Psy 8960, Spring ’07 Introduction to MRI1 Introduction to MRI: NMR Physics reminders –Nuclei and atoms –Electromagnetic spectrum and Radio Frequency –Magnets.

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 2Psy 8960, Spring ’07

Electromagnetic spectrum

http://www.nps.gov

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 5Psy 8960, Spring ’07

Nuclei and subatomic particles

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 8Psy 8960, Spring ’07

Periodic table: some nuclei are magnetic

Introduction to MRI 9Psy 8960, Spring ’07

Water

www.lsbu.ac.uk/water/

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 17Psy 8960, Spring ’07

Gyromagnetic (magnetogyric) ratio

B L

B

B

L I(I 1) L

BL

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

Introduction to MRI 20Psy 8960, Spring ’07

Proton NMR spectrum: ethanol

/grupper/KS-grp/microarray/slides/drablos/Structure_determination