Section 2 Basic fMRI Physics

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Section 2 Basic fMRI Physics

Other Resources These slides were condensed from several excellent online sources. I have tried to give credit where appropriate. If you would like a more thorough introductory review of MR physics, I suggest the following: Robert Cox’s slideshow, (f)MRI Physics with Hardly Any Math, and his book chapters online. See “Background Information on MRI” section Mark Cohen’s intro Basic MR Physics slides Douglas Noll’s Primer on MRI and Functional MRI For a more advanced tutorial, see: Joseph Hornak’s Web Tutorial, The Basics of MRI

Recipe for MRI 1) Put subject in big magnetic field (leave him there)
2) Transmit radio waves into subject [about 3 ms] 3) Turn off radio wave transmitter 4) Receive radio waves re-transmitted by subject Manipulate re-transmission with magnetic fields during this readout interval [ ms: MRI is not a snapshot] 5) Store measured radio wave data vs. time Now go back to 2) to get some more data 6) Process raw data to reconstruct images 7) Allow subject to leave scanner (this is optional) Source: Robert Cox’s web slides

History of NMR NMR = nuclear magnetic resonance
Felix Block and Edward Purcell 1946: atomic nuclei absorb and re-emit radio frequency energy 1952: Nobel prize in physics nuclear: properties of nuclei of atoms magnetic: magnetic field required resonance: interaction between magnetic field and radio frequency Bloch Purcell NMR  MRI: Why the name change? less likely but more amusing explanation: subjects got nervous when fast-talking doctors suggested an NMR most likely explanation: nuclear has bad connotations

History of fMRI MRI -1971: MRI Tumor detection (Damadian)
-1973: Lauterbur suggests NMR could be used to form images -1977: clinical MRI scanner patented -1977: Mansfield proposes echo-planar imaging (EPI) to acquire images faster 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 Ogawa

Necessary Equipment Magnet Gradient Coil RF Coil 4T magnet RF Coil
(inside) Magnet Gradient Coil RF Coil Source: Joe Gati, photos

The Big Magnet B0 x 80,000 = Very strong 1 Tesla (T) = 10,000 Gauss
Source: 1 Tesla (T) = 10,000 Gauss Earth’s magnetic field = 0.5 Gauss x 80,000 = 4 Tesla = 4 x 10,000  0.5 = 80,000X Earth’s magnetic field Robarts Research Institute 4T Continuously on Main field = B0 B0

Source: http://www.simplyphysics.com/
Magnet Safety The whopping strength of the magnet makes safety essential. Things fly – Even big things! Source: Source: flying_objects.html Screen subjects carefully Make sure you and all your students & staff are aware of hazzards Develop stratetgies for screening yourself every time you enter the magnet Do the metal macarena!

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 (fillings 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) 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

Protons Can measure nuclei with odd number of neutrons
1H, 13C, 19F, 23Na, 31P 1H (proton) abundant: high concentration in human body high sensitivity: yields large signals

Protons align with field
Outside magnetic field Protons align with field randomly oriented Inside magnetic field spins tend to align parallel or anti-parallel to B0 net magnetization (M) along B0 spins precess with random phase no net magnetization in transverse plane only % of protons/T align with field M longitudinal axis Longitudinal magnetization transverse plane Source: Mark Cohen’s web slides M = 0 Source: Robert Cox’s web slides

Turn your dial to 4T fMRI -- Broadcasting at a frequency of 170.3 MHz!

Larmor Frequency Larmor equation f = B0  = 42.58 MHz/T
At 1.5T, f = MHz At 4T, f = MHz 170.3 Resonance Frequency for 1H 63.8 1.5 4.0 Field Strength (Tesla)

RF Excitation Excite Radio Frequency (RF) field
transmission coil: apply magnetic field along B1 (perpendicular to B0) for ~3 ms oscillating field at Larmor frequency frequencies in range of radio transmissions B1 is small: ~1/10,000 T tips M to transverse plane – spirals down analogies: guitar string (Noll), swing (Cox) final angle between B0 and B1 is the flip angle Transverse magnetization B1 B0 Source: Robert Cox’s web slides

Cox’s Swing Analogy Source: Robert Cox’s web slides

Relaxation and Receiving
Receive Radio Frequency Field receiving coil: measure net magnetization (M) readout interval (~ ms) relaxation: after RF field turned on and off, magnetization returns to normal longitudinal magnetization  T1 signal recovers transverse magnetization  T2 signal decays Source: Robert Cox’s web slides

T1 and TR T1 = recovery of longitudinal (B0) magnetization
used in anatomical images ~ msec (longer with bigger B0) TR (repetition time) = time to wait after excitation before sampling T1 Source: Mark Cohen’s web slides

Field Strength (T) ~ z position Freq Gradient coil add a gradient to the main magnetic field How can we encode spatial position? Example: axial slice excite only frequencies corresponding to slice plane Use other tricks to get other two dimensions left-right: frequency encode top-bottom: phase encode Gradient switching – that’s what makes all the beeping & buzzing noises during imaging!

Precession In and Out of Phase
protons precess at slightly different frequencies because of (1) random fluctuations in the local field at the molecular level that affect both T2 and T2*; (2) larger scale variations in the magnetic field (such as the presence of deoxyhemoglobin!) that affect T2* only. over time, the frequency differences lead to different phases between the molecules (think of a bunch of clocks running at different rates – at first they are synchronized, but over time, they get more and more out of sync until they are random) as the protons get out of phase, the transverse magnetization decays this decay occurs at different rates in different tissues Source: Mark Cohen’s web slides

T2 and TE T2 = decay of transverse magnetization
TE (time to echo) = time to wait to measure T2 or T2* (after refocussing with spin echo or gradient echo) Source: Mark Cohen’s web slides

Echos 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

T1 vs. T2 Source: Mark Cohen’s web slides

T2* T2* relaxation dephasing of transverse magnetization due to both:
- microscopic molecular interactions (T2) - spatial variations of the external main field B (tissue/air, tissue/bone interfaces) exponential decay (T2*  ms, shorter for higher Bo) Mxy Mo sin T2 T2* time Source: Jorge Jovicich

Susceptibility Adding a nonuniform object (like a person) to B0 will make the total magnetic field nonuniform This is due to susceptibility: generation of extra magnetic fields in materials that are immersed in an external field For large scale (10+ cm) inhomogeneities, scanner-supplied nonuniform magnetic fields can be adjusted to “even out” the ripples in B — this is called shimming 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

Hemoglobin Hemoglogin (Hgb): - four globin chains
- each globin chain contains a heme group - at center of each heme group is an iron atom (Fe) - each heme group can attach an oxygen atom (O2) - oxy-Hgb (four O2) is diamagnetic  no B effects - deoxy-Hgb is paramagnetic  if [deoxy-Hgb]   local B  Source: Jorge Jovicich

BOLD signal Blood Oxygen Level Dependent signal
neural activity   blood flow   oxyhemoglobin   T2*   MR signal Mxy Signal Mo sin T2* task T2* control Stask S Scontrol time TEoptimum Source: fMRIB Brief Introduction to fMRI Source: Jorge Jovicich

BOLD signal Source: Doug Noll’s primer

First Functional Images
Source: Kwong et al., 1992

Hemodynamic Response Function
% signal change = (point – baseline)/baseline usually 0.5-3% initial dip -more focal and potentially a better measure -somewhat elusive so far, not everyone can find it time to rise signal begins to rise soon after stimulus begins time to peak signal peaks 4-6 sec after stimulus begins post stimulus undershoot signal suppressed after stimulation ends

Review Magnetic field Tissue protons align with magnetic field (equilibrium state) RF pulses Protons absorb RF energy (excited state) Relaxation processes Spatial encoding using magnetic field gradients Relaxation processes Protons emit RF energy (return to equilibrium state) NMR signal detection Repeat RAW DATA MATRIX Fourier transform IMAGE Source: Jorge Jovicich

K-Space Source: Traveler’s Guide to K-space (C.A. Mistretta)

A Walk Through K-space single shot two shot vs.
K-space can be sampled in many “shots” (or even in a spiral) 2 shot or 4 shot less time between samples of slices allows temporal interpolation Note: The above is k-space, not slices both halves of k-space in 1 sec 1st half of k-space in 0.5 sec 2nd half of k-space in 0.5 sec 1st half of k-space in 0.5 sec 2nd half of k-space 2nd volume in 1 sec vs. interpolated image 1st volume in 1 sec