1. Quiz In a 2D spin warp or FT MR scan, aliasing should only occur
a) in the slice select direction
b) in the readout direction
c) in the phase encoding direction
Between adjacent phase encodes, the larger phase encode has
an additional p phase wrap across the FOV in the y direction.
Between k-space samples in the readout direction, there is a
relative 2 p phase wrap across the FOV in the x direction.

2. Imaging Considerations
We have touched earlier on some the effects that make the imaged slice magnetization look complex. Let’s quantify some of them.
Main field inhomogeneity
Bo inhomogeneity ( also know as shim)
a) magnet
1.5 T shim specifications to 1/3 ppm (parts per million)
over a 20 cm diameter sphere
~ 20 Hz at 1.5 T
Is this significant?

3. Patient-Induced Inhomogeneity
Main field inhomogeneity
Tissue’s bulk magnetic susceptibility, , can vary.
 varies by to 10-5
1 ppm to 12 ppm
Worst areas: tissue-air interface
lung / abdomen
sinus
intestines
Chemical Shift:
Electronic shielding reduces the magnetic field seen by the fat molecules.

4. Patient-Induced Inhomogeneity
z component of magnetic field
is the field inhomogeneity term.
- unintended
- due to local
neighborhood
inhomogeneity
- T2 effect
T2*
Varying magnetic field in immediate neighborhood (within a voxel) causes in-plane spins to dephase earlier than intended T2 decay. The faster decay has a decay constant referred to as T2*

5. T2* is actual decay in gradient echo experiment.
T2* Equation
T2* is actual decay in gradient echo experiment.
T2 is actual spin-spin decay of material. We will see how to easily measure this today.
Last term is decay due to local magnetic environment

6. Causes of Phase Error Main field inhomogeneity,
patient-induced inhomogeneity,
gradient non-linearity,
and blood flow
all cause phase errors (or frequency errors, depending on your point of view). That is, spins will resonate faster or slower than our basic formula predicts.
Chemical shift is another type of phase error.
Let’s study the effects of these phenomena on the two major classes of MR imaging sequences.

7. Gradient Echo  This is what we have studied to date:
90º RF t Gx t
s(t) t t  2
Where does the gradient echo form?
What happens when we push the echo time out?

8. 2D Fourier Transform (2) 2D Fourier Transform: (2D FT or Spin Warp) 1)RF t
6GRADECH.AVI
The location or phase of spins throughout the x,y plane The first time point shows the spins immediately after the RF pulse.
In the left plot, no gradient is played. In the right plot, the gradient waveform has equal positive and negative areas.
The marker on top labeled “MAG1” or “MAG2” gives the magnitude of the signal in each case.
In the left plot, a local magnetic field distortion is present that causes the
vectors to become dephased naturally and the vector sum of the vectors to become smaller over
time (T2* decay). This dephasing can be observed over a period of 16 frames in the vector plot
on the left. The vector sum of the magnetization vectors during T2* decay is indicated by
MAG1. On the right is shown the same distribution of magnetization vectors in the same local
field distortion, but with the addition of an applied magnetic field gradient along the x-direction.
The vector sum of the magnetization vectors with this additional dephasing is indicated by
MAG2. The additional dephasing caused by this gradient can be seen by comparing the left and
right vector-field plots, as well as by comparing MAG1 and MAG2. After 8 frames, the field
gradient is reversed. This can be seen by observing the behavior of the vectors in the bottom-
most row on the right. As well, the value of MAG2 begins to increase. The reversed gradient
undoes the dephasing of the originally applied gradient so that, after 16 frames, the vector field
plots and their sums are equal. As shown here, a gradient echo does not restore the signal decay
caused by field inhomogeneities or other sources of dephasing. It merely corrects its own effects.In the left plot, spins dephase due to a magnetic field inhomogeneity.
Gx(t)

9. Susceptibility Artifacts
Short echo time
Water /plastic interface
has large susceptibility.
Notice dropout of signal
around water discs in bottom image.
Note: Not exactly the same slice and so bottom slice has some water signal also around discs.
Longer echo time

10. Perils of Gradient Echo Imaging and T2*
TE = 8 ms
TE = 24 ms
0.17 T GE Orthopedic Scanner

11. Spin Echo Phenomenon

12.   Spin Echo Generation Spin Echo Generation:
90º
180º
(a)
(b)
(c)
(d)
(e)
Spin Echo Generation:
Following a 90º excitation pulse, (a -b)
the spin vectors begin to fan out and dephase because of precessional frequency differences (c) at time ,
a 180º excitation rotates all the spins about the x’ axis (d)
The spin vectors continue to precess at their slightly different frequencies, rephasing at time 2 (e).
(alternate to slide 7 - original caption)
Nishimura
Image Copyright Nishimura

13. Tip Bulk Magnetizationy' x'

14. Tip Bulk Magnetization1 y' x'

15. Tip Bulk Magnetization1 y' x'

16. Tip Bulk Magnetization1 y' x'

17. Tip Bulk Magnetization1 y' x'

18. Transverse Magnetizationy'
Mtrans x'

19. T2 Decay z' s y' f x'
T2 relaxation is dephasing of transverse magnetization

20. T2 Decay z' s y' f x'
T2 relaxation is dephasing of transverse magnetization

21. T2 Decay z' s y' f x'
T2 relaxation is dephasing of transverse magnetization

22. Refocusing Pulse z' s y' B 1 f x'

23. Refocusing Pulse z' s y' B 1 f x'

24. Refocusing Pulse z' s y' B 1 f x'

25. Rephasing z' s y' f x'

26. Rephasing z' s y' f x'

27. Rephasing z' s y' f x'

28. Echo Formation z' y'
Mtrans x'

29. Spin Echoes
The phase errors E are for the most part out of our control, but there is a method around them called a spin echo.
Chemical shift, CS , can be compensated with techniques beyond the scope of this class. But these require more scan time also..
However, we can use a “spin echo” to correct for both effects. Spin echoes form the second major class of pulse sequences.
Spin echoes use a 90º pulse as we have seen, but also a second RF pulse, a 180º pulse. Let’s first consider just the effects of off-resonance and ignore the imaging gradients.
180º
90º RF t  2

30. Spin Echo Generation in Rotating Frame 
90º
180º
(a)
(b)
(c)
(d)
(e)
The phase error just prior to the 180º pulse is
Just after the 180º pulse, it is
Then we let the spins progress for another .
A “spin echo” is said to be formed at t=2
Image Copyright Nishimura

31. Effect of echo delay on signal loss
Effect of echo delay on susceptibility-induced signal losses:
(a) TE = 15 ms
(b) TE = 10 ms
(c) TE = 5 ms
Note artifactual signal reduction in the region of the nasal and mastoid sinuses.
Notice homogeneity of water discs
and air bubble appearance.
image source?

32. Spin Echo Pulse Sequencet t
Echo Time (TE) = 2 t
Z grad 90
180 90 RF
X Grad TE Gy
Y Grad TR

33. Spin Echo Signal Plus X Readout Gradient
6SPINECH.AVI
Left plot experiences no refocusing pulse. Right plot experiences
refocusing pulse half way through time series. Sum of magnitude of
spins given on top. Time series ends at echo time.

34. Spin Echo RF Sequence T2
T2* TE TR
T2* 1 = T2 +
B0

35. Spin Echo Sequence with 180 y pulse
Fig from Illustrator mag 120%

36. Spin Echo Sequence – Long Versus Short T2
long T2
long T2
short T2
short T2
T2-weighting: long TE, long TR
PD-weighting: short TE, long TR

37. T1, T2, and Density-Weighted Images
T1_brain_w_tumor.tif, t2_brain_w_tumor.tif, density_brain_w_tumor.tif
From wesolak, janet, series 2, image 16, series 3, image 38, series 3, image 37
T1-weighted
T2-weighted
r-weighted

38. Scan Duration
Scan Time = TR  PE  NEX
TR = repetition time
PE = number of phase encoding values
NEX = number of excitations (averages)

39. Spin Echo Formation
For spins to be refocused, they must experience the same magnetic field after the 180 refocusing pulse as they experienced before the 180 refocusing pulse.
Thus, only dephasing due to macroscopic inhomogeneities (B0) is refocused. Dephasing due to microscopic inhomogenieties (T2) is not refocused.

40. Spin Echo Parameters TR TE T1-weighting short (400 msec)
long (3000 msec)
long (100 msec)
-weighting

41. Signal vs Weighting T1-weighted T2-weighted r-weighted T1-weighting
long T1, small signal
short T1, large signal
T2-weighting
long T2, large signal
short T2, small signal
-weighting
high , large signal
low , small signal

42. Images of the Knee
-weighted
T2-weighted
Needs longer TE

43. T2 & T2* Relaxation: Image Contrast Sources
Mxy
T2*
Time
T2* 1 = T2 +
B0

44. FSE Pulse Sequence Timing Diagram
90°
180°
180°
180°
180° rf
Slice
Select
Phase
Encode
Freq.
Encode
ETL=4
Signal
ESP

45. Filling k-space FSE
Phase
Direction
Frequency Direction

46. Scan Duration
Scan Time = TR  PE/ETL  NEX
TR = repetition time
PE = number of phase encoding values
NEX = number of excitations (averages)
ETL = echo train length

47. T2 Weighting (Various Sequences)
TR = 2500
TE = 116
ETL = 16
NEX = 2
24 slices
17 slices/pass
2 passes
Time = 2:51
TR = 2500
TE = 112
ETL = N/A
NEX = 1
24 slices
20 slices/pass
2 passes
Time = 22:21
FSE SE

48. Inversion Recovery RF Sequence

49. Inversion Recovery (IR) Sequence & Spin Behavior

50. Inversion Recovery rf Slice Select Phase Encode Freq. Encode Signal TI
180°
90°
180° rf
Slice
Select
Phase
Encode
Freq.
Encode
Signal

51. IR Sequence – Short Versus Long T1
Fig from Illustrator mag 150%, separate sections

52. Inversion Recovery Signal
Mlong
short T1
longer T1
Short T1 = brighter
Long T1 = darker TI

53. Inversion Recovery Signal
Mlong
short T1
longer T1
Short T1 = brighter
Long T1 = null TI

54. Short Tau Inversion Recovery (Fat Nulled)
STIR
Mlong
short T1 (fat)
longer T1
Short T1 = null
Long T1 = brighter TI

55. Spine: T1 versus T2 versus STIR

56. Inversion Recovery II IR pulse precedes T2-weighted sequence
Coronal Tumor
Here the inversion recovery delay is very long ( ~2 s). Here the idea
is to null CSF so one can distinguish tumor from CSF. Notice tumor
still has positive contrast.

57. MR: SNR vs Field Strength
Signal
- energy separation of Zeeman levels
- Faraday’s Law of Induction
Signal amplitude is
Noise Power
Receiver
- electronics
- patient electrons in Brownian motion
Patient
Patient noise dominates at most field strengths

58. SNR
We will first consider the case where we ignore T1 and T2 of the tissue involved.
leave sequence dependent effects for later

59. SNR Noise Power Study for impulse at x=0, y = 0
Each k-space point has signal A, noise power 2
Each sampled point is independent with respect to noise. ky
Amplitude of Signal = NxNyA
Noise Power = NxNy 2 Ny kx Nx
sampling interval in time

60. voxel size since this determines the # of protons per voxel
SNR
voxel size since this determines the
# of protons per voxel
Replace A above by voxel size
Together,
SNR
Time
Resolution

61. Scan Time Image b) has twice the SNR as a)
at an expense of four times the scan time

62. Axial Forearm T2-Weighted
TE = 15 ms
TE = 45 ms
TE = 75 ms
TR = 4000 ms for all
Notice appearance of supinator
Muscle ( arrow) on all images.
One arm had an exercise protocol.
Which one? What is in between arms?
TE = 105 ms

63. q q q q TR
During each TR, Mz will recover.
When in steady-state,
Where n-1 is the n-1th RF pulse
and n is the nth RF pulse.