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, so the spins happen in different directions and cancel out.

9. But when applying a very strong external magnetic field.
Spin alignment
But when applying a very strong external magnetic field.

10. Magnetic field direction
Precession
Putting the hydrogen into an external magnetic field generates the magnetic moment and causes the hydrogen to precess around the axis of the magnetic field.
Magnetic field direction

11. Energy states
The hydrogen aligns in parallel (low energy) and anti-parallel (high energy – less stable) states.

12. Energy states change with excitation and relaxation
fMRI measurements = energy release during relaxation!

13. Proportions
For every million hydrogen atoms 500,001 will position in the parallel state and 499,999 will position in anti-parallel state. Luckily we have 1023 hydrogen atoms in every gram of tissue…

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

15. Gyromagnetic ratio ( )
A spinning hydrogen atom within an external magnetic field has a particular magnetic moment. It also has a particular angular momentum because it has mass. Angular momentum is a rotation force pulling perpendicular to the rotation plane according to the right hand rule. Magnetic moment / angular momentum = gyromagnetic ratio Combination of mechanical and electromagnetic forces.

16. Larmor frequency B = 1.0 T B = 2.0 T B = 3.0 T
The gyromagnetic ratio ( ) will determine how fast (v) the hydrogen will spin around the axis of a magnetic field with a given strength (Bo). v = Bo * /2π The spin velocity of an atom/molecule is called its Larmor frequency (for hydrogen MHz/Tesla)
B = 1.0 T
B = 2.0 T
B = 3.0 T
TIME

17. Larmor frequency
Because different atoms/molecules have different Larmor frequencies, we can “tune into” the Hydrogen frequency and isolate it from other atoms/molecules in the scanned tissue. We’ll do this by exciting and “reading out” relaxation within a small window around the Hydrogen Larmor frequency. This is also how spectroscopy methods determine the molecular composition of a sample…

18. The hydrogen atoms are precessing around z (direction of B0)
Lab/Rotating frame
The hydrogen atoms are precessing around z (direction of B0)

19. Excite the sample into a less stable perpendicular direction
Excitation pulses: B1
Excite the sample into a less stable perpendicular direction

20. Before excitation Low Energy M0 External Magnetic Field (B0)
High Energy

21. At excitation
Low Energy M0
External
Magnetic
Field (B0)
High Energy

22. 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 much we excite our sample… x y z
<900 pulse x y z
900 pulse x y z
>900 pulse x y z
1800 pulse

23. Relaxation
Once the sample has been excited, it relaxes into a more stable (lower energy state) and emits energy in the process

24. What frequency is the hydrogen energy at?
Relaxation
What frequency is the hydrogen energy at?
time
Magnetization

25. Analogous to amplitude and phase…
T1 and T2/T2*
T1: relaxation in the longitudinal plane T2: relaxation in the transverse plane
Analogous to amplitude and phase…

26. Realignment with main magnetic field direction
Static main field
Excitation pulse M0 M0 M0
Longitudinal relaxation

27. T1 T1 = 63% recovery of original magnetization value M0 Magnetization
vector
Longitudinal
magnetization

28. 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”…

29. De-phasing in the transverse plane
T2/T2*
De-phasing in the transverse plane M0
Static main field
Excitation pulse
Transverse relaxation

30. T2/T2*
Spin phase
Transverse
magnetization

31. What influences T2/T2*?
Again has to do with the molecular neighborhood of the excited spinning atom.
The more spin-spin interactions there are the quicker the decay and the shorter the T2.
The higher the static magnetic field, the more interactions there are, quicker T2 decay.
Different tissues have different molecular neighborhoods and different T2 constants…

32. 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.

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

34. Source of MR signal
The energy source driving the MR signal used to determine T1 and T2 is identical!
The only thing we can measure is the energy released by hydrogen atoms moving from excited to relaxed state.
But we can derive T1, T2, T2’, and T2* relaxation properties by exciting the sample and measuring its “resonating” energy release in clever ways (i.e. using different pulse sequences).

35. Image contrast
Using different MRI sequences we can contrast different features of the tissues like their T1/T2/T2* relaxation times. Since neighboring tissues will have different relaxation times this will enable us to visualize particular tissues (e.g. gray & white matter):
T2* 40ms

36. TR and TE
Two important time constants are defined for each sequence: TR – repetition time between excitation pulses. TE – time between excitation pulse and data acquisition (“read out”). Contrasting different attributes of the tissue depends on the choice of these two variables. The TR length will determine the contribution of T1 relaxation to the contrast and the TE length will determine the contribution of T2 relaxation to the contrast.

37. T1 and TR length
The amount of post-excitation signal depends on how relaxed the sample was during the excitation time. M0
Static main field M0 M0 M0
Think about exciting a sample at different stages of longitudinal relaxation.

38. T1 and TR length
Choosing a short TR means less energy release (MR signal) on consecutive scans.

39. Transverse relaxation
T2/T2* and TE length M0
Static main field
Excitation pulse
Transverse relaxation

40. TE: When to acquire the data
The relaxing hydrogen atoms emit a decaying amount of energy. The question is how soon after excitation to measure the energy? For a T2 contrast you would want to wait a bit and let the energy decay.

41. Only one signal source!
Remember that the only thing we can measure is in phase energy release of the precessing hydrogen atoms. To generate an electric current in the receiving magnet coil we need a “large” number of hydrogen atoms to spin together (remember electric induction – moving magnetic fields generate an electric current). Measuring T1/T2/T2* relaxation properties is only a consequence of the order in which we excite, relax, and acquire the energy released by the sample.

42. This is done using a very long TR and very short TE
Proton density
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

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

44. 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…

45. 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

46. We can combine a T2 acquisition with proton density…
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…

47. 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

48. 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

49. 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…

50. 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?

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

52. Bloch equation

53. 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

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

55. Spatial gradients
Having the gradients in place changes the local magnetic field experienced by hydrogen at different spatial points inside the magnet. This means the hydrogen will have different magnetic moments and will precess at slightly different speeds at each spatial location. By “focusing in” on the precession speed (larmor frequency) at each location we can achieve spatial resolution. Similarly to how we “focused in” on hydrogen atoms…

56. Determining power in particular frequencies
Fourier Transform
Determining power in particular frequencies + +
Frequency
Intensity

57. Separates a complex signal into its sinusoidal components
Fourier Transform
Separates a complex signal into its sinusoidal components
time
Magnetization
time
Magnetization
time
Magnetization
Frequency
Intensity

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

59. 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

60. The magnet

61. Main static field
Main magnet field is generated by a 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.

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

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

64. 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.