1. Basics of Magnetic Resonance Imaging

2. Angular Momentum Orbital Angular Momentum
Principles of Medical Imaging – Shung, Smith and Tsui

3. Angular Momentum Spin Angular Momentum Spin is an intrinsic property
of the nucleons (protons
and neutrons) in a nucleus
HOWEVER –
The name doesn’t mean that
spin results from the nucleons
rotating about an axis!!!

4. Spin Angular Momentum
Spin is quantized – it can only take certain values
Here I is the total spin quantum number of the
nucleus. The proton has I = ½. Lz is the
angular momentum due to that spin.

5. Spin Angular Momentum To get the total spin of a nucleus we add up
(separately) the spins of the protons and neutrons
15N has spin ½ .
We do pairwise
addition:
7 protons
8 neutrons
Only nuclei with an odd number of protons
or neutrons will be visible to MRI
Note: 14N has spin 1.

6. Alignment of Spins in a Magnetic Field, B0
The spin angular momentum yields
a magnetic moment
Principles of Medical Imaging – Shung, Smith and Tsui

7. Energy Levels of Spins and B0
Principles of Medical Imaging – Shung, Smith and Tsui

8. Energy Levels and Spin E1 = B0 E2 = -B0 E = E1 - E2 = 2 B0
= (h/2) B0 for spin-1/2 particles
B0 is the main magnetic field

9. Energy Level Population and Field Strength
2,000,000
1,000,002
999,999
999,995
1,000,005
999,987
1,000,014
B0 = 0
n = 0
B0 = 0.5T
n = 3
B0 = 1.5T
n = 10
B0 = 4.0T
n = 27
Spins are distributed according to the Boltzmann distribution

10. Larmor Frequency
Principles of Medical Imaging – Shung, Smith and Tsui

11. Excitation Energy and Frames of ReferenceB0 B1
Beff
B0 = main magnetic field
B1 = applied field (pulse)
Beff = vector sum B0+B1 z z   y y
lab frame
rotating frame x x

12. Net Magnetization, M, and the
Rotating Frame
While B1  0, M
precesses around B1 z z M M y y B1 x x
B0  0
B1 = 0
B0  0
B1  0

13. Net Magnetization, M, and the
Rotating Frame
We turn B1 “on” by a applying radiofrequency (RF) to the sample at the Larmor frequency. This is a resonant absorption of energy.
If we leave B1 on just long enough for M to rotate into the x - y plane, then we have applied a “90 pulse”. In this case, Nupper = Nlower.
If we leave B1 on just long enough for M to rotate along the -z axis, then we have applied a “180 pulse” (inversion). In this case, Nupper = Nlower + M.

14. Free Induction Decay What is the effect of applying a 90  pulse? /2RF
time

15. Free Induction Decay
The effect of a 90 pulse is to rotate M into the x - y
(transverse) plane. If we place a detection coil (a loop of wire)
perpendicular to the transverse place, we will detect an induced
current in the loop as M precesses by (in the lab frame).
Minitial y x z
Mfinal B1
Principles of Medical Imaging – Shung, Smith and Tsui

16. Signal Processing of Free Induction Decay
Principles of Medical Imaging – Shung, Smith and Tsui
We can characterize the signal by its:
Amplitude
Phase
Frequency
Fourier Transform

17. Signal Processing of Free Induction Decay
We see that after a 90 pulse, we get a cosinusoidal signal.
To quantitatively describe the signal we
calculate its Fourier transform.
(think: Larmor frequency)
Principles of Medical Imaging – Shung, Smith and Tsui

18. Fourier Transform of Time Domain Data

19. Will it be a useful image?
Image Contrast (I)
We can detect the signal from water molecules in the body.
Can we make an image?
Will it be a useful image?

20. Relaxation Processes
Fortunately for us, the signal we get from water molecules
in the body depends on their local environment.
Spins can interact by exchanging or losing energy (or both).
As in all spectroscopy methods, we put energy into the
system and we then detect the emitted energy to learn
about the composition of the sample.
We then use some variables to characterize the emission of
energy which (indirectly) tell us about the environment of
the spins.
Image Contrast!

21. Relaxation Processes (T2)
1. Spin-spin relaxation time (T2): when spins interact
With each others magnetic field, they can exchange energy (perform a spin flip). They can lose phase coherence, however. Only affects Mxy.
Signal without T2
interaction between
spins
T2*
Signal including T2
interactions between
spins
T2*???

22. T2* and T2
T2 is an intrinsic property of the sample. This is what we are interested in to use for contrast generation.
T2* is the time constant of the decay of the free induction decay. It is related to the intrinsic T2 in the following way:
depends upon the local
magnetic field
sample
only

23. T2* and T2 Not a random random process process
Inhomogeneity term - dephasing due to magnet (B0) imperfections depends upon position
Susceptibility term - dephasing due to the interaction of
different sample regions with B0
(depends upon position)

24. Relaxation Processes (T2)
/2 pulse
 (delay)

25. Effect of Spin Coherence on Signalx y z x y z
T2*

26. Irreversible versus Reversible
Start
Reverse

27. Hahn Spin Echo Pulse Sequence

28. Hahn Spin Echo and T2
We can calculate T2 by changing the echo spacing, , and recording the signal at 2.
Signal
Echo spacing , 

29. Spin-Lattice Relaxation, T1
To look at the behavior of the longitudinal component of M (Mz), we start by putting M along the -z axis and then read it out with a 90 pulse.

30. Spin-Lattice Relaxation, T1 Energy levels and Inversion
Equilibrium
After Inversion
Net
Magnetization: = =

31. Relaxation Processes (T1)
 pulse
long TI
short TI
/2 pulse
/2 pulse

32. Image Contrast and T1 In (a) the TI is chosen to null the signal from
curve [ii], while the TI in (b) nulls out [i]

33. Now Can We Make A Useful Image?

34. Magnetic Resonance Imaging

35. Magnetic Resonance Image Formation
What do we need?
Ability to image thin slices
2. No projections - image slices with arbitrary orientation
3. Way to control the spatial resolution
4. Way to carry over the spectroscopic contrast mechanisms
to imaging.

36. Magnetic Resonance Image Formation
How can we spatially encode this signal?
Principles of Medical Imaging – Shung, Smith and Tsui

37. Magnetic Resonance Image Formation - Slice Selection
Magnetic field gradients: B = B(position)
precessional frequency is
now a function of position

38. Magnetic Resonance Image Formation - Slice Selection
 = frequency bandwidth
z = slice thickness
MRI: Basic Principles and Applications - Brown, Semelka

39. Magnetic Resonance Image Formation - Slice Selection
How do we excite only a slice of spins?
Fourier Pairs!
sinc
rect FT
time
frequency

40. Magnetic Resonance Image Formation - Phase Encoding
So far we have a slab of tissue whose spins are
excited. The next step is to place a grid over
the slab and define pixels.

41. Magnetic Resonance Image Formation - Phase Encoding
eff < 0 Gy
eff > 0
Center of
magnet

42. Magnetic Resonance Image Formation - Phase Encoding
Apply gradient for a finite duration   = (y)
(the phase of M over each region of the sample depends
upon it’s position)
This is because the gradient makes each spin precess with
an angular frequency that depends on it’s position. For
the duration of the gradient, t, spins move faster or slower
than 0 depending upon where they are. After the gradient
is turned off, all spins again precess at 0.
The phase accumulated
during time, t, is:

43. Magnetic Resonance Image Formation - Phase Encodingx’ y’ z’
M after a 90
pulse
Turn on the phase encoding gradient x’ y’ z’ x’ y’ z’ x’ y’ z’
Gy = 0
Gy < 0
Gy > 0

44. Magnetic Resonance Image Formation Frequency Encoding (Readout)
Now we need to encode the x-direction...
How do we spatially encode the
frequency of the signal?
Can we turn on another gradient?
When? And for how long?

45. Magnetic Resonance Image Formation Frequency Encoding (Readout)
We apply a gradient while the signal is being acquired
as the spin-echo is being formed. 
/2 RF
Signal Gx
time
Therefore, the precessional frequency is a function of position

46. Magnetic Resonance Image Formation Spin-echo Pulse Sequence
?(3)
? (1)
?(2)

47. (1) Phase Encoding: Each acquisition is separately encoded
with a different phase.
The sum total of the N
acquisitions is called
the ‘k-space’ data.

48. The Effect of Frequency Encoding on the Signal (dephasing gradient)
(2)
MRI: Basic Principles and Applications - Brown, Semelka

49. Slice-select refocusing gradient (3) z y x
The effect of having the gradient on during the time that
the magnetization is moving from the z-axis to the y-axis is
to curve the path. In general, one needs to apply a slice
refocussing gradient of opposite magnitude after the RF
pulse so that the spins are in phase at the end of the pulse.
The area of the negative gradient must be one half the area
of the slice selection gradient pulse.

50. Structure of MRI Data: k-space

51. Structure of MRI Data: k-space
What is k-space?
The time-domain signal that we collect from each
spatially encoded spin echo gets put in a matrix.
This data is called k-space data and is a space of
spatial frequencies in an image.
To get from spatial frequencies to image space
we perform a 2-D Fourier Transform of the
k-space data.
General intensity level is represented by low spatial
frequencies; detail is represented by high spatial freq’s.

52. low spatial frequencies high spatial frequencies all frequencies

53. Structure of MRI Data: k-spaceFT
k-space data
image data