MRI

from chapter 1 of The Statistical Analysis of Functional MRI Data http://www.springerlink.com/content/978-0-387-78191-4/#section=212959&page=1&locus=0

Particles and Atoms

• atomic number - number of protons, determines kind of atom
• atomic weight - number of protons and neutrons, determines isotope
• spin
  • 0 if atomic number and atomic weight are both even
  • half-integer if atomic weight odd
  • integer if atomic number odd, atomic weight even

¹H (proton) has spin 1/2 and is the predominant subject of MRI

Fields and Precession

• one Tesla = 10,000 Gauss
• earth's magnetic field is 0.5 Gauss or 50 microTesla
• Larmor equation - atoms of nonzero spin absorb electromagnetic radiation of frequency <math>\omega</math>
  • <math>\omega = \gamma B_0</math>
  • <math>\gamma</math> is gyromagnetic ratio of the nucleus
  • For a 3T magnet studying ¹H nuclei, <math>\gamma</math> is 42.58 MHz/T, and <math>\omega</math> is 127.74 MHz (radio waves of length 2.347 m)
• particles with spin naturally precess around an axis aligned with the magnetic field
• Zeeman effect - as field strength goes up, proportionally more protons align parallel to field than anti-parallel

Acquiring Images

• A gradient coil induces a small gradient to the background field to give each position of the brain its own resonance frequency
• An RF pulse stimulates just those protons at exactly the right frequency to flip and precess in concert.
• As the spins relax back to the low-energy parallel state, they emit radiation that gets picked up by receiver coils
• by applying a gradient that is uniform along one axis, parallel slices can be selected by incrementing the frequency

Relaxation Times

• T₁ spin-lattice or longitudinal relaxation time - time required by the z component of the tissue magnetization to return to 63% of its original value
  • <math>M_z = M_0 (1 - e^{ - t/T_1} ).</math>
• T₂ spin-spin or transverse relaxation time - time required by the transverse component of the magnetization to return to 37% of its original value
  • <math>M_{xy} = M_0 e^{ - t/T_2}</math>
• <math>T_2^*</math> free induction decay (FID) relaxation time - decay constant for an exponentially damped sinusoidal
• In general, <math>T_2^* < T_2 < T_1</math>

values at 1.5T (ms)	T1	T2
gray matter	900	100
white matter	600	80
cerebrospinal fluid	4000	2000

fMRI

(see also fMRI)

• Measures increase in oxygenated blood flow to regions with active neurons
• hemodynamic response function (HRF) - the ratio of deoxygenated to oxygenated blood as a function of time
• 
• blood oxygenation level dependent (BOLD) effect - deoxygenated blood has a magnetic susceptibility that is 20% greater than that of oxygenated blood
• the density of hydrogen nuclei at a given point is the inverse Fourier transform of the measured magnetizations over specific frequencies and phases
• the signal from the center of k-space overwhelms everything else and has to be damped down to see the rest
• repetition time (TR, eg 2s) is the time between consecutive scans of the brain (in which a full set of slices is obtained)
• TR may be varied to optimize contrast between a particular pair of tissue types
• echo time (TE) is the time between the RF pulse and the peak of the echoing response signal (how is this under the control of the experimenter?)
• T₁ - weighted images (intermediate TR, short TE) emphasize white and gray matter
• T2 - weighted images (long TR, intermediate TE) emphasize cerebrospinal fluid, good for structurals
• <math>T_2^*</math> - weighted images (long TR, intermediate TE) emphasize deoxygenated blood
• signal to noise ratio (SNR) is proportional to the volume of a voxel and <math>\sqrt{\frac{N_y NEX}{BW}}</math>, where
  • <math>N_y</math> is the number of phase encoding steps (i.e. number of voxels in the y direction)
  • NEX is the number of excitations (number of times the scan is repeated)
  • BW is the bandwidth (?)