1. fMRI Methods Lecture2 – MRI Physics

2. magnetized materials and moving electric charges.
Magnetic fields
magnetized materials and moving electric charges.

3. Electric induction
Similarly a moving magnetic field can be used to create electric current (moving charge).

4. Or you could use an electric current to move a magnet…
Electric induction
Or you could use an electric current to move a magnet…

5. Force and field directions
Right hand rule
Force and field directions

6. Nuclear spins
Protons are positively charged atomic particles that spin about themselves because of thermal energy.

7. Magnetic moment
μ (magnetic moment) = the torque (turning force) felt by a moving electrical charge as it is put in a magnet field.
The size of a magnetic moment depends on how much electrical charge is moving and the strength of the magnetic field it is in.
A Hydrogen proton has a constant electrical charge.

8. Spin alignment
Earth’s magnetic field is relatively small ( Tesla), so the spins happen in different directions and cancel out.

9. But when in a strong external magnetic field (e.g. 1.5 Tesla).
Spin alignment
But when in a strong external magnetic field (e.g. 1.5 Tesla).

10. Net magnetization (M)
Sum of magnetic moments in a sample with a particular volume at a given time.

11. Precession
Hydrogen protons not only spin. They also precess around the axis of the magnetic field.
Magnetic field direction
True for all atoms with an odd number of protons

12. Precession speed
Two factors govern the speed of precession (Larmor frequency): magnetic field strength & gyromagnetic ratio Larmor frequency = Bo * /2π

13. Gyromagnetic ratio
Gyromagnetic ratio ( ) Magnetic moment / Angular momentum Combination of electromagnetic and mechanical forces. Angular momentum is dependant on the mass of the atom.

14. Different atoms have different gyromagnetic ratios:
Nucleus
Gyromagnetic ratio (γ) 1H
7Li
13C
67.262
19F
23Na
70.761
31P

15. Larmor Frequency at 1 Tesla
Different atoms placed in the same magnetic field have different Larmor frequencies: “Tune in” to the Hydrogen frequency.
Nucleus
Larmor Frequency at 1 Tesla 1H
MGHz
7Li
MGHz
13C
MGHz
19F
MGHz
23Na
MGHz
31P
MGHz

16. The hydrogen atoms are precessing around z (direction of B0)
Longitudinal & transverse directions
The hydrogen atoms are precessing around z (direction of B0)

17. Net magnetization is all pointing in the z direction
Steady state
Net magnetization is all pointing in the z direction

18. Applying a perpendicular magnetic field “flips” the protons
Excitation pulses
Applying a perpendicular magnetic field “flips” the protons

19. Excitation & Relaxation
Excite the sample in a perpendicular direction and let it relax. Net magnetization of the sample changes as it relaxes, inducing current to move in a near by coil.
Larmor frequency

20. Flip angle
Defined by the strength of B1 pulse and how long it lasts (T) θ = *B1*T This is one of the parameters we set during a scan It defines how far we “flip” the protons… x y z
<900 pulse x y z
900 pulse x y z
>900 pulse x y z
1800 pulse

21. Changes in the direction of the sample’s net magnetization
T1 and T2/T2*
T1: relaxation in the longitudinal direction T2*: relaxation in the transverse plane
Changes in the direction of the sample’s net magnetization

22. Realignment of net magnetization with main magnetic field direction
Before excitation
At excitation
Relaxation
Net magnetization along the longitudinal direction

23. T1
T1 = 63% recovery of original magnetization value M0

24. What influences T1?
Has something to do with the surroundings of the excited atom. The excited hydrogen needs to “pass on” its energy to its surroundings (the lattice) in order to relax.
Different tissues offer different surroundings and have different T1 relaxation times…
We can also introduce external molecules to a particular tissue and change its relaxation time. These are called “contrast agents”…

25. Loss of net magnetization phase in the transverse plain
T2*/T2
Loss of net magnetization phase in the transverse plain
Before excitation
At excitation
Relaxation
Net magnetization in the transverse plain

26. T2/T2*
T2 = 63% decay of magnetization in transverse plain

27. T2* = T2 - T2’
Two main factors effect transverse relaxation: 1. Intrinsic (T2): spin-spin interactions. Mechanical and electromagnetic interactions Extrinsic (T2’): Magnetic field inhomogeneity. Local fluctuations in the strength of the magnetic field experienced by different spins.

28. Magnetic field inhomogeneities
Examples of causes:
Transition to air filled cavities (sinusoids)
Paramagnetic materials like cavity fillings
Most importantly – Deoxygenated hemoglobin

29. What influences T2?
Again, has to do with the molecular neighborhood affecting the amount and quality of spin-spin interactions.
Different tissues will have different T2 relaxation times.
The stronger the static magnetic field, the more interactions there are, quicker T2 decay.

30. We only have one measurement:
MR signal
We only have one measurement:
Measurement of the net magnetization in the transverse plain as the sample relaxes.
Once T2* relaxation is complete
Protons precess out of phase in the transverse plain
Net magnetization in transverse plain = 0

31. TR and TE
Two important scanning parameters: TR – repetition time between excitation pulses. TE – time between excitation pulse and data acquisition (“read out”). Creating scanning protocols with different TR and TE lengths will allow us to derive T1 and T2/T2* relaxation times.

32. Short TR = weaker MR signal on consecutive pulses.
TR length & MR signal strength
Short TR = weaker MR signal on consecutive pulses.
With short TRs relaxation in the longitudinal direction will not be complete. So there will be fewer relaxed protons to excite.

33. TE: when to measure MR signal
We can measure the amplitude of net magnetization immediately after excitation or we can wait a bit.
Longer TEs will allow more transverse relaxation to happen and the MR signal will be weaker.

34. Different image contrasts
We can scan the brain using different pulse sequences by choosing particular TR and TE values to create images with different contrasts.
TR length will determine how much time the sample has had to relax in the longitudinal direction.
TE will determine how much time the sample has had to relax (loose phase) in the transverse plain.

35. Proton density contrast
Measuring the amount of hydrogen in the voxels regardless of their T1 or T2 relaxation constants.
This is done using a very long TR and very short TE

36. Higher intensity in voxels containing more hydrogen protons
Proton density
Higher intensity in voxels containing more hydrogen protons

37. T1 contrast
Measuring how T1 relaxation differs between voxels. This is done using a medium TR and very short TE
You need to know when largest difference between the tissues will take place…

38. T1 contrast
Images have high intensity in voxels with shorter T1 constants (faster relaxation/recovery = release of more energy)
CSF: ms
Gray matter: ms
White matter: ms
Muscle: ms
Fat: ms

39. We can combine a T2 acquisition with proton density…
T2/T2* contrast
Measuring how T2 relaxation differs between voxels. This is done using a long TR and medium TE
We can combine a T2 acquisition with proton density…

40. T2 contrast
Images have high intensity in voxels with longer T2 constants (slower relaxation = more detectable energy)
CSF: ms
Gray Matter: 80 ms
White Matter: 60 ms
Muscle: 50 ms
Fat: 50 ms

41. Same as T2 only smaller numbers (faster relaxation)
T2* contrast
Same as T2 only smaller numbers (faster relaxation)
CSF: ms
Gray Matter: 40 ms
White Matter: 30 ms
Fat: 25 ms

42. T2* and BOLD fMRI
T2* = T2 +T2’ T2: Spin-spin interactions T2’: field inhomogeneities Exposed iron (heme) molecules create local magnetic inhomogeneities
BOLD – blood oxygen level dependant
Assuming everything else stays constant during a scan one can measure BOLD changes across time…

43. T2* and BOLD
More deoxygenated blood = more inhomogeneity more inhomogeneity = faster relaxation (shorter T2*) Shorter T2* = weaker energy/signal (image intensity) So what would increased neural activity cause?

44. So what happened in particular time points of this scan?
T2* and BOLD
So what happened in particular time points of this scan?

45. Bloch equation

46. MR images
So far we’ve talked about a bunch of forces and energies changing in a sample across time… How can we differentiate locations in space and create an image?
2004 Nobel prize in Medicine
Paul Lauterbur
Peter Mansfield

47. Spatial gradients
Create magnetic fields in each direction (x,y,z) that move from stronger to weaker (hence gradient).

48. Spatial gradients
Different magnetic fields at different points in space. Hydrogen will precess at a different speed in each spatial location. By “tunning in” on the specific precession speed we can separate different spatial locations. Similarly to how we “tunned in” on hydrogen atoms…

49. Spatial gradients
(-)
62 MHz
63 MHz
64 MHz G
65 MHz
66 MHz
(+)

50. Spatial gradients
Lot’s of Fourier transforms. Work in k-space (a vectorial space that keeps track of the spin phase & frequency variation across magnet space). It’s possible to turn gradients on and off very quickly (ms). Image reconstruction Pulse sequences

51. The magnet

52. Main static field
Extremely large electric charge spinning on a helium cooled (-271o c) super conducting coil.
Earth’s magnetic field microtesla.
MRI magnets suitable for scanning humans T.

53. Main coils
The bulk of the structure contains the coils generating the static magnetic field and the gradient magnetic fields.

54. RF coil
Transmit and receive RF coils located close to the sample do the actual excitation and “read out”.

55. Homework!
Read Chapters 3-5 of Huettel et. al. Explain how a spin-echo pulse does the magic of separating T2 relaxation from T2* relaxation. You can include figures/drawings if you like.