Introduction to MRI 1Psy 8960, Spring ’07
Introduction to MRI: NMR
• Physics reminders– Nuclei and atoms– Electromagnetic spectrum and
Radio Frequency– Magnets– Vectors
• NMR phenomena– nuclei, atoms and electron clouds
(molecular environment)– excitation and energy states,
Zeeman diagram– precession and resonance
quantum vs. classical pictures of proton(s)
Introduction to MRI 3Psy 8960, Spring ’07
Electromagnetic spectrum
www.yorku.ca/eye/spectru.htm
c = = 3 x 108 m/s /
Introduction to MRI 4Psy 8960, Spring ’07
RF Antennae vs. RF coils
www.yorku.ca/eye/spectru.htm
Antennae disperse energy Coils focus energy
Introduction to MRI 6Psy 8960, Spring ’07
Stern-Gerlach experiment: discovery of spin
http://www.upscale.utoronto.ca/GeneralInterest/Harrison/SternGerlach/SternGerlach.html
• Discovery of magnetic moment on particles with spins
• Electron beam has (roughly) even mix of spin-up and spin-down electrons– Beam should be bent to the side
because a force is exerted on moving charge in a magnetic field
– Beam was also split vertically, because electrons posses inherent magnetic moment
Introduction to MRI 7Psy 8960, Spring ’07
Spin and magnetic moment• Sub-atomic particles have intrinsic
angular momentum (spin), L• Aligned with L is , a magnetic
moment• The quantum number I determines
how many spin states a particle might be found in– For a nucleus, the number of
protons and neutrons determines I
• L and are related by , the gyromagnetic ratio
L I(I 1) L
Lz mz Lz
Introduction to MRI 10Psy 8960, Spring ’07
MagnetsDipole in a static field
BN
S
N
S
Lowest energy
Highest energy
E
B
B
Units of magnetic field: 1 Tesla = 104 Gauss 0.5 G = earth’s magnetic field ~50 G = refrigerator magnet
Introduction to MRI 11Psy 8960, Spring ’07
MagnetsProton in a static magnetic fieldDipole in a static field
BN
S
N
S
Lowest energy
Highest energy
E
B
B
: magnetic dipole
Introduction to MRI 12Psy 8960, Spring ’07
Nucleus in magnetic fieldNucleus in free space
L I(I 1) L
Lz mz Lz
Lz 2
z Lz
B
E
m 1
2
m 1
2
Single spin-1/2 particle in an external magnetic field
All orientations possess the same potential energy
Spin-up and spin-down are different energy levels; difference depends linearly on static magnetic field
Introduction to MRI 13Psy 8960, Spring ’07
Resonant frequency
B
E
m 1
2
m 1
2Transition emits energy
Excitation promotes transition
• Resonant frequency is determined by gyromagnetic ratio, a property of the nucleus• At 3T, protons resonate at ~128 MHz• At 7T, protons resonate at ~300 MHz
Introduction to MRI 14Psy 8960, Spring ’07
Electromagnetic spectrum
www.yorku.ca/eye/spectru.htm
c = = 3 x 108 m/s /
Introduction to MRI 15Psy 8960, Spring ’07
Hydrogen spectrum: electron transitions
http://csep10.phys.utk.edu/astr162/lect/light/absorption.html
1 electron volt = 1.6 × 10-19 JFixed energy transitions result in discrete absorption lines
Introduction to MRI 16Psy 8960, Spring ’07
Lz 2
z Lz
B
E
m 1
2
m 1
2
Precession and resonant frequency
Spin-up and spin-down are different energy levels; difference depends linearly on static magnetic field
Torque exerted by magnetic force on dipole creates precession.
BL
B
E
2
BLL
B
BL
Bdt
Ld
z
z
)sin(
)sin(
Introduction to MRI 18Psy 8960, Spring ’07
BM: net (bulk) magnetization
M
M
M||
From spin-1/2 particles to bulk magnetization
Equilibrium: ~ 1 ppm excess in spin-up (low energy) state creates a net magnetization
Excitation affects phase and distribution betweenspin-up and spin-down, rotating bulk magnetization
isochromat
Introduction to MRI 19Psy 8960, Spring ’07
Information in proton NMR signal
• Resonant frequency depends on • Static magnetic field
• Molecule
• Relaxation rate depends on physical environment• Microscopic field perturbations
– Tissue interfaces– Deoxygenated blood
• Molecular environment– Gray matter– White matter– CSF
Relaxation
Excitation