Principles of MRI

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Nov 16, 2013 (3 years and 11 months ago)

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Principles of MRI

Physics and Engineering

Allen W. Song

Brain Imaging and Analysis Center

Duke University

Magnetic resonance imaging, commonly known as

MRI, can non
-
invasively provide high resolution

anatomical images of human structures, such as brain,

heart and other soft tissues. It is used routinely in

clinical diagnosis.


Functional MRI advances from the traditional static

scans to image dynamic time course of the brain signal

during specific tasks. It is widely used now in studying

the working mechanism of the human brain. Clinical

application is mainly seen in presurgical planning.

MRI


Cool (and Useful) Pictures

2D slices extracted from a 3D image

[resolution about 1

1

1 mm]

axial

coronal

sagittal

Synopsis of MRI


1)

Put subject in big magnetic field


2)

Transmit radio waves into subject [2~10 ms]


3)

Turn off radio wave transmitter


4)

Receive radio waves re
-
transmitted by subject



Manipulate re
-
transmission with magnetic fields during
this
readout

interval
[10
-
100 ms: MRI is not a snapshot]


5)

Store measured radio wave data vs. time



Now go back to

2)

to get some more data


6)

Process raw data to reconstruct images


7)

Allow subject to leave scanner

Lecture Components

I)

Magnetic fields and magnetization,



fundamental ideas about NMR signal

II)


How to form an image,



introduction to k
-
space

III)


MRI contrast mechanisms,



various imaging techniques



Part I


Magnetic Fields

And Magnetization,
Fundamental of NMR Signal

Magnetic Fields, Magnetization,

NMR Signal Generation

Transmit

Receive


rf

coil


rf

coil


main

magnet


main

magnet

gradient

Shimming


Control

Computer

Things needed for a typical MRI scanner


Strong magnetic field, usually from
superconducting magnets.


RadioFrequency coils and sub
-
system.


Gradient coils and sub
-
system.


Shimming coils and sub
-
system.


Computer(s) that coordinate all sub
-
systems.

Magnetic and Electromagnetic Fields



Magnetic fields generate the substance we “see”:
magnetization

of the H protons in H
2
O



Magnetic fields also let us manipulate magnetization so that
we can make a map [or
image
] of its distribution inside the
body’s tissue



Static

magnetic fields change slowly (< 0.1 ppm / hr):


main field; static inhomogeneities


RF

fields are electromagnetic fields that oscillate at
R
adio
F
requencies (tens of millions of times per second)



transmitted radio waves into subject



received signals from subject


Gradient magnetic fields change quickly (switching up to
thousands of times per second)


Vectors and Fields



Magnetic field
B

and magnetization
M

are
vectors
:



Quantities with direction as well as size



Drawn as arrows ....................................



Another example: velocity is a vector (speed is its size)


Vector operations:


dot product AB cos
q


cross product AB sin
q


Magnetic field exerts torque to line magnets up in a given
direction



direction of alignment is direction of
B



torque proportional to size of
B

[units=
Tesla, Gauss=
10

4

T
]


Main Magnet Field
Bo



Purpose is to align H protons in H
2
O (little magnets)

[Little magnets lining up with external lines of force]

[Main magnet and some of its lines of force]

Common nuclei with NMR property


Criteria:


Must have ODD number of protons or ODD number of neutrons.


Reason?


It is impossible to arrange these nuclei so that a zero net angular


momentum is achieved. Thus, these nuclei will display a magnetic


moment and angular momentum necessary for NMR.


Examples:


1
H,
13
C,
19
F,
23
N, and
31
P with gyromagnetic ratio of 42.58, 10.71,


40.08, 11.27 and 17.25 MHz/T.


Since hydrogen protons are the most abundant in human body, we use

1
H MRI most of the time.

A Single Proton

+

+

+

There is electric charge

on the surface of the
proton, thus creating a
small current loop and
generating magnetic
moment
m
.

The proton also has
mass which
generates an

angular momentum

J

when it is
spinning.

J

m

Thus proton “magnet” differs from the magnetic bar in that it

also possesses angular momentum caused by spinning.

Magnetic Moment

I

B

F

L

F = IBL

B

L

W

t
= IBLW = IBA


m

= t
max

/ B


= IA



t

=
m



B


= m B
sin
q

Force

Torque

Angular Momentum

J

= m
w
=m
v
r

m

v

r

J



m

=
g

J



where
g

is the gyromagnetic ratio,

and it is a constant for a given nucleus

Similarity between a spinning proton

and a spinning magnetic bar

N

S

m

+

+

+

+

+

+

+

J

Protons in Free Space

What happens if they are in a magnetic field ?

Magnetic Bar in a Magnetic Field

Bo

N

S

Static magnetic bar

Spinning magnetic bar

Protons in a Magnetic Field

Bo


Parallel

(low energy)

Anti
-
Parallel

(high energy)

Spinning protons in a magnetic field will assume two states.

If the temperature is 0
o

K, all spins will occupy the lower energy state.

Net Magnetization

Bo

M

T
B
c
M
o
=


Small
B
0

produces small net magnetization
M




Thermal motions

try to randomize alignment of proton

magnets




Larger
B
0

produces larger net magnetization
M
, lined up

with
B
0




At room temperature, the population ratio is roughly

100,000 to 100,006 per Tesla of
B
0

Basic Quantum Mechanics Theory of MR

The Energy Difference Between

the Two States


D

E

=
h

n


D

E = 2
m
z

B
o




n = g
/2
p B
o


known as larmor frequency


g
/2
p
= 42.57 MHz / Tesla for proton

Basic Quantum Mechanics Theory of MR

Eqn. [3.9]

-

[3.16]

Knowing the energy difference allows us to use

electromagnetic waves with appropriate energy

level to irradiate the spin system so that some spins

at lower energy level can absorb right amount of

energy to “flip” to higher energy level.

Basic Quantum Mechanics Theory of MR

Spin System Before Irradiation

Bo

Lower Energy

Higher Energy

Basic Quantum Mechanics Theory of MR

The Effect of Irradiation to the Spin System

Lower

Higher

Basic Quantum Mechanics Theory of MR

Spin System After Irradiation

Basic Quantum Mechanics Theory of MR



If
M

is not parallel to
B
, then

it precesses clockwise around

the direction of
B
.




However, “normal” (
fully
relaxed
)

situation has
M

parallel to
B
, which means there won’t be any

precession


Classical Description of Magnetization: Precession



Magnetic field causes

M

to rotate (or
precess
) about the direction of
Bo

at a frequency proportional to the size of
Bo



42 million times
per second (42 MHz), per Tesla of
Bo.

To visualize the rotation, the
magnetization M is
tipped away

from the
Bo

direction.



N.B.: part of
M

parallel to
Bo

(
M
z
)


does not precess

Bo

A Mechanical Analogy



A gyroscope in the Earth’s gravitational field is like
magnetization in an externally applied magnetic field

Derivation of precession frequency

This says that the precession frequency is the SAME as the larmor frequency

t
=
m

×

B
o

t

= d
J

/ dt

J =
m
/
g


d
m
/dt =
g

(
m

×

B
o
)

m
(t) = (
m
xo
cos
g
B
o
t +
m
yo
sin
g
B
o
t)
x

+ (
m
yo
cos
g
B
o
t
-

m
xo
sin
g
B
o
t)
y

+
m
zo
z


How do we detect magnetization?

We need to perturb it.


Analogy: you have to lift the object to see

how much it weighs.

How to perturb
M

so it is not Parallel to
B
?



A way that does
not

work:



Turn on a second big magnetic field
B
1

perpendicular to main
B
0

(for a few seconds)





Then turn
B
1

off;
M

is now not parallel to magnetic field
B
0



This fails because cannot turn huge (Tesla) magnetic
fields on and off quickly



But it contains the kernel of the necessary idea:




A magnetic field
B
1

perpendicular to
B
0

B
0

B
1

B
0
+
B
1



M

would drift over to be aligned

with sum of
B
0

and
B
1


RF Coil: Transmitting
B1

Field



Left alone,
M

will align itself with
Bo

in about 2

3 s



So don’t leave it alone
: apply (transmit) a magnetic field
B
1

that fluctuates at the precession frequency and points
perpendicular to
B
0

(how do we achieve this?


by making a
coil)



The effect of the tiny
B
1

is


to cause
M

to spiral away


from the direction of the


static
B

field



B
1

10

4

Tesla



This is called
resonance



If
B
1

frequency is not close to


resonance,
B
1

has no effect

Time = 2

4 ms

Nutation

Another Mechanical Analogy: A Swingset



Person sitting on swing at rest is “aligned” with
externally imposed force field (gravity)



To get the person up high, you could simply supply
enough force to overcome gravity and lift him (and the
swing) up



Analogous to forcing
M

over by turning on a huge static
B
1



The other way is to push back and forth with a tiny
force, synchronously with the natural oscillations of
the swing


Analogous to using the tiny RF
B
1

to slowly flip
M

over

g

Rotating Frame (compared to Laboratory Frame)

Rotating Frame

Laboratory Frame

w
o

Spin Excitation using Rotating Frames Reference

M

B
1

Notice that the nutation becomes simple rotation in the rotating frame

M

q

q

=
g

B
1

t


What if the RF field is not synchronized?

Using the swingset example: now the driving force is no longer

synchronized with the swing frequency, thus the efficiency of

driving the swing is less.

In a real spin system, there is a term called “effective B1 field”,

given by


B
1eff

=
B
1

+
Dw
/
g

where


Dw

=
w
o



w
e

B
1

B
1eff

Dw
/
g

RF Coil: Signal Receiver



When excitation RF is turned off,
M

is left
pointed off at some angle to

B
0

[
flip angle
]



Precessing part of
M

[
M
xy
] is like having a magnet
rotating around at very high speed (at RF frequencies)



Will generate an oscillating voltage in a coil of wires
placed around the subject


this is magnetic
induction

RF Coil: Signal Receiver


This voltage is the
RF signal

whose measurements
form the raw data for MRI



At each instant in time, can measure one voltage
V
(
t
)
, which
is proportional to the sum of all transverse
M
xy

inside the coil



Must find a way to separate signals from different regions

Various RF Coils


Separated by function:


Transmit / receive coil (most common)


Transmit only coil (can only excite the system)


Receive only coil (can only receive MR signal)



Separated by geometry


Volume coil (low sensitivity but uniform coverage)


Surface coil (High sensitivity but limited coverage)



Relaxation Characteristics

About the NMR Signal

Relaxation: Nothing Lasts Forever



In absence of external
B
1
,
M

will go back to
being aligned with static field
B
0



this is
called
relaxation



Part of
M

perpendicular to
B
0

shrinks [
M
xy
]



This part of
M

is called
transverse magnetization



It provides the detectable RF signal



Part of
M

parallel to
B
0

grows back [
M
z
]




This part of
M
is called
longitudinal magnetization



Not directly detectable, but is converted into
transverse magnetization by externally applied
B
1




Relaxation Times and Rates



Times: ‘
T
’ in exponential laws like
e

t
/
T



Rates:
R

=
1/T
[so have relaxation like
e

R
t
]



T1
: Relaxation of
M

back to alignment with
B
0



Usually 500
-
1000 ms in the brain [lengthens with bigger
B
0
]



T2
: Intrinsic decay of the transverse magnetization over
a microscopic region (


5
-
10
micron size)



Usually 50
-
100 ms in the brain [shortens with bigger
B
0
]



T2*
: Overall decay of the observable RF signal over a
macroscopic region (millimeter size)



Usually about half of
T2
in the brain

[i.e., faster relaxation]

T2* Relaxation

S = So * e

t/T2*

Material Induced Inhomogeneities Will Affect T2*



Adding a nonuniform object (like a person) to
B
0

will make
the total magnetic field
B

nonuniform



This is due to
susceptibility
: generation of extra magnetic fields in
materials that are immersed in an external field



Diamagnetic

materials produce negative
B

fields



Paramagnetic

materials produce positive
B

fields



Size about
10

7

B
0

= 1

10 Hz change in precession
f



Which makes the precession frequency nonuniform, affecting
the image intensity and quality


For large scale (10+ cm) inhomogeneities, scanner
-
supplied
nonuniform magnetic fields can be adjusted to “even out” the
ripples in
B


this is called
shimming



Nonuniformities in
B

bigger than voxel size affect whole image



Nonuniformities in
B

smaller than voxel size affect voxel “brightness”

Frequency and Phase



RF signals from different regions that are at
different frequencies will get
out of phase

and thus
tend to cancel out



Phase = the
w
t

in
cos(
w
t
)

[frequency
f =

w
/2
p
]

Sum of 500 Cosines with Random Frequencies


Starts off large when all phases are about equal

High frequency gray curve is at the average frequency


Decays away as different


components get different phases

T2* relaxation (decay) and NMR Signal



Random frequency differences inside intricate tissue
environment cause RF signals (from
M
xy
) to
dephase



Measurement = sum of RF signals from many places



Measured signal decays away over time [
T2*

40 ms at 1.5 T]



At a microscopic level (microns),
M
xy

signals still exist; they
just add up to zero when observed from outside (at the RF coil)



Contents of tissue can affect local magnetic field



Signal decay rate depends on tissue structure and material



Measured signal strength will depend on tissue details



If tissue contents change, NMR signal will change



e.g., oxygen level in blood affects signal strength

Hahn Spin Echo: Retrieving Lost Signal



Problem:
M
xy

rotates at different rates in different spots



Solution: take all the
M
xy
’s that are ahead and make
them get behind (in phase) the slow ones



After a while, fast ones catch up to slow ones


re
-
phased!

Fast & slow

runners

Magically “beam”

runners across track

Let them run the

same time as before



The “magic” trick:
Flip

of the
magnetization
M





Apply a second
B
1

pulse to produce a
flip angle of 180


about the
y
-
axis (say)




Time between first
and second
B
1

pulses
is called
TE/2




“Echo” occurs at
time
TE

Spin Echo
:




Excite




Precess


& dephase




180


flip




Precess


& rephase

T2 Relaxation (Decay)



Spin echo doesn’t work forever (
TE

can’t be too big)



Main reason: water molecules diffuse around randomly



About 5
-
10 microns during 10
-
100 ms readout window



They “see” different magnetic fields and so their precession
frequency changes from fast to slow to fast to ................



This process cannot be reversed by the inversion RF pulse


Time scale for irreversible decay of
M
xy

is called
T2






S = So * e
-
t/T2

T1 Relaxation



Longitudinal relaxation of
M
z

back to “normal”
(
T1
)


Caused by internal RF magnetic fields in matter



Thermal agitation of H
2
O molecules



Can be enhanced by magnetic impurities in tissue




S = So (1
-
e
t/T1
)

Proton Density Weighted Image

T1 Weighted Image

T2 Weighted Image

Factors Influencing Relaxation Rates


Magnetic impurities


* In general, it will shorten the relaxation time such as T2*,


T2 and T1




Local physiological and chemical environment changes


* For example, bounded water molecules will have shorter


T2 then free water molecules




Strength of the magnetic fields


* Usually stronger field prolongs T1, however, shortens T2*


and T2 due to increased susceptibility
-
induced magnetic


inhomogeneities

Contrast Agents that Affects Relaxation Rate

Drugs containing certain impurities can alter
T1
,
T2
,
and
T2*



contrast agents

(e.g., CuSO
4
, Gd
-
DTPA)