eleg 479 lecture # 9 magnetic resonance (mr) imaging
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ELEG 479Lecture #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 transmitterStep #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 imagesStep#7: Allow subject to leave scanner (this is optional)
Equipment
Magnet Gradient Coil RF Coil
RF Coil
4T magnet
gradient coil(inside)
B0
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?
proton
electron
Quantum mechanical property called proton spin
Quantum mechanical property called electron spin
Let’s first look at a simple hydrogen atom without any appliedexternal 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 appliedexternal magnetic field.
proton
electron
Quantum mechanical property called proton spin
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 appliedexternal magnetic field.
proton
electron
Quantum mechanical property called proton spin
Quantum mechanical property called electron spin
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.
Belectron
Bproton
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 appliedexternal magnetic field.
proton
electron
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.
Belectron
Bproton
S
N
N
S
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 appliedexternal magnetic field.
proton
electron
Quantum mechanical property called proton spin
Quantum mechanical property called electron spin
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.
Belectron
Bproton
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 appliedexternal magnetic field.
proton
electron
Quantum mechanical property called proton spin
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?
H11 C13
6 O178 F19
9 Na2311 P31
15 K3919
These guys will also possess a non-zero magnetic spin.
.093.0161.0 .066
Relative sensitivity compared to hydrogen
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 appliedexternal magnetic field.
proton
electron
Quantum mechanical property called proton spin
Quantum mechanical property called electron spin
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?
Belectron
Bproton
So what happens to things that are normally non-magnetic when you put them inside big magnetic fields?
RandomOrientation
= No NetMagnetization
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?
Now, let’s look at a proton when we apply an external static magnetic field Bo
Bore(55 – 60 cm)
Shim(B0 uniformity)
Magnetic field (B0)
Body RF(transmit/receive)
Gradients
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
FirstThe 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
FirstThe 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
SecondThe 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 PrecessionNow, 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)
x
yxy (transverse plane)
x
y
z
zm m
xymf
a
zzytxtt zxyzyx ˆˆˆ)(ˆ)()( mmmmmm
Magnetic moment vector
zzytxtt zxyzyx ˆˆˆ)(ˆ)()( mmmmmm
x
y
z
zm m
xymf
a
(longitudinalmagnetization vector)
(transverse magnetization vector)
Magnetic Moment Vector of Proton
Net Magnetization
z
x
y
zm m
xym
Add all the magnetic moments from all the protons together at some instant in time
x
y
z
zm
m
xym
x
y
z
zm m
xym
z
x
y
zm
m
xymx
y
z
zm
m
xym
z
x
y
zm m
xym
Add all the magnetic moments from all the protons together at some instant in time
x
y
z
zm
m
xym
x
y
z
zm m
xym
z
x
y
zm
m
xymx
y
z
zm
m
xym
Net Magnetization Vector
zMtMtM
tzyxtM
zxy
N
nnnnn
ˆ)()(
),,,()(1
m
Net Magnetization
z
x
y
zm m
xym
Question: Anything we can say about Mxy?
x
y
z
zm
m
xym
x
y
z
zm m
xym
z
x
y
zm
m
xymx
y
z
zm
m
xym
Net Magnetization Vector
zMtMtM
tzyxtM
zxy
N
nnnnn
ˆ)()(
),,,()(1
m
Net Magnetization
Question: Anything we can say about Mxy?
zMtM
tzyxtM
z
N
nnnnn
ˆ)(
),,,()(1
m
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?
x
y
z
zM M
xyM
(transverse magnetization vector)
(longitudinalmagnetization vector)
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!
Net Magnetization
RF Excitation
time
B1
x
y
zm m
xym
x
y
z
zm
m
xym
x
y
z
zm m
xym
x
y
zm
m
xym
B1
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.
RF Excitation
time
B1
x
y
z
zm
xym
x
y
z
zm
xym
B1
t=0
t=0
x
y
z
M
xyM
=+
t=Dt
x
y
z
zm
xym
x
y
z
zm
xym
x
y
zM
xyM
=+
RF Excitation
time
B1
x
y
z
zm
xym
x
y
z
zm
xym
B1
t=0
t=2Dt
x
y
z
M
xyM
=+
t=3Dt
x
y
z
zm
xym
x
y
z
zm
xym
x
y
z
M
xyM
=+
wBo
wDtB1Dt
Tip Angle Amplitude of RFPulse
Time of Applicationof RF Pulse
Larmor Equation
Tip Angle
DC or static external magnetic field(the big one)
Resonant Larmorfrequency
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
RF Coil
4T magnet
gradient coil(inside)
Gradient Coil RF Coil
BoB1
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
time
B1
Question: What happens to the all the little spinning protons when we turn off the RF excitation?
At this time we turn off the RF excitation and use the coil as a receiver
MR Signal
time
B1
Question: What happens to all the little spinning protons when we turn off the RF excitation?
At this time we turn off the RF excitation and use the coil as a receiver
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).
zMMzMytMxtMtM
BtMdttMd
zxyzyx
o
ˆˆˆ)(ˆ)()(
)()(
Simple Bloch Equation
x
y
z
zM M
xyMf
a
(transverse magnetization vector)
(longitudinalmagnetization vector)
Net Magnetization
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