1. Interlude: A primer on Fourier Analysis

2. A Brief Primer on Fourier Analysis
Sine waves can be characterized by frequency and amplitude
peak: high point
trough: low point
frequency: number of cycles within a certain time (e.g., cycles per sec = Hz) or space (e.g., cycles per cm)
amplitude: height of wave
phase: starting point
amplitude
peak
trough
(b) has same frequency as (a) but lower amplitude
(c) has lower frequency than (a) and (b)
(d) has same frequency and amplitude as (c) but different phase
Source: DeValois & DeValois, Spatial Vision, 1990

3. Fourier Decomposition
Any wave form can be decomposed into a series of sine waves
Frequency spectrum
fundamental
Frequency
space
(1D pattern)
3rd harmonic (3X freq; 1/3 ampl)
5th harmonic (5X freq; 1/5 ampl)
7th harmonic (7X freq; 1/7 ampl)
Source: DeValois & DeValois, Spatial Vision, 1990

4. Temporal Analysis
In a simple “square wave” block design, you expect the time course to have strong energy at the fundamental frequency
changes at other frequencies are noise

5. Spatial Analysis Spatial waveforms
can be one dimensional (e.g., sine wave gratings in vision) or two dimensional (e.g., a 2D image)
e.g., image analysis
e.g., an fMRI slice (k-space)
Adapted from DeValois & DeValois, Spatial Vision, 1990

6. Fourier Synthesis centre = low frequencies
periphery = high frequencies
You can see how the image quality grows as we add more frequency information
Source: DeValois & DeValois, Spatial Vision, 1990

7. Step 6: Convert Frequencies to Brain Space
k-space contains information about frequencies in image
We want to see brains, not frequencies

8. The Mona Lisa in K-Space
low frequencies in centre
high frequencies in surround
Original Mona
different orientations around the clock
Source: Traveler’s Guide to K-space (C.A. Mistretta)

9. The Mona Lisa in K-Space
Low-Frequency Mona
High-Frequency Mona
Original Mona
Source: Traveler’s Guide to K-space (C.A. Mistretta)

10. A Walk Through K-space echo-planar imaging
single shot EPI
single shot spiral
echo-planar imaging
sample k-space in a linear zig-zag trajectory
spiral imaging
sample k-space in a spiral trajectory

11. Field Map Correction
Brain reconstructed without considering field map
Brain reconstructed considering field map
Field map
Ideally, we want the magnetic field to be uniform (except for gradients we apply) but in reality, it isn’t homogenous
This can lead to spatial distortions after image reconstruction from k-space
Field map correction can fix the distortions

12. Magnetic Field Non-uniformities and Shimming
Adding a non-uniform object (like a person) to B0 will make the total magnetic field non-uniform
Shimming: applying non-uniform shimming gradients to “even out” coarse non-uniformities in the magnetic field
If the subject moves after shimming, the magnetic field uniformity may change
Barry et al., 2010, MRI
Shim coils:

13. T2 and T2* Dephasing of transverse magnetization due to both:
spin-spin interactions (T2)
static magnetic field inhomogeneities (additional T2* effects)
Mxy
spin echo sequences
-sensitive to T2 but not T2* effects
gradient echo sequences
-sensitive to T2+T2* effects T2
T2*
time
Source: Adapted from Jorge Jovicich

14. Spin Echo Sequence
Use a 180-degree flip to get rid of effects of local field inhomogenities on transverse decay
Effects of spin-spin interactions still lead to some transverse decay
Thus spin-echo sequences are sensitive to T2 but not T2* decay
Goebel (2007) book chapter

15. Spin Echo Animation
Animation from

16. Spin Echo Analogy
Making the runners reverse gets rid of differences in speed

17. Pulse Sequence series of excitations, gradient triggers and readouts
Gradient echo
pulse sequence
Echos – refocussing of signal
Spin echo:
use a 180 degree pulse to “mirror image” the spins in the transverse plane
when “fast” regions get ahead in phase, make them go to the back and catch up
measure T2
ideally TE = average T2
Gradient echo:
flip the gradient from negative to positive
make “fast” regions become “slow” and vice-versa
measure T2*
ideally TE ~ average T2*
t = TE/2
A gradient reversal (shown) or 180 pulse (not shown) at this point will lead to a recovery of transverse magnetization
TE = time to wait to measure refocussed spins
Source: Mark Cohen’s web slides

18. Gradient-Echo Echo-planar Imaging (GE-EPI)
Pulse Sequence commonly used for T2*-weighted imaging (which is sensitive to local field inhomogeneities)
As we will see, for imaging brain activation, we can turn local field inhomogeneities into a feature rather than a bug

19. Putting the f in fMRI

20. Susceptibility
Susceptibility: generation of extra magnetic fields in materials that are immersed in an external field
Susceptibility Artifact
-occurs near junctions between air and tissue
sinuses, ear canals
-spins become dephased so quickly (quick T2*), no signal can be measured
sinuses
ear
canals
Aha!
Susceptibility variations can also be seen around blood vessels where deoxyhemoglobin affects T2* in nearby tissue
Source: Robert Cox’s web slides

21. History of fMRI fMRI -1990: Ogawa observes BOLD effect with T2*
blood vessels became more visible as blood oxygen decreased
-1991: Belliveau observes first functional images using a contrast agent
-1992: Ogawa et al. and Kwong et al. publish first functional images using BOLD signal
Seiji Ogawa

22. First Functional Images
Flickering Checkerboard
OFF (60 s) - ON (60 s) - OFF (60 s) - ON (60 s)
Source: Kwong et al., 1992

23. Hemoglobin Hemoglogin (Hgb): - can attach up to four oxygen atoms (O2)
- oxy-Hgb (four O2) is diamagnetic  no B effects
- deoxy-Hgb is paramagnetic  if [deoxy-Hgb]   local B 
Source: Jorge Jovicich

24. BOLD signal At Rest: Active: Blood Oxygen Level Dependent signal
neural activity   blood flow   oxyhemoglobin   T2*   MR signal
At Rest:
Mxy
Signal
Mo sin
T2* task
T2* control
Stask S
Scontrol
Active:
time
TEoptimum
Source: Jorge Jovicich
Figure Source: Huettel, Song & McCarthy, 2004, Functional Magnetic Resonance Imaging

25. MRI Safety

26. Magnetic Fields main magnetic field is very strong
BUT static magnetic fields are less of a concern than changing magnetic fields
moving quickly through a magnetic field, especially the head, is a BAD idea -- like doing whole brain TMS on yourself
some people experience dizziness, nausea, metallic tastes
BUT these were also reported in 45% of subjects when the magnet was OFF!
typical consent form phrasing: “no known risks”
you can never prove anything is safe, only that something is unsafe

27. Magnet Safety: Big Things
Source:
Source:
flying_objects.html
“Large ferromagnetic objects that were reported as having been drawn into the MR equipment include a defibrillator, a wheelchair, a respirator, ankle weights, an IV pole, a tool box, sand bags containing metal filings, a vacuum cleaner, and mop buckets.”
-Chaljub et al., (2001) AJR

28. Very Serious Risk Westchester NY, 2001
Source:

29. Magnet Safety: Little Things
Aneurysm clips can be pulled off vessels, leading to death
Flying things can kill people.
Even in less severe incidents, they can fly into the magnet and damage it or require an expensive shutdown.

30. Subject Safety
Anyone going near the magnet – subjects, staff and visitors – must be thoroughly screened:
Subjects must have no metal in their bodies:
pacemaker
aneurysm clips
metal implants (e.g., cochlear implants)
interuterine devices (IUDs)
some dental work (but fillings are okay)
Subjects must remove metal from their bodies
jewellery, watch, piercings
coins, etc.
wallet
any metal that may distort the field (e.g., underwire bra)
Females must not be pregnant or at risk of conceiving
Some institutions even require pregancy tests for any female, every session
Subjects must be given ear plugs (acoustic noise can reach 120 dB)
This subject was wearing a hair band with a ~2 mm copper clamp. Left: with hair band. Right: without.
Source: Jorge Jovicich

31. Fall-off of Magnetic Field
actively shielded magnet

32. Very Serious Risk
Source:

33. Magnet Safety
Principal Investigators should be sure all lab members are aware of hazards.
Make sure that anyone who is about to enter the magnet room has been filled out consent and screening forms (subjects, lab members, visitors).
Remove all metal, coins, credit cards etc. as soon as you enter the magnet area.
Think! Train yourself to mini-screen yourself every time you approach the threshold of the magnet room.
Do not enter the magnet room with any tools (e.g., scissors). Use only magnet-friendly tools in the toolbox in the magnet room.
Think!
Do the “Metal Macarena!”

34. Specific Absorption Rate (SAR)
excess energy heats body tissues
if body heats faster than natural cooling, temperature rises
Specific Absorption Rate (SAR) = amount of heat absorbed by body
magnets have SAR limits to prevent overheating
limited to 1 degree rise in core body temperature
depends on body size, geometry, thermoregulation
depends on pulse sequences (e.g., larger flip angles = greater SAR)

35. Other safety issues fire safety quenching burns
always give subjects a panic button
make sure that subject can be evacuated quickly if needed
have an MR-compatible fire extinguisher available
operator must know safety protocols
quenching
rapid decrease in magnetic field strength
helium boils off and can fill room (displacing oxygen)
can occur spontaneously
only voluntarily initiated in extreme situations
burns
do not loop any wires or cables
do not place electrodes on subjects’ skin

36. Other safety issues claustrophobia peripheral nerve stimulation
subject screening
peripheral nerve stimulation
rapid switching of gradients can lead to generation of currents in the body that stimulate the nerves (e.g., twitching)
manufacturers limit rate of gradient switching to avoid problems
acoustic noise
without ear protection, could cause hearing loss
soundproofing
earplugs
headphones