1. MR Signal Generation FMRI Undergraduate Course (PSY 181F)
FMRI Graduate Course (NBIO 381, PSY 362)
Dr. Scott Huettel, Course Director
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

2. Housekeeping Undergraduate students Graduate students
Syllabus has incorrect course number: 181F = correct
Go with TAs to Bell Building laboratory after lecture
Graduate students
Syllabus refers to old grading system; you are now graded on standard A,B, etc. system
Please complete self-assessment questions weekly; to me (with “SAQ”, “Ch1” etc., in the title)
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

3. Outline for Today Lecture: MR Signal Generation
Protons and the NMR property
Protons in a magnetic field: Alignment, Precession
Excitation and resonance
Reception and relaxation
Laboratory: Introducing MRI / fMRI data
Basic MATLAB use
Properties of MRI data
Basic neuroanatomy
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

4. Synopsis of MRI M: Put subject in strong magnetic field
R: Transmit radio waves into subject, turn off transmitter, receive radio waves emitted by subject’s brain (the MR signal).
I: Modulate the strength of the magnetic field slightly over space (next week).
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

5. 1. Protons and the NMR property
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

6. Properties of Atomic Nuclei
Nuclei have two properties:
Spin (conceptual, not literal)
Charge (property of protons)
Nuclei are made of protons and neutrons
Both have spin values of ½
Protons have charge
Pairs of spins tend to cancel, so only atoms with an odd number of protons or neutrons have spin
A nucleus has the NMR Property if it has both angular momentum and a magnetic moment. Such nuclei have an odd number of protons or an odd number of neutrons.
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

7. The spinning mass of the proton generates an angular momentum J.
The electric charge on the surface of the proton creates a small current loop, which generates magnetic moment μ.
Both μ and J are vectors that point along the spin axis and whose direction is given by the right hand rule.
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

8. What nuclei can we measure?
Most common in our bodies:
12C
16O 1H
14N
Of these, only Hydrogen has the NMR property.
But, Hydrogen is the most abundant atom in the body
Mostly in water (H2O)
This means that nearly all forms of MRI are measuring properties of Hydrogen.
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

9. 2. Protons in a magnetic field
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

10. M
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

11. Protons in no magnetic field
In the absence of a strong magnetic field, the spins are oriented randomly.
Thus, there is no net magnetization (M).
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

12. Introduction of a Magnetic Field (B)Bo
Image from G.A. Glatzmaier
Computer simulation of Earth’s magnetic field (~ Gauss, or T)
Helmholtz Pair
Solenoid
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

13. Some Terminology Bo Bo Longitudinal Axis (z direction)
B is used for magnetic fields.
B0 is the scanner’s main field.
Transverse Plane (xy plane)
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

14. Alignment with a magnetic field
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

15. Protons align with a magnetic field…
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

16. … but move around the field axis in a motion known as precession.
Precession axis
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

17. In a magnetic field, protons can take high- or low-energy states
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

18. The difference between the numbers of protons in the high-energy and low-energy states results in a net magnetization (M).
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

19. Energy states: Temperature effects
Low-energy protons at room temperature in Earth’s B:
~ %
High-energy protons at room temperature in Earth’s B:
~ %
Protons move back and forth between states because of thermal energy As temperature decreases to near absolute zero, all protons move to lower-energy state.
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

20. Energy states: Magnetic field effects
When the magnetic field is weak, little energy is required for a proton to change between high and low states (ΔE is small).
But, when the magnetic field is strong, much more energy is required (ΔE is large).
Thus, protons in the lower-energy state tend to stay in that state
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

21. The net magnetization (M) increases with increasing field strength (B0), but decreases with increasing temperature (T).
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

22. 3. Excitation and Resonance
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

23. R
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

24. Excitation: Conceptual Overview
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

25. Key Concept: To measure magnetization we must perturb it
Protons must absorb energy to change between states
Parallel (aligned with) to B0 is lowest-energy state
Anti-parallel (aligned against) to B0 is highest-energy state
We can apply energy as electromagnetic radiation
Higher frequency radiation  more energy
How can we calculate how much energy (i.e., at what frequency) to apply?
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

26. Let’s try adding another magnetic field…
(net magnetization) M
(main field of scanner) B0
(net magnetization) M θ B1
(another very strong field)
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

27. Why is this impractical?
So, we could reorient some of the protons (i.e., change the net magnetization) by introducing a second, very strong magnetic field.
Why is this impractical?
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

28. Magnetic Moment and Angular Momentum have a constant relation!
The angular momentum (J) is the product of the proton’s mass (m), it’s velocity (v), and the rotation radius (r).
Cool Fact #1:
The current flow (I) and velocity (v) are vectors in the same direction (i.e., the charge is precessing just like the mass).
Cool Fact #2:
The rotation radius (r) and area (A) are proportional.
The magnetic moment (μ) is given by the rotational force experienced by the proton (torque, or τmax) divided by the strength of the magnetic field. These are proportional to the moving charge of the proton (I) times the area around which it precesses (A).
Magnetic Moment and Angular Momentum have a constant relation!
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

29. Magnetic Moment and Angular Momentum have a constant relation!
If we assume that the proton is a point charge moving around in a circle, then the gyromagnetic ratio is given by a very simple equation (see book for derivation).
The constant γ (gamma) is known as the gyromagnetic ratio. It is fixed for any given atomic nucleus.
The gyromagnetic ratio (γ) depends on only two things: charge (q) and mass (m).
That’s it.
Magnetic Moment and Angular Momentum have a constant relation!
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

30. The gyromagnetic ratio (γ) is critical for MRI.
It allows us to calculate the energy (expressed in electromagnetic frequency, v) needed to change an atomic nucleus from the low- to high-energy states in a given magnetic field (B0).
This frequency (v) is known as the Larmor Frequency.
It is the same as the precession frequency of the nucleus!
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

31. The Canonical Analogytm for resonance: a swing set
Option #1
A single, strong push to lift the person off the ground
Requires an enormous amount of exertion, delivered very rapidly
Option #2
Many small pushes at the resonant frequency of the swing set
Allows distribution of the energy over time!
This is a random illustrative photo. The internet is great.
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

32. … moving from happy kids to atomic nuclei
Option #1
Using a very strong perpendicular field
Impractical (perhaps impossible) to do quickly in a real device
Option #2
Many small pushes at the resonant frequency of the atomic nucleus of interest
Allows distribution of the energy over time!
Giving energy for a longer time period increases the flip angle.
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

33. “Tipping” in a rotating frame of reference
The RF energy is called B1 because it is, effectively, a second magnetic field.
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

34. Resonance Frequencies of Common Nuclei
Remember, the resonant frequency is constant for a given atomic nucleus and proportional to magnetic field strength.
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

35. What are the consequences of electromagnetic energy at this frequency?
X-Ray, CT
MRI (e.g., 6 x 107Hz)
MRI uses electromagnetic energy in the radio wave portion of the electromagnetic spectrum. It can cause heating of biological tissue, but does not break molecular bonds.
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

36. Radiofrequency Coils for Excitation (and Reception)
Defined by their function:
Transmit / receive coil (most common)
Transmit only coil (can only excite the system)
Receive only coil (can only receive MR signal)
Defined by geometry
Volume coil (low sensitivity but uniform coverage)
Surface coil (High sensitivity but limited coverage)
Phased-array coil (High sensitivity, near-uniform coverage)
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

37. 4. Reception and relaxation
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

38. Tipping the net magnetization provides measurable MR signal!
During Excitation (to)
During Excitation (t1)
The amount of current oscillates at the (Larmor) frequency of the net magnetization.
Before Excitation
After Excitation
fmri-fig jpg
Excitation tips the net magnetization (M) down into the transverse plane, where it can generate current in detector coils (i.e., via induction).
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

39. Relaxation: Nothing Lasts Forever
Once we stop applying energy, M will go back to being aligned with static field B0
This process is called relaxation
The part of M perpendicular to B0 shrinks [Mxy]
This part of M is called transverse magnetization
It provides the detectable RF signal
Part of M parallel to B0 grows back [Mz]
This part of M is called longitudinal magnetization
Mz is not directly detectable, but can be again converted into transverse magnetization by energy (e.g., B1)
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

40. T1 T2
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

41. Relaxation Times and Rates
Net magnetization changes in an exponential fashion
Constant rate (R) for a given tissue type in a given magnetic field
R = 1/T, leading to equations like e–Rt
T1 (recovery): Relaxation of M back to alignment with B0
Usually ms in the brain (lengthens with bigger B0)
T2 (decay): Loss of transverse magnetization over a microscopic region ( 5-10 micron size)
Usually ms in the brain (shortens with bigger B0)
T2*: Overall decay of the observable RF signal over a macroscopic region (millimeter size)
Usually about half of T2 in the brain (i.e., faster relaxation)
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

42. T1 and T2 parameters
By selecting appropriate pulse sequence parameters (Week 4’s lecture), images can be made sensitive to tissue differences in T1, T2, or a combination.
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

43. T1 and T2 values at 1.5T Tissue T1 (s) T2 (ms) CSF 2 - 6 110 - 2000
White matter
Gray matter
Meninges
Muscle
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

44. What about “I”?
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

45. I
fmri-fig jpg
We just have signal, so far. We need spatial gradients to generate images. Next week.
FMRI – Week 2 – MR Signal Scott Huettel, Duke University

46. MR Signal Generation
Scanners use very strong static fields (Tesla range) to generate net magnetization (M)
Protons in magnetic fields precess around the longitudinal axis of a field at the Larmor Frequency
Electromagnetic energy, when supplied at the Larmor frequency (radio waves) by head coils, is absorbed by the protons
This tips the net magnetization down into the transverse plane
As the net magnetization rotates through the transverse plane, it induces a changing current in the head coils.
This current is the MR signal
FMRI – Week 2 – MR Signal Scott Huettel, Duke University