ELEG 479
Lecture #9
Magnetic Resonance (MR) Imaging
Mark Mirotznik, Ph.D.
Professor
The University of Delaware
Process of MR Imaging
Step#1: Put subject in a big magnetic field (leave him there)
Step#2: Transmit radio waves into subject (about 3 ms)
Step #3: Turn off radio wave transmitter
Step #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)
Step#5: Store measured radio wave data vs. time
– Now go back to transmit radio waves into subject and get more data.
Step#6: Process raw data to reconstruct images
Step#7: Allow subject to leave scanner (this is optional)
Equipment
4T magnet
RF Coil
B0
gradient coil
(inside)
Magnet
Gradient Coil
RF Coil
Magnetic Fields are Huge!
Typical MRI Magnet: 0.5-4.0 Tesla (T)
Earth’s magnetic field: 50 mTesla
So what happens to things that are
normally non-magnetic when you
put them inside big magnetic
fields?
So what happens to things that are normally non-magnetic
when you put them inside big magnetic fields?
Let’s first look at a simple hydrogen atom without any applied
external magnetic field.
electron
Quantum
mechanical
property called
proton spin
proton
Quantum
mechanical
property called
electron spin
So what happens to things that are normally non-magnetic
when you put them inside big magnetic fields?
Let’s first look at a simple hydrogen atom without any applied
external magnetic field.
electron
Quantum
mechanical
property called
proton spin
proton
Quantum
mechanical
property called
electron spin
We can think of spin from a classical point of view as the proton or
electron rotating about some axis.
So what happens to things that are normally non-magnetic
when you put them inside big magnetic fields?
Let’s first look at a simple hydrogen atom without any applied
external magnetic field.
electron
Quantum
mechanical
property called
proton spin
Belectron
proton
Quantum
mechanical
property called
electron spin
Bproton
Since both the proton and electron are electrically charge when
they spin they look like a tiny current loop (called a magnetic
dipole). We know that a current loop produces a magnetic field.
So what happens to things that are normally non-magnetic
when you put them inside big magnetic fields?
Let’s first look at a simple hydrogen atom without any applied
external magnetic field.
electron
Belectron
proton
Bproton
Since both the proton and electron are electrically charge when
they spin they look like a tiny current loop (called a magnetic
dipole). We know that a current loop produces a magnetic field.
So what happens to things that are normally non-magnetic
when you put them inside big magnetic fields?
Let’s first look at a simple hydrogen atom without any applied
external magnetic field.
electron
Quantum
mechanical
property called
proton spin
Belectron
proton
Quantum
mechanical
property called
electron spin
Bproton
Since the proton is so much larger than the electron it will produce a
much larger magnetic dipole. So most practical applications of this
phenomenon relate to the nuclear magnetic properties.
So what happens to things that are normally non-magnetic
when you put them inside big magnetic fields?
Let’s first look at a simple hydrogen atom without any applied
external magnetic field.
electron
Quantum
mechanical
property called
proton spin
proton
Quantum
mechanical
property called
electron spin
Question: So do the nucleus of all atoms possess this magnetic
property or is hydrogen special?
So what happens to things that are normally non-magnetic
when you put them inside big magnetic fields?
Question: So do the nucleus of all atoms possess this magnetic
property or is hydrogen special?
• To be imaged, nuclei must:
– have an odd number of neutrons, protons, or both
– be abundant in the body
• Hydrogen in the water molecule satisfies both:
– The hydrogen nucleus is composed of a single proton (odd
number of nucleons)
– Water comprises 70% of the body by weight (very
abundant)
– Most widely imaged
• Termed spins in MRI
So what happens to things that are normally non-magnetic
when you put them inside big magnetic fields?
Question: So do the nucleus of all atoms possess this magnetic
property or is hydrogen special?
These guys will also possess a non-zero magnetic spin.
1
1
H
1.0
13
6
C
.016
17
8
O
19
9
F
23
11
Na
.093
Relative sensitivity compared to hydrogen
31
15
P
.066
39
19
K
So what happens to things that are normally non-magnetic
when you put them inside big magnetic fields?
Let’s first look at a simple hydrogen atom without any applied
external magnetic field.
electron
Quantum
mechanical
property called
proton spin
Belectron
proton
Quantum
mechanical
property called
electron spin
Bproton
Question: So if all hydrogen atoms possess this magnetic property
and we have lots of hydrogen atoms (we are mostly water) then why
are we not magnetic?
So what happens to things that are normally non-magnetic
when you put them inside big magnetic fields?
Question: So if all hydrogen atoms possess this magnetic property
and we have lots of hydrogen atoms (we are mostly water) then why
are we not magnetic?
=
Random
Orientation
No Net
Magnetization
So what happens to things that are normally non-magnetic
when you put them inside big magnetic fields?
Now, let’s look at a proton when we apply an external static
magnetic field Bo
Bore
(55 – 60 cm)
Body RF
(transmit/receive)
Gradients
Magnetic field (B0)
Shim
(B0 uniformity)
So what happens to things that are normally non-magnetic
when you put them inside big magnetic fields?
Now, let’s look at a proton when we apply an external static
magnetic field Bo
First
The
proton’s
magnetic
dipoles tend to orient
themselves in 1 or 2 states
(spin ½ and spin - ½ or spin
parallel and spin anti-parallel)
with respect to the external
magnetic field
So what happens to things that are normally non-magnetic
when you put them inside big magnetic fields?
Now, let’s look at a proton when we apply an external static
magnetic field Bo
First
The
proton’s
magnetic
dipoles tend to orient
themselves in 1 or 2 states
(spin ½ and spin - ½ or spin
parallel and spin anti-parallel)
with respect to the external
magnetic field
Question: So if the magnetic dipoles align both up and down why
don’t they just cancel each other out and again give a zero net
magnetization?
So what happens to things that are normally non-magnetic
when you put them inside big magnetic fields?
Now, let’s look at a proton when we apply an external static
magnetic field Bo
Question: So if the magnetic dipoles align
both up and down why don’t they just cancel
each other out and again give a zero net
magnetization?
Answer: At any temperature above absolute
zero we get a few more in one state than the
other.
So what happens to things that are normally non-magnetic
when you put them inside big magnetic fields?
Now, let’s look at a proton when we apply an external static
magnetic field Bo
So what happens to things that are normally non-magnetic
when you put them inside big magnetic fields?
Now, let’s look at a proton when we apply an external static
magnetic field Bo
So what happens to things that are normally non-magnetic
when you put them inside big magnetic fields?
Now, let’s look at a proton when we apply an external static
magnetic field Bo
Enough to get a measurable net
magnetization! This is called the
longitudinal magnetization.
So what happens to things that are normally non-magnetic
when you put them inside big magnetic fields?
Now, let’s look at a proton when we apply an external static
magnetic field Bo
Second
The proton is spinning (think of a
spinning top) so it has a non-zero
angular momentum, J. When we
place it in the magnetic field the
proton experiences a torque.
This torque causes the tip of the
magnetic field vector to precess at
some angular frequency, wo.
Larmor Precession
Now, let’s look at a proton when we apply an external static
magnetic field Bo
So what happens to things that are normally non-magnetic
when you put them inside big magnetic fields?
Precession Demo
Magnetic Moment Vector of Proton
Components of the Precessing Proton
Z (longitudinal)
z

m
mz
y
a
xy (transverse plane)
x
f
y

m xy
x


m (t )  m x (t ) xˆ  m y (t ) yˆ  m z zˆ  m xy  m z zˆ
Magnetic moment vector
Magnetic Moment Vector of Proton
z
(longitudinal
magnetization vector)

m
mz
a
f
x

y

m xy
(transverse magnetization vector)

m (t )  m x (t ) xˆ  m y (t ) yˆ  m z zˆ  m xy  m z zˆ
Net Magnetization
z
z

m
mz
mz

m


y
m xy
x
m xy
z
y
mz

m
x
z
mz
Add all the magnetic
moments from all the
protons together at some
instant in time

m

m

z
m xy
y
mz
x


m xy
m xy
y
y
x
x
Net Magnetization
Add all the magnetic
moments from all the
protons together at some
instant in time
z
z

m
mz
mz

m
z

m xy
y

m xy
x
m xy
y
mz

x

m xy
m xy
y
y
x

z

m

m
mz

m
x
z
mz
y
x
Net Magnetization Vector
N


M (t )   m n ( xn , yn , zn , t )
n 1


M (t )  M xy (t )  M z zˆ
Net Magnetization
Question: Anything we
can say about Mxy?
z
z

m
mz
mz

m
z

m xy
y

m xy
x
m xy
y
mz

x

m xy
m xy
y
y
x

z

m

m
mz

m
x
z
mz
y
x
Net Magnetization Vector
N


M (t )   m n ( xn , yn , zn , t )
n 1


M (t )  M xy (t )  M z zˆ
Net Magnetization
Question: Anything we
can say about Mxy?
N


M (t )   m n ( xn , yn , z n , t )
n 1

M (t )  M z zˆ
Answer: At any instant in
time the magnetic dipoles
are precessing at the
same frequency but all
out of phase. The net
summation of all those
vectors in the transverse
plane is zero!
z
(longitudinal
magnetization vector) M z

M
y

M xy
x
(transverse magnetization vector)
Another Question: What
can we do to get a net
magnetization vector in
the transverse plane?
Net Magnetization
Answer: At any instant in
time the magnetic dipoles
are precessing at the
same frequency but all
out of phase. The net
summation of all those
vectors in the transverse
plane is zero!
Another Question: What
can we do to get a net
magnetization vector in
the transverse plane?
Assume these kids are all swinging at the
same frequency but out of phase. How can
we get them all in phase?
Net Magnetization
Answer: At any instant in
time the magnetic dipoles
are precessing at the
same frequency but all
out of phase. The net
summation of all those
vectors in the transverse
plane is zero!
Another Question: What
can we do to get a net
magnetization vector in
the transverse plane?
Assume these kids are all swinging at the
same frequency but out of phase. How can
we get them all in phase? You push them at
the same time and at the same frequency!
RF Excitation
Add a RF field whose
frequency is the same as the
Lamor resonant frequency of
the proton and is oriented in
the xy or transverse plane.
B1
time
z
B1
z

m
mz
mz


m

m xy
y
y
m xy
x
x
mz
mz

m xy

m xy
y
x

m

m
y
x
RF Excitation
B1
B1
time
t=0
z
z

M
mz
mz
t=0
+

m xy
=

m xy
y
y

M xy
z
z
z
mz
mz
+
t=Dt

m xy

m xy
y
x
y
x
x
x
x
z

M
=
y

M xy
x
y
RF Excitation
B1
B1
time
t=0
z
z

M
mz
mz
t=2Dt
+

m xy
=

m xy
y
y

M xy
z
z
z
mz
mz
+
t=3Dt

m xy

M

m xy
y
x
y
x
x
x
x
z
=
y

M xy
x
y
Larmor Equation
Resonant Larmor
frequency
wBo
DC or static external
magnetic field
(the big one)
Tip Angle
 wDtB1Dt
Tip Angle
Amplitude of RF Time of Application
Pulse
of RF Pulse
RF Excitation
RF Excitation
• transmission coil: apply magnetic field
along B1 (perpendicular to B0)
• oscillating field at Larmor frequency
• frequencies in RF range
• tips M to transverse plane – spirals
down
• gets all the little magnetic moments to
precess at the same phase: analogy:
children’s swingset
• final angle between B0 and B1 is the flip
angle
•B1 is small: ~1/10,000 T
Equipment
4T magnet
RF Coil
gradient coil
(inside)
B1
Gradient Coil
Bo
RF Coil
Radiofrequency Coils
Other kinds of RF Coils
Summarize
A large DC magnetic field applied to a patient aligns
his/her protons and gets them precessing like a top at the
lamor resonant frequency.
The net magnetization in the transverse plane is zero
because they are all out of phase.
 If we apply a RF field at the same Lamor resonant
frequency and oriented orthogonal to the large DC field
then we can get them all moving together (i.e. coherent
rotation). The tip angle is a function of the amplitude of
the RF pulse and how long it is applied for.

Summarize
A large DC magnetic field applied to a patient aligns
his/her protons and gets them precessing like a top at the
lamor resonant frequency.
The net magnetization in the transverse plane is zero
because they are precessing all out of phase.
 If we apply a RF field at the same Lamor resonant
frequency and oriented orthogonal to the large DC field
then we can get them all moving together (i.e. coherent
rotation). The tip angle is a function of the amplitude of
the RF pulse and how long it is applied for.

 That is all well and good but how do we get out a signal
we can measure for imaging?
MR Signal
B1
At this time we turn off the RF
excitation and use the coil as a
receiver
time
Question: What happens to the all the little
spinning protons when we turn off the RF
excitation?
MR Signal
B1
At this time we turn off the RF
excitation and use the coil as a
receiver
time
Question: What happens to all the little spinning
protons when we turn off the RF excitation?
Answer: Two things
(1) The M vector starts uncoiling back to its position
without any RF excitation
(2) The phase coherence between all the spinning
protons starts go away (i.e. they get out of
phase again).
This process is called relaxation
Signal Detection via RF coil
As the net magnetization changes we can use a
detector coil (often the same coil used for
excitation) to sense it. This is the same idea as a
electric generator (i.e. time varying magnetic fields
cutting through a coil of wire produces a voltage).
Net Magnetization
z
(longitudinal
magnetization vector)

M
Mz
a
f
x
y

M xy
(transverse magnetization vector)
Simple Bloch Equation



dM (t )
  M (t )  Bo
dt


M (t )  M x (t ) xˆ  M y (t ) yˆ  M z zˆ  M xy  M z zˆ