class 2: basics of fmri 2012 spring fmri: theory & practice 1

Class 2: Basics of fMRI

2012 spring fMRI: theory & practice1

fMRI Setup

2012 spring fMRI: theory & practice 2

The Briefest Possible Explanation of MR Physics I Could Manage

(while still covering important ideas and jargon)


Necessary Equipment

Magnet Gradient Coil RF Coil

Source for Photos: Joe Gati

RF Coil

4T magnet

gradient coil(inside)

2012 spring fMRI: theory & practice 42012 spring fMRI: theory & practice

Step 1: Put Subject in Big Magnet

Protons (hydrogen atoms) have “spins” (like tops). They have

an orientation and a frequency.

When you put a material (like your subject) in an MRI

scanner, some of the protons become oriented with the

magnetic field.2012 spring fMRI: theory & practice 5

2012 spring fMRI: theory & practice

Step 2: Apply Radio Waves

When you apply radio waves (RF pulse) at the appropriate frequency, you can change the orientation of the spins as the protons absorb energy.

After you turn off the radio waves, as the protons return to their original orientations, they emit energy in the form of radio waves.


Step 3: Measure Radio Waves

T1 measures how quickly the protons realign with the main magnetic field

T2 measures how quickly the protons give off energy as they recover to equilibrium

fat has high signal bright

CSF has low signal dark

T1-WEIGHTED ANATOMICAL IMAGE T2-WEIGHTED ANATOMICAL IMAGE

fat has low signal dark

CSF has high signal bright



Protons

Can measure nuclei with odd number of neutrons1H, 13C, 19F, 23Na, 31P

1H (proton)abundant: high concentration in human bodyhigh sensitivity: yields large signals


Protons align with fieldOutside magnetic field

Inside magnetic field

• randomly oriented

• 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 0.0003% of protons/T align with field

Source: Mark Cohen’s web slides

M

M = 0Source: Robert Cox’s web slides

longitudinalaxis

transverseplane

Longitudinalmagnetization


http://porkpie.loni.ucla.edu/BMD_HTML/SharedCode/slides/BasicMRPhysics/ppframe.htm



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 tissues2012 spring fMRI: theory & practice 10





Radio Frequency


Larmor Frequency

Larmor equationf = B0

= 42.58 MHz/T

At 1.5T, f = 63.76 MHzAt 4T, f = 170.3 MHz

Field Strength (Tesla)

ResonanceFrequency for 1H

170.3

63.8

1.5 4.0


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

Source: Robert Cox’s web slides

Transversemagnetization


Relaxation and Receiving

Receive Radio Frequency Field• receiving coil: measure net magnetization (M)• readout interval (~10-100 ms)• relaxation: after RF field turned on and off, magnetization returns to normal

longitudinal magnetization T1 signal recoverstransverse magnetization T2 signal decays



T1 and TR


T1 = recovery of longitudinal (B0) magnetization• used in anatomical images• ~500-1000 msec (longer with bigger B0)

TR (repetition time) = time to wait after excitation before sampling T1


T2 and TE


T2 = decay of transverse magnetizationTE (time to echo) = time to wait to measure T2 or T2* (after refocussing with spin echo or gradient echo)


T2*

Source: Jorge Jovicich

time

Mxy

Mo sinT2

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* 30 - 100 ms, shorter for higher Bo)


Echos


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*

pulse sequence: series of excitations, gradient triggers and readouts

Gradient echopulse sequence

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



T1 vs. T2



Jargon Watch

• T1 = the most common type of anatomical image• T2 = another type of anatomical image• TR = repetition time = one timing parameter• TE = time to echo = another timing parameter• flip angle = how much you tilt the protons (90 degrees

in example above)


Step 4: Use Gradients to Encode Space

Remember that radio waves have to be the right frequency to excite protons.

The frequency is proportional to the strength of the magnetic field.

If we create gradients of magnetic fields, different frequencies will affect protons in different parts of space.

lower magnetic field;

lower frequencies

higher magnetic field;

higher frequencies

space

field strength


Spatial Coding:GradientsHow can we encode spatial position?

• Example: axial slice

Use other tricks to get other two dimensions

• left-right: frequency encode

• top-bottom: phase encode

excite only frequencies

corresponding to slice plane

Field Strength (T) ~ z position

Fre

q

Gradient coil

add a gradient to the main magnetic

field

Gradient switching – that’s what makes all the beeping & buzzing noises during imaging!

22


Step 5: Convert Frequencies to Brain Space

k-space contains information about

frequencies in image

We want to see brains, not frequencies


A Walk Through K-space

echo-planar imaging• sample k-space in a linear zig-zag trajectory

spiral imaging• sample k-space in a spiral trajectory

single shot imaging• sample k-space with one trajectory

multi-shot imaging• sample k-space with multiple (typically 2 or 4) trajectories

• Our technicians at RRI prefer spiral and multishot acquisitions because they’re more efficient

single shot EPI two shot EPI

Note: The above is k-space, not slices

single shot spiral two shot spiral

(forgive the hand drawn spirals)


Susceptibility Artifacts

-In addition to T1 and T2 images, there is a third kind, called T2* = “tee-two-star”-In T2* images, artifacts occur near junctions between air and tissue

• sinuses, ear canals

•In some ways this sucks, but in one way, it’s fabulous…

sinuses

earcanals

T1-weighted imageT2*-weighted image


K-Space

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


A Walk Through K-space

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

both halves of k-space in 1 sec

1st half of k-spacein 0.5 sec

2nd half of k-spacein 0.5 sec

vs.

single shot two shot

1st volume in 1 sec interpolatedimage

Note: The above is k-space, not slices

1st half of k-spacein 0.5 sec

2nd half of k-spacein 0.5 sec

2nd volume in 1 sec 27


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

earcanals

Susceptibility variations can also be seen around blood vessels where deoxyhemoglobin affects T2* in nearby tissue


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