1. MRI Pulse Sequences: IR, EPI, PC, 2D and 3D
Lawrence P. Panych
Radiology Department
Brigham and Women’s Hospital
Harvard Medical School

2. Selective Excitation RFmz mz mz mz my my my my mx mx mx mx mz mz mz mz my my my my mx mx mx mx mz mz mz mz my my my my mx mx mx mx
Excite magnetization in transverse plane where it can be detected

3. Special gradient coils give a linear variation of mz my mx
w w w w4
Resonant
frequency, w x
Good reason that data comes Fourier encoded.
In general, is not that easy to locally interrogate the spin system. In response to an interrogation the spins all `talk’ at once and we only have one listening device. To localize information, an effective way is to vary the frequency of the local responses, record the responses over the full frequency spectrum and then do a frequency analysis.
Special gradient coils give a linear variation of
field strength with spatial location.
The result is a proportional mapping between
resonant frequency and spatial location

4. Gradient on during RF With an applied field
Excite spins here
With an applied field
gradient, the resonant frequency
varies with position
Excite spins here

5. Slice selection with shaped RF
Excite spins here
Resonant frequency
varies with position
Excite spins here

6. Slice selection with shaped RF

7. my mx mz

8. Fourier Encoding – 2D example, 2x2 FOV
Initial State After RF Excitation my my
a b mx
a b mx mz mz y
c d
c d
In exploring non-Fourier encoding it is best to first be clear about Fourier encoding.
I find a simple 2x2 example to be useful to follow the steps in Fourier encoded MRI.
Imagine that we are resolving 4 voxels within the imaging volume.
The system is represented by 4 magnetization vectors arranged as shown
Initially, along Mz.
After RF excitation, magnetization vector is titled to produce some component in the transverse plane.
In the 2x2 example, the transverse components are encoded on two separate excitations using x and y gradients to manipulate the phases of each vector. RF
Pulse x
There are 4 unknowns (a-d), therefore, we need 4 measurements.
Since there are 2 dimensions, we need 2 spatial gradients.

9. Fourier Encoding (Step 1)
t t t2
a b
c d
Initially after excitation, all vectors are aligned.
Assume that the goal is to detemine the magnitudes of the individual vectors, [abcd].
What we record is a phase sensitive signal proportional to the vector magnitudes.
On first excitation, at t1 before the effect of any gradients is felt, signal A is recorded and is equal to a+b+c+d.
A second measurement is acquired at t2 at which time the effect of the x gradient is to change the phase of magnetization vectors on the right side of the volume.
RF excitation Y Gradient Off X Gradient On
Signal at time t1 = A = a + b + c + d
Signal at time t2 = B = a - b + c - d

10. Fourier Encoding (Step 2)
t t t2
a b
c d
So far only have 2 measurements but have 4 variables. Also, there has not been any variation in the vertical direction.
Therefore, organize a 2nd encoding step. This time put on a y gradient right after the excitation to invert the phase of the mag vectors at the bottom.
At t1, signal C is recorded as above.
At t2, the effect of the x gradient is again to invert the phase of mag vectors on the right side of the volume.
A final signal D is recorded.
RF excitation Y Gradient On X Gradient On
Signal at time t1 = C = a + b - c - d
Signal at time t2 = D = a - b - c + d

11. Fourier Encoding – Matrix Representation
System of Equations:
Alternate Form:
From 1st Excitation:
A = a + b + c + d
B = a - b + c - d
From 2nd Excitation:
C = a + b - c - d
D = a - b - c + d
A a
B b
C c
D d =
A B a b
C D c d
Summary.
Four equations and 4 unknowns. Can solve for [a,b,c,d]. Easy to invert the 4x4 matrix above.
Can represent in an alterative form showing explicitly the encoding matrices for the vertical and horizontal directions. =
Image
matrix
Data matrix
(k-space)
Horizontal (x)
Encoding
Vertical (y)
Encoding

12. Fourier Encoding - using gradients to encode phaseB
A + B
A - B 2 4 8
x = A B C D
A + B + C + D
A - iB - C + iD
A - B + C - D
A + iB - C - iD
x = A B C D E F G H x

13. Fy Fx Echo-Planar Imaging (EPI) A B D C a b d c t0 t1 t2 t3 t4
c d
Xgrad
Ygrad
Initially after excitation, all vectors are aligned.
Assume that the goal is to detemine the magnitudes of the individual vectors, [abcd].
What we record is a phase sensitive signal proportional to the vector magnitudes.
On first excitation, at t1 before the effect of any gradients is felt, signal A is recorded and is equal to a+b+c+d.
A second measurement is acquired at t2 at which time the effect of the x gradient is to change the phase of magnetization vectors on the right side of the volume.
A = a + b + c + d
A B
D C
a b
d c
Fy Fx
B = a - b + c - d RF
C = a - b - c + d
D = a + b - c - d
k-space image space

14. Fy Fx Echo-Planar Imaging (EPI) Xgrad Ygrad
Xgrad
Ygrad RF
………. 1 2 3 4 5 6 7 8 9 10 11 12
Fy Fx
Initially after excitation, all vectors are aligned.
Assume that the goal is to detemine the magnitudes of the individual vectors, [abcd].
What we record is a phase sensitive signal proportional to the vector magnitudes.
On first excitation, at t1 before the effect of any gradients is felt, signal A is recorded and is equal to a+b+c+d.
A second measurement is acquired at t2 at which time the effect of the x gradient is to change the phase of magnetization vectors on the right side of the volume.
k-space data acquired in 1 shot

15. Echo-Planar Imaging (EPI)
Xgrad RF
……….
time
Variable acquisition time for each k-space line results in image distortion.
What is the TE?

16. Single Value Single Echo EPI TE TE ? TE ? RF NxN shots N shots 1 shotGx Gy
Acquire
Single Value TE
N shots Gx Gy
Acquire
TE ?
Single Echo
1 shot Gx Gy
Acquire
TE ?
EPI

17. General Structure of a MR Pulse Sequence
Preparation
Excitation
Evolution
Encode/Acquire
Variation in TR delay
Alter T1 weighting
Variation in TE delay
Alter T2 weighting

18. General Structure of a MR Pulse Sequence
Preparation
Excitation
Evolution
Encode/Acquire
Saturation pulse or
Inversion pulse
Velocity encoding or
Diffusion encoding

19. Phase Contrast MR Pulse Sequences
Preparation
Excitation
Evolution
Encode/Acquire
Velocity encoding
gradient

20. Bi-polar gradient pulse
Resonant
frequency x
Position of static spins

21. Bi-polar gradient pulse
Resonant
frequency x
Position of static spins

22. Bi-polar gradient pulse
Resonant
frequency x
Position of static spins

23. Bi-polar gradient pulse
Resonant
frequency x
Position of static spins

24. Bi-polar gradient pulse
Resonant
frequency x
Position of static spins

25. Resonant
frequency x

26. Resonant
frequency x

27. Resonant
frequency x

28. Resonant
frequency x

30. What happens if spins are not static ?

31. Resonant
frequency x
Position of moving spins

32. Resonant
frequency x
Position of moving spins

33. Resonant
frequency x
Position of moving spins

34. Resonant
frequency x
Position of moving spins

35. Resonant
frequency x
Position of moving spins

36. Resonant
frequency x
Position of moving spins

37. Resonant
frequency x
Position of moving spins

38. Resonant
frequency x
Position of moving spins

39. Resonant
frequency x
Position of moving spins

41. Inversion Recovery MR Pulse Sequences
Preparation
Excitation
Evolution
Encode/Acquire TI
Inversion
pulse

42. Inversion Recovery MR Pulse SequencesMz Mz
Gray Matter
White Matter
Blood
MS lesion
CSF
Recovery of Mz after IR pulse
Mz = Mo (1 - 2exp(-TI/T1))
-Mz TI
Gray matter = 950ms, White matter = 650ms,
CSF = 4200ms, Blood = 1200ms, MS lesions = 1300

43. Inversion Recovery - Gray/White ContrastMz
Gray Matter
White Matter
Mz (White Matter) - Mz (Gray Matter) TI

44. Inversion Recovery - Flow SensitiveMz
Blood
Blood Null point TI
Acquisition 1
Acquisition 2
Non-selective inversion
Not flow sensitive
Selective inversion
Flow sensitive
Selected Slice

45. Inversion Recovery - Fluid Suppression
Other spins have
mostly recovered Mz
CSF
CSF Null point TI