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Interlude: A primer on Fourier Analysis

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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


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