1. ELEG 479 Lecture #9 Magnetic Resonance (MR) Imaging
Mark Mirotznik, Ph.D.
Professor
The University of Delaware

2. 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 ( 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)

3. Equipment B0 Magnet Gradient Coil RF Coil 4T magnet RF Coil
(inside)
Magnet
Gradient Coil
RF Coil

4. Magnetic Fields are Huge!
Typical MRI Magnet: Tesla (T)
Earth’s magnetic field: 50 mTesla

5. So what happens to things that are normally non-magnetic when you put them inside big magnetic fields?

6. 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 electron spin
Quantum mechanical property called proton spin
proton

7. 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 electron spin
Quantum mechanical property called proton spin
proton
We can think of spin from a classical point of view as the proton or electron rotating about some axis.

8. 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 electron spin
Quantum mechanical property called proton spin
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.

9. 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 N S S N
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.

10. 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 electron spin
Quantum mechanical property called proton spin
Belectron
proton
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.

11. 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 electron spin
Quantum mechanical property called proton spin
proton
Question: So do the nucleus of all atoms possess this magnetic property or is hydrogen special?

12. To be imaged, nuclei must:
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

13. 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. H 1 C 13 6 O 17 8 F 19 9 Na 23 11 P 31 15 K 39 19
1.0
.016
.093
.066
Relative sensitivity compared to hydrogen

14. 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 electron spin
Quantum mechanical property called proton spin
Belectron
proton
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?

15. = No Net Magnetization Random Orientation
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? =
No Net
Magnetization
Random
Orientation

16. 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

17. 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

18. 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?

19. 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.

20. 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

21. 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

22. 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.

23. 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.

24. Larmor Precession
Now, let’s look at a proton when we apply an external static magnetic field Bo

25. So what happens to things that are normally non-magnetic when you put them inside big magnetic fields?
Precession Demo

26. Magnetic Moment Vector of Proton
Components of the Precessing Proton
Z (longitudinal) x y z f a y
xy (transverse plane) x
Magnetic moment vector

27. Magnetic Moment Vector of Protonx y z f a
(longitudinal
magnetization vector)
(transverse magnetization vector)

28. Net Magnetization
Add all the magnetic moments from all the protons together at some instant in time x y z x y z x y z z z x y x y

29. Net Magnetization
Add all the magnetic moments from all the protons together at some instant in time x y z x y z x y z z z x y x y
Net Magnetization Vector

30. Net Magnetization Question: Anything we can say about Mxy? z z z y y x
Net Magnetization Vector

31. Net Magnetization Question: Anything we can say about Mxy?
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! x y z
(longitudinal
magnetization vector)
Another Question: What can we do to get a net magnetization vector in the transverse plane?
(transverse magnetization vector)

32. 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?

33. 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!

34. 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 x y z x y z B1 x y x y

35. RF Excitation B1 + = + = B1 time t=0 z z z t=0 y y y x x x z z z t=Dt

36. RF Excitation B1 + = + = B1 time t=0 z z z t=2Dt y y y x x x z z z

37. Bo  = DtB1Dt Larmor Equation Tip Angle Tip Angle
DC or static external
magnetic field
(the big one)
Resonant Larmor
frequency
Bo
Tip Angle
 = DtB1Dt
Tip Angle
Amplitude of RF
Pulse
Time of Application
of RF Pulse

38. 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

39. Equipment Gradient Coil RF Coil Bo B1 4T magnet RF Coil gradient coil
(inside)

40. Radiofrequency Coils

41. Other kinds of RF Coils

42. 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.

43. 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?

44. MR Signal
At this time we turn off the RF excitation and use the coil as a receiver B1
time
Question: What happens to the all the little spinning protons when we turn off the RF excitation?

45. MR Signal
At this time we turn off the RF excitation and use the coil as a receiver B1
time
Question: What happens to all the little spinning protons when we turn off the RF excitation?
Answer: Two things
The M vector starts uncoiling back to its position without any RF excitation
The phase coherence between all the spinning protons starts go away (i.e. they get out of phase again).
This process is called relaxation

46. 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).

56. Net Magnetization z (longitudinal magnetization vector) a y f x
(transverse magnetization vector)
(longitudinal
magnetization vector)
Simple Bloch Equation