1. Principles of MRI Physics and Engineering
Allen W. Song
Brain Imaging and Analysis Center
Duke University

2. 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.

3. MRI  Cool (and Useful) Pictures
axial
coronal
sagittal
2D slices extracted from a 3D image
[resolution about 111 mm]

4. 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 [ 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

5. Lecture Components I) Magnetic fields and magnetization,
fundamental ideas about NMR signal
II) How to make an image,
introduction to k-space
III) MRI contrast mechanisms,
various imaging techniques

6. And Magnetization, Fundamental of NMR Signal
Part I
Magnetic Fields
And Magnetization, Fundamental of NMR Signal

7. Magnetic Fields, Magnetization,
NMR Signal Generation

8. rf coil main magnet gradient Shimming Control Computer Receive
Transmit
Receive rf
coil
main
magnet
gradient
Shimming
Control
Computer

9. 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.

10. Magnetic and Electromagnetic Fields
Magnetic fields generate the substance we “see”: magnetization of the H protons in H2O
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
Gradient magnetic fields change quickly (switching up to thousands of times per second):
RF fields are electromagnetic fields that oscillate at Radio Frequencies (tens of millions of times per second)
transmitted radio waves into subject
received signals from subject

11. 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)
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]

12. Main Magnet Field Bo
Purpose is to align H protons in H2O (little magnets)
[Main magnet and some of its lines of force]
[Little magnets lining up with external lines of force]

13. 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:
1H, 13C, 19F, 23N, and 31P with gyromagnetic ratio of 42.58, 10.71,
40.08, and MHz/T.
Since hydrogen protons are the most abundant in human body, we use
1H MRI most of the time.

14. A Single Proton m 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 = g J where g is the gyromagnetic ratio
Thus proton “magnet” differs from the magnetic bar in that it
also possesses angular momentum caused by spinning.

15. Similarity between a spinning proton and a spinning magnetic bar+ + + + + + + S

16. Protons in Free Space
What happens if they are in a magnetic field ?

17. Magnetic Bar in a Magnetic FieldBo N S S
Static magnetic bar
Spinning magnetic bar

18. Protons in a Magnetic FieldBo
Parallel
(low energy)
Anti-Parallel
(high energy)
Spinning protons in a magnetic field will assume two states.
If the temperature is 0o K, all spins will occupy the lower energy state.

19. Net Magnetization Bo M

20. Small B0 produces small net magnetization M
Basic Quantum Mechanics Theory of MR
Small B0 produces small net magnetization M
Thermal motions try to randomize alignment of proton magnets
Larger B0 produces larger net magnetization M, lined up with B0
At room temperature, the population ratio is roughly 100,000 to 100,006 per Tesla of B0

21. The Energy Difference Between
Basic Quantum Mechanics Theory of MR
The Energy Difference Between
the Two States
D E = h n
where n = g Bo / 2p,
known as larmor frequency
g = MHz / Tesla

22. Knowing the energy difference allows us to use
Basic Quantum Mechanics Theory of MR
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.

23. Spin System Before Irradiation
Basic Quantum Mechanics Theory of MR
Spin System Before Irradiation Bo
Lower Energy
Higher Energy

24. The Effect of Irradiation to the Spin System
Basic Quantum Mechanics Theory of MR
The Effect of Irradiation to the Spin System
Lower
Higher

25. Spin System After Irradiation
Basic Quantum Mechanics Theory of MR
Spin System After Irradiation

26. Precession of Magnetization M
Classical Mechanics Theory of MR
Precession of Magnetization M
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. Bo
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
N.B.: part of M parallel to Bo (Mz)
does not precess

27. Classical Mechanics Theory of MR
A Mechanical Analogy
A gyroscope in the Earth’s gravitational field is like magnetization in an externally applied magnetic field

28. How to Make M not be Parallel to B?
Classical Mechanics Theory of MR
How to Make M not be Parallel to B?
A way that does not work:
Turn on a second big magnetic field B1 perpendicular to main B0 (for a few seconds)
Then turn B1 off; M is now not parallel to magnetic field B0
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 B1 perpendicular to B0 B1
B0+B1 B0
M would drift over to be aligned with sum of B0 and B1

29. RF Coil: Transmitting B1 Field
Classical Mechanics Theory of MR
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 B1 that fluctuates at the precession frequency and points perpendicular to B0 (how do we achieve this? – by making a coil)
The effect of the tiny B1 is
to cause M to spiral away
from the direction of the
static B field
B110–4 Tesla
This is called resonance
If B1 frequency is not close to
resonance, B1 has no effect
Time = 2–4 ms

30. Another Mechanical Analogy: A Swingset
Classical Mechanics Theory of MR
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 B1
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 B1 to slowly flip M over g

31. Rotating Frame (compared to Laboratory Frame)
Classical Mechanics Theory of MR
Rotating Frame (compared to Laboratory Frame) w
Rotating Frame
Laboratory Frame

32. Spin Excitation using Rotating Frames Reference
Classical Mechanics Theory of MR
Spin Excitation using Rotating Frames Reference M
q = g B1 t B1 M q
Notice the disappearance of the Bo term in rotating frame

33. What if the RF field is not synchronized?
Classical Mechanics Theory of MR
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
B1eff = B1 + Dw/g
where
Dw = wo – we
Dw/g
B1eff B1

34. RF Coil: Signal Receiver
Classical Mechanics Theory of MR
RF Coil: Signal Receiver
When excitation RF is turned off, M is left pointed off at some angle to B0 [flip angle]
Precessing part of M [Mxy] 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

35. RF Coil: Signal Receiver
Classical Mechanics Theory of MR
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 Mxy inside the coil
Must find a way to separate signals from different regions

36. 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)

37. Gradient Coils: Spatially Nonuniform B:
Extra static magnetic fields (in addition to B0) that vary their intensity in a linear way across the subject
Precession frequency of M varies across subject
Center
frequency
[63 MHz at 1.5 T] f
60 KHz
Gx = 1 Gauss/cm = 10 mTesla/m
= strength of gradient field
x-axis
Left = –7 cm
Right = +7 cm

38. A 3-D gradient field (dB/dx, dB/dy, dB/dz) would
allow a unique correspondence between the spatial
location and the magnetic field. Using this information,
we will be able to generate maps that contain spatial
information – images.

39. Gradient Coils Gradient coils generate varying magnetic field so thatz z z y y y x x x
X gradient Y gradient Z gradient
Gradient coils generate varying magnetic field so that
spins at different location precess at frequencies unique
to their location, allowing us to reconstruct 2D or 3D
images.

40. Spatial Encoding – along x

41. Spatial Encoding of the MR Signal
0.8
Spatial Encoding of the MR Signal
Constant
Magnetic
Field
Varying
Magnetic
Field
w/o encoding
w/ encoding

42. Spatial Encoding of the MR Signal
Fourier Transform

43. Spatial Encoding – along y

44. Relaxation Characteristics
About the NMR Signal

45. Relaxation: Nothing Lasts Forever
In absence of external B1, M will go back to being aligned with static field B0 — this is called relaxation
Part of M perpendicular to B0 shrinks [Mxy]
This part of M is called transverse magnetization
It provides the detectable RF signal
Part of M parallel to B0 grows back [Mz]
This part of M is called longitudinal magnetization
Not directly detectable, but is converted into transverse magnetization by externally applied B1

46. Relaxation Times and Rates
Times: ‘T’ in exponential laws like e–t/T
Rates: R = 1/T [so have relaxation like e–Rt]
T1: Relaxation of M back to alignment with B0
Usually ms in the brain [lengthens with bigger B0]
T2: Intrinsic decay of the transverse magnetization over a microscopic region ( 5-10 micron size)
Usually ms in the brain [shortens with bigger B0]
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]

47. T2* Relaxation
S = So * e –t/T2*

48. Material Induced Inhomogeneities Will Affect T2*
Adding a nonuniform object (like a person) to B0 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B0 = 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”

49. 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 t in cos(t) [frequency f = /2]

50. Sum of 500 Cosines with Random Frequencies
Starts off large when all phases are about equal
Decays away as different
components get different phases
High frequency gray curve is at the average frequency

51. T2* relaxation (decay) and NMR Signal
Random frequency differences inside intricate tissue environment cause RF signals (from Mxy) 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), Mxy 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

52. Hahn Spin Echo: Retrieving Lost Signal
Problem: Mxy rotates at different rates in different spots
Solution: take all the Mxy’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

53. The “magic” trick: Flip of the magnetization M
Apply a second B1 pulse to produce a flip angle of 180 about the y-axis (say)
Time between first and second B1 pulses is called TE/2
“Echo” occurs at time TE

54. Spin Echo:  Excite  Precess  180 flip  Precess & dephase
& rephase

55. 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 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 Mxy is called T2
S = So * e-t/T2

56. T1 Relaxation Longitudinal relaxation of Mz back to “normal” (T1)
Caused by internal RF magnetic fields in matter
Thermal agitation of H2O molecules
Can be enhanced by magnetic impurities in tissue
S = So (1-et/T1)

57. Proton Density Weighted Image

58. T1 Weighted Image

59. T2 Weighted Image

60. 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

61. Contrast Agents that Affects Relaxation Rate
Drugs containing certain impurities can alter T1, T2, and T2* — contrast agents (e.g., CuSO4, Gd-DTPA)