x
(t) dt if G x is constant ky = g
0 t’ if G y
G y
(t) dt is constant kx = ky = g g
G
G y x t t’
The kx, ky frequency coordinates are established by durations (t) and strength of gradients (G).

Simple MRI Frequency Encoding:
RF Excitation
Slice
Selection (G z
)
Frequency
Encoding (G x
)
Readout digitizer on
Exercise drawing k-space manipulation

Frequency
Encoding
Gradient
( G x
)
Move to left side of k-space.
The k-space Trajectory
(0,0) ky
Digitizer records N samples along kx where ky = 0 kx

Simple MRI Frequency Encoding: Spin
Echo
Excitation
Slice
Selection
Frequency
Encoding (G x
)
Readout digitizer on
Exercise drawing k-space representation

Digitizer records N samples of kx where ky = 0
The K-space Trajectory
180 pulse

Frequency and Phase Encoding for 2D
Spin Echo Imaging
90
180
Excite kx ky
Slice
Select
Frequency
Encode
Phase
Encode digitizer on
Readout

Digitizer records N samples of kx and
N samples of ky
The 2D K-space Trajectory
180 pulse

Raw 2D k-space data Processed data
Imaging time - N p
TR
Magnitude of Fourier transform

Using G x for frequency encoding let the readout FOV range from -x m
Within this FOV frequencies range from g
(B
0
+ G x x to +x m
) m
Frequency change is 2 g
G x x m
.
- G x x m
) to + g
(B
0
Since 2 x m
= FOV then the frequency range is g
G x
FOV
RF receiver bandwidth (BW) is adjusted to cover this range of frequencies.
Therefore BW = g
G x
FOV.
FOV f
= BW/( g
*G f
)
Same as equation for slice thickness seen before
• If BW is fixed increasing G f
• If G f reduces FOV is fixed increasing BW increases FOV

BW = 2 f max in MRI (-f max
Digitizer must sample at rate R s avoid aliasing so R s
= BW .
to +f max
)
= 2 f max to
Example: For receiver with BW = 32 kHz
With R s
= 32K samples/second what is time to acquire one line of 256 samples along kx?
256 samples/32K samples/sec = 8 msec.

Calculation of the Field of View (FOV) along phase encoding direction g
G p
FOV p
= N p
/ T p where T p is the duration and N p the number of the phase encoding gradients, Gp is the maximum amplitude of the phase encoding gradient.
FOV p
= (N p
/ T p
)/ ( g
G p
)

What is BW/pixel if BW = 32 kHZ in 256x256 image?
32 kHz/256 pixels = 125 Hz/sample.
What is spread in Larmor frequencies for a 3T magnet with 0.1 ppm range in B
0 within a voxel?
3T x 43 mHz/T = 129 MHz
129 x10 6 Hz x 0.1/1x10 6 = 12.9 Hz
What is potential phase shift at TE = 20 msec due to this inhomogeneity?
12.9 cycles/sec -1 x 20 x10 -3 sec = 0.258 of a cycle

1
2
8
2
5
6
Partial Fourier or K-Space Imaging to Shorten k y
Scan Time k x
256
Decreasing number of phase (ky) lines reduces scan time proportionally.
256
256
Decreases y-direction spatial resolution.

k y
2
5
6
1
2
8
256 k y k x k x
256
Retains resolution but decreased SNR

• Contrast = difference in image values between different tissues
• T1 weighted example: gray-white contrast is possible because T1 differs between these two types of tissue

• T1-Relaxation: Recovery
– Recovery of longitudinal orientation of M along z-axis.
– ‘T1 time’ refers to time interval for
63% recovery of longitudinal magnetization.
– Spin-Lattice interactions .
• T2-Relaxation: Dephasing
– Loss of transverse magnetization
M xy
.
– ‘T2 time’ refers to time interval for
37% loss of original transverse magnetization.
– Spin-spin interactions,and more .

Tissue T1 (ms) T2 (ms)
Grey Matter (GM) 950 100
White Matter (WM)
Muscle
600
900
80
50
Cerebrospinal Fluid (CSF) 4500 2200
Fat
Blood
250 60
1200 100-200
T1 values for B
0
~ 1Tesla.
T2 ~ 1/10 th T1 for soft tissues

Average Values of T1 and T2 in the
Human Brain
Relaxation Times (msec)
Tissue 1.5T
3.0T
4.0T
WM-T1 640
GM-T1 880
860
1200
1040
1410
WM-T2 80
GM-T2 80
80
110
50
50
Large frequency dependence for T1 values.
Data from textbook.

T1 is shorter in fat (large molecules) and longer in
CSF (small molecules). T1 contrast is higher for lower
TRs.
(sec)
(msec)
•
TR determines T1 contrast
• TE determines T2 contrast.
T2 is shorter in fat and longer in CSF. Signal contrast increased with TE.

T1 Contrast Weighting
• T1W Contrast
 Echo (TE) at T2 contrast min
 Repeat (TR) at T1 contrast max
• T2W Contrast
 Echo (TE) at T2 contrast max
 Repeat (TR) at T1 contrast min
TR TE
Max T1 Contrast
Min T2 Contrast
T2 Contrast Weighting
S

S
0




1
 e

TR
T 1
 





 e


TE
T 2
 

 re cov ery decay
TR
TE
Min T1 Contrast Max T2 Contrast


S ( TR , TE ) 
T1W r 
1  e  TR / T
1
or r 
1  e  TR / T
1
T2W
  
SE
  e  TE / T
2
*

GRE r
- proton density
SE – spin echo imaging
GRE – gradient echo imaging
Short TEs reduce T2W
Long TRs reduce T1W

PDW Three Common Clinical MRIs
T1W
T2W
Largest Signal
Good GM-WM Contrast
Note: Display contrast adjusted for best viewing of each.
Fluids are bright

Inversion Recovery T1 Contrast
S o
S = S o
* (1 – 2 e
–t/T1
)
S = S o
* (1 – 2 e
–t/T1’
)
-S o
Sampling signal at this time suppresses tissue with T1’

T2W
Inversion Recovery
(CSF Attenuated)

• Signal is generated by magnetic field refocusing mechanism only (the use of negative and positive gradient)
• Signal intensity is governed by
S = S o e -TE/T2*
• Can be used to measure T2* value of the tissue
• R2* = R2 + R2 ih
+R2 ph
(R2=1/T2)
• Used in 3D and BOLD fMRI ph – other phase related


E
.
Excitation
Slice
Selection
Frequency
Encoding
Phase
Encoding digitizer on
Readout
Ernst angle (

E
) for optimum SNR .
cos( 
E
)  e
 TR
T 1


B
1
G z
G y
G x
B
1
G z
G y
G x
TR
1 refocus
FLASH Pulse Sequence
TR
2 acquire
TR
N/2
TR
N
Fig. 3.19. Courtesy of Peter Jezzard.
TR
N
TR
N/2
2D Gradient Echo
RF (10-15 degrees)
Short TR (10-50 msec)
N= 256 (2.5-13 sec per slice)
TR
2
TR
1

read acq
G x phase
G y
Select
& phase
G z
RF
B
1 k x
Scan time = N y
N z
TR
Good for high resolution T1W images of brain k z k y

3D T1W brain image
0.8mm spacing
Time = 25 min

a)
B
1
G z
G y
G x refocus
2D Echo Planar
Imaging (EPI) b) acquire
Fig. 3.20. Courtesy of Peter Jezzard.
2d Gradient Echo
Entire 2D slice within one TR
64x64 or 128x128
Time per slice (30-50 msec)
Whole volume (2-4 sec)
Good for fMRI studies

FLASH Image T2* Weighted
TE = 30 msec
CSF is bright
Signal loss and distortions due to local differences in magnetic field
Sources of Contrast in Brain
- Endogenous - BOLD
- Exogenous - could be contrast agent (Gd based)
- Other - Susceptibility
R2* = net T2 relaxation rate = 1/T2*
R2* = R2 tis
+ R2 ih
+ R2
BOLD
+ R2 suc
Fig. 3.23 courtesy of Peter Jezzard.

BOLD EPI Functional MRI
Task
(Task - Rest)
3 %
0
R
Rest
L
Subtraction converted to t- or z-values z = (Task - Rest)/SD
Task-Rest

fMRI (BOLD EPI) – With Statistical Parametric
Mapping
R Finger
Tongue z-values > 3

R Finger
Movement
Tongue
Movement