1. MRI Physics in a Nutshell Christian Schwarzbauer

2. MR images: What do we see ?
MRI images are usually based on the signal from protons
A Proton is the nucleus of the hydrogen atom
Hydrogen is the most common element in tissue
The signal from protons is due to their „spin“

3. The nuclear spin Elementary property of an atomic nucleus
Each spin carries an elementary magnetization
Spins align in an external magnetic field (like a compass needle)

4. Macroscopic sample

5. Macroscopic sample B0 M

6. Excitation B0 M
radio waves
 =  B0

7.  =  B0 Precession and signal induction M 123 MHz @ 3T receiver coil
NMR signal

8. Longitudinal and transverse componentsMz M
Mxy

9. Exication with different pulse angles
equilibrium state
90o pulse (maximum signal)
30o pulse
180o pulse
(no signal)

10. Relaxation non-equilibrium state RF pulse relaxation equilibrium state

11. 1 Ml M0 T1 2 Mt 0 T2 Relaxation Two independent relaxation processes:
T1: “longitudinal relaxation time” ( 1 s)
T2: “transverse relaxation time” ( 100 ms)

12. Relaxation Transverse Magnetization vanishes quickly (short T2)
Longitudinal Magnetization relaxes slowly (long T1)

13.  =  B0 Signal loss due to magnetic field inhomogeneities
t = 10 ms
 =  B0
t = 20 ms
has higher frequency than

14. Effective transverse relaxation (T2* < T2)
Spin dephasing as a
result of magnetic field
inhomogeneities
Transverse relaxation (T2)
Effective transverse relaxation (T2* < T2)

15. Effective transverse relaxation
time [ ms ] 20 40 60 80
No inhomogeneities (T2* = 100 ms)
Moderate inhomogeneities (T2* = 40 ms)
Strong inhomogeneities (T2* = 10 ms)

16. T2* related signal dropouts
T2* reduction due to local field inhomogeneities
 signal dropouts
reduced T2*
normal T2*
(about 40 ms)
EPI image

17. B0  =  B0 B  =  (B0 + s Gs) Gs The principle of MRI
Homogeneous magnetic field B0
 =  (B0 + s Gs)
Add magnetic field gradient Gs B

18. Slice selective excitation
 =  (B0 + s Gs) Gs
w > w0
w = w0
RF pulse (0)
w < w0
Only spins in slice of interest have frequency w0
RF pulse with frequency w0 excites only spins in slice of interest

19. Slice position Gs s1 s0
 =  (B0 + s Gs)

20. Slice orientation Gs
 =  (B0 + s Gs)

21. Mulit-slice MRI Gs 4 3 2 1
 =  (B0 + s Gs)

22. Slice profile  =  (B0 + s Gs) Frequency (w) Dw Position (s)
A rectangular-shaped frequency distribution only exists in theory
Position (s) Ds

23. Slice profile  =  (B0 + s Gs) Frequency (w) Dw Position (s)
Gaussian-shaped frequency distribution
Position (s) Ds

24. Slice thickness (SLTH)
SLTH = Full width at half maximum of the slice profile

25. Multi-slice MRI SLTH Gap Slice 1 Slice 2 Slice 3
Tissue in the inter-slice gap contibutes to the signal of the adjacent slices

26. Spatial encoding Slice selective excitation
Transverse magnetization precesses in the excited slice ( =  B0)

27. Spatial encoding
Gradient pulse in x-direction Gx

28. Spatial encoding Gy Gradient pulse in x-direction
Gradient pulse in y-direction

29. Spatial encoding Gradient pulse in x-direction
Gradient pulse in y-direction
Signal:

30. Image reconstruction and k-space (Simple example: 3 x 3 matrix)
Fast
Fourier Transform
(FFT) y ky x kx
Object space (9 unknown parameters)
K space

31. Image reconstruction and k-space (Experimental data: 128 x 128 matrix)
FFT
K space (raw data)
Object space (image)

32. Conventional MRI (e.g. MP-RAGE)Gx Gy
Signal acquisition (digital sampling)
Selective excitation 1 kx ky
K space

33. Conventional MRI (e.g. MP-RAGE)Gx Gy
Signal acquisition (digital sampling)
Selective excitation 2 kx ky
K space

34. Conventional MRI (e.g. MP-RAGE)Gx Gy
Signal acquisition (digital sampling)
Selective excitation 5 kx ky
K space

35. Conventional MRI (e.g. MP-RAGE)
1st excitation
2nd excitation
nth excitation
Problem: This sequence is rather slow
K space is sampled line by line
After each excitation one must wait for the longitudinal magnetization to recover
Example: n = 256, TR = 2s T = n TR = 8.5 min

36. Echo-planar imaging (EPI)kx ky
K space
Signal acquisition (digital sampling) Gx Gy
Selective excitation

37. EPI: A technical challenge
Signal decay due to transverse relaxation (Example: T2* = 40ms)
time [ ms ] 20 40 60 80
Within 80 ms the signal has decayed to nothing
Complete image must be acquired in less than 80 ms (in general: T = 2 T2*)
High temporal, but low spatial resolution

38. Acquisition time: 62.5 ms per slice
EPI at the CBU
Slice thickness: 3 mm
Inter-slice gap: 0.75 mm (25 %)
Number of slices: 32 (whole brain coverage)
Matrix size: 64 x 64
Field of view: 192 x 192 mm
Spatial resolution (in-plane): 3 x 3 mm
Echo time (TE): 30 ms Repetition time (TR): 2000 ms
Acquisition time: 62.5 ms per slice

39. Standard slice orientation
How many slices ?
120 mm
= 32
3 mm mm
And the minimum TR ?
32 * 62.5 ms = 2000 ms
120 mm

40. Coronal slice orientation
How many slices ?
180 mm
= 48
3 mm mm
And the minimum TR ?
48 * 62.5 ms = 3000 ms
180 mm