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BME 595 - Medical Imaging Applications
Part 2: INTRODUCTION TO MRI
Lecture 1
Fundamentals of Magnetic Resonance
Feb. 16, 2005
James D. Christensen, Ph.D.
IU School of Medicine
Department of Radiology
Research II building, E002C
[email protected]
317-274-3815
References
Books covering basics of MR physics:
E. Mark Haacke, et al 1999 Magnetic Resonance Imaging: Physical Principles and
Sequence Design.
C.P. Slichter 1978 (1992) Principles of Magnetic Resonance.
A. Abragam 1961 (1994) Principles of Nuclear Magnetism.
References
Online resources for introductory review of MR physics:
Robert Cox’s book chapters online
http://afni.nimh.nih.gov/afni/edu/
See “Background Information on MRI” section
Mark Cohen’s intro Basic MR Physics slides
http://porkpie.loni.ucla.edu/BMD_HTML/SharedCode/MiscShared.html
Douglas Noll’s Primer on MRI and Functional MRI
http://www.bme.umich.edu/~dnoll/primer2.pdf
Joseph Hornak’s Web Tutorial, The Basics of MRI
http://www.cis.rit.edu/htbooks/mri/mri-main.htm
Timeline of MR Imaging
1972 – Damadian
patents idea for large
NMR scanner to
detect malignant
tissue.
1924 - Pauli suggests
that nuclear particles
may have angular
momentum (spin).
1920
1973 – Lauterbur
publishes method for
generating images
using NMR gradients.
1937 – Rabi measures
magnetic moment of
nucleus. Coins
“magnetic resonance”.
1930
1940
1985 – Insurance
reimbursements for
MRI exams begin.
MRI scanners
become clinically
prevalent.
NMR renamed MRI
1950
1946 – Purcell shows
that matter absorbs
energy at a resonant
frequency.
1946 – Bloch demonstrates
that nuclear precession can be
measured in detector coils.
1960
1959 – Singer
measures blood flow
using NMR (in
mice).
1970
1980
1973 – Mansfield
independently
publishes gradient
approach to MR.
1975 – Ernst
develops 2D-Fourier
transform for MR.
1990
2000
1990 – Ogawa and
colleagues create
functional images
using endogenous,
blood-oxygenation
contrast.
Nobel Prizes for Magnetic Resonance
•
1944: Rabi
Physics (Measured magnetic moment of nucleus)
•
1952: Felix Bloch and Edward Mills Purcell
Physics (Basic science of NMR phenomenon)
•
1991: Richard Ernst
Chemistry (High-resolution pulsed FT-NMR)
•
2002: Kurt Wüthrich
Chemistry (3D molecular structure in solution by NMR)
•
2003: Paul Lauterbur & Peter Mansfield
Physiology or Medicine (MRI technology)
Magnetic Resonance Techniques
Nuclear Spin Phenomenon:
• NMR (Nuclear Magnetic Resonance)
• MRI (Magnetic Resonance Imaging)
• EPI (Echo-Planar Imaging)
• fMRI (Functional MRI)
• MRS (Magnetic Resonance Spectroscopy)
• MRSI (MR Spectroscopic Imaging)
Electron Spin Phenomenon (not covered in this course):
• ESR (Electron Spin Resonance)
or EPR (Electron Paramagnetic Resonance)
• ELDOR (Electron-electron double resonance)
• ENDOR (Electron-nuclear double resonance)
Equipment
4T magnet
RF Coil
B0
gradient coil
(inside)
Magnet
Gradient Coil
RF Coil
Main Components of a Scanner
•
•
•
•
•
Static Magnetic Field Coils
Gradient Magnetic Field Coils
Magnetic shim coils
Radiofrequency Coil
Subsystem control computer
• Data transfer and storage computers
• Physiological monitoring, stimulus display, and
behavioral recording hardware
Shimmingrf
rf gradient
coil
coil
main
magnet
main
magnet
Transmit
Receive
Control
Computer
Main Magnet Field Bo
• Purpose is to align H protons in H2O (little
magnets)
[Main magnet and some of its lines of force]
[Little magnets lining up with external lines of force]
Common nuclei with NMR properties
•Criteria:
Must have ODD number of protons or ODD number of neutrons.
Reason?
It is impossible to arrange these nuclei so that a zero net angular
momentum is achieved. Thus, these nuclei will display a magnetic
moment and angular momentum necessary for NMR.
Examples:
1H, 13C, 19F, 23N, and 31P with gyromagnetic ratio of 42.58, 10.71,
40.08, 11.27 and 17.25 MHz/T.
Since hydrogen protons are the most abundant in human body, we use
1H MRI most of the time.
Angular Momentum
J = mw=mvr
J
m
r
v
magnetic moment m = g J
where g is the gyromagnetic ratio,
and it is a constant for a given nucleus
A Single Proton
There is electric charge
on the surface of the
proton, thus creating a
small current loop and
generating magnetic
moment m.
m
+
+
+
J
The proton also
has mass which
generates an
angular
momentum
J when it is
spinning.
Thus proton “magnet” differs from a magnetic bar in that it
also possesses angular momentum caused by spinning.
Protons in a Magnetic Field
Bo
Parallel
(low energy)
Anti-Parallel
(high energy)
Spinning protons in a magnetic field will assume two states.
If the temperature is 0o K, all spins will occupy the lower energy state.
Protons align with field
Outside 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
longitudinal
axis
Inside magnetic field
Mz
Mxy = 0
M
transverse
plane
Longitudinal
magnetization
Transverse
magnetization
Net Magnetization
Bo
M
Bo
M c
T
The Boltzman equation describes the population ratio of the two energy states:
N-/N+ = e –E/kT
 Larger B0 produces larger net magnetization M, lined up with B0
 Thermal motions try to randomize alignment of proton magnets
 At room temperature, the population ratio is roughly 100,000 to 100,006 per Tesla
of B0
Energy Difference Between States
Energy Difference Between States
DE  hn
D E = 2 mz Bo
n  g/2p Bo
known as Larmor frequency
g/2p = 42.57 MHz / Tesla for proton
Knowing the energy difference allows us to use
electromagnetic waves with appropriate energy
level to irradiate the spin system so that some spins
at lower energy level can absorb right amount of
energy to “flip” to higher energy level.
Basic Quantum Mechanics Theory of MR
Spin System Before Irradiation
Bo
Lower Energy
Higher Energy
Basic Quantum Mechanics Theory of MR
The Effect of Irradiation to the Spin
System
Lower
Higher
Basic Quantum Mechanics Theory of MR
Spin System After Irradiation
Precession – Quantum Mechanics
Precession of the quantum expectation value of the magnetic moment
operator in the presence of a constant external field applied along the Z axis.
The uncertainty principle says that both energy and time (phase) or
momentum (angular) and position (orientation) cannot be known with
precision simultaneously.
Precession – Classical
= m × Bo torque
 = dJ / dt
J = m/g
dm/dt = g (m × Bo)
m(t) = (mxocos gBot + myosin gBot) x + (myocos gBot - mxosin gBot) y + mzoz
A Mechanical Analogy of Precession
• A gyroscope in the Earth’s gravitational field is like
magnetization in an externally applied magnetic field
Equation of Motion: Block equation
T1 and T2 are time constants describing
relaxation processes caused by interaction with
the local environment
RF Excitation:
On-resonance
Off-resonance
RF Excitation
Excite Radio Frequency (RF) field
• transmission coil: apply magnetic field along B1
(perpendicular to B0)
• oscillating field at Larmor frequency
• frequencies in RF range
• B1 is small: ~1/10,000 T
• tips M to transverse plane – spirals down
• analogy: childrens swingset
• final angle between B0 and B1 is the flip angle
Transverse
magnetization
B0
B1
Signal Detection via RF coil
Signal Detection
Signal is damped due to relaxation
Relaxation via magnetic field
interactions with the local environment
Spin-Lattice (T1) relaxation via
molecular motion
Effect of temperature
Effect of viscosity
T1 Relaxation efficiency as function
of freq is inversely related to the
density of states
Spin-Lattice (T1) relaxation
Spin-Spin (T2) Relaxation via Dephasing
Relaxation
Relaxation
T2 Relaxation
Efffective T2 relaxation rate:
1/T2’ = 1/T2 + 1/T2*
Total = dynamic + static
Spin-Echo Pulse Sequence
Spin-Echo Pulse Sequence
Multiple Spin-Echo
HOMEWORK Assignment #1
1) Why does 14N have a magnetic moment, even though its nucleus contains an even number of particles?
2) At 37 deg C in a 3.0 Tesla static magnetic field, what percentage of proton spins are aligned with the field?
3) Derive the spin-lattice (T1) time constant for the magnetization plotted below having boundary conditions:
Mz=M0 at t=0 following a 180 degree pulse; M=0 at t=2.0 sec.