2004 week2 physics

Basic Physical Principles
of MRI
James Voyvodic, Ph.D.
Brain Imaging and Analysis Center


Synopsis of MRI
1) Put subject in big magnetic field
2) Transmit radio waves into subject [2~10 ms]
3) Turn off radio wave transmitter
4) Receive radio waves re-transmitted by subject0
5) Convert measured RF data to image


Many factors contribute to MR
imaging
•
•
•
•
•

Quantum properties of nuclear spins
Radio frequency (RF) excitation properties
Tissue relaxation properties
Magnetic field strength and gradients
Timing of gradients, RF pulses, and signal
detection


MRI uses a combination of Magnetic

and Electromagnetic Fields
• NMR measures magnetization of atomic nuclei in the
presence of magnetic fields
• Magnetization can be manipulated by manipulating the
magnetic fields (this is how we get images)
• Static magnetic fields don’t change (< 0.1 ppm / hr):
The main field is static and (nearly) homogeneous
• RF (radio frequency) fields are electromagnetic fields that
oscillate at radio frequencies (tens of millions of times per
second)
• Gradient magnetic fields change gradually over space and can
change quickly over time (thousands of times per second)


Radio Frequency Fields
• RF electromagnetic fields are used to manipulate the
magnetization of specific types of atoms
• This is because some atomic nuclei are sensitive to
magnetic fields and their magnetic properties are tuned to
particular RF frequencies
• Externally applied RF waves can be transmitted into a
subject to perturb those nuclei
• Perturbed nuclei will generate RF signals at the same
frequency – these can be detected coming out of the
subject


Electromagnetic Radiation Energy

X-Ray, CT

MRI


What kinds of nuclei can be used
for NMR?
• Nucleus needs to have 2 properties:
– Spin
– charge

• Nuclei are made of protons and neutrons
– Both have spin ½
– Protons have charge

• Pairs of spins tend to cancel, so only atoms with
an odd number of protons or neutrons have spin
– Good MR nuclei are 1H, 13C, 19F, 23Na, 31P


Hydrogen atoms are best for MRI
• Biological tissues are predominantly 12C, 16O, 1H,
and 14N
• Hydrogen atom is the only major species that is
MR sensitive
• Hydrogen is the most abundant atom in the body
• The majority of hydrogen is in water (H2O)
• Essentially all MRI is hydrogen (proton) imaging


Nuclear Magnetic Resonance Visible Nuclei

Why do protons interact with a
magnetic field?
• Moving (spinning) charged particle
generates its own little magnetic field
• Spinning particles with mass have angular
momentum


A Single Proton
There is electric charge
on the surface of the
proton, thus creating a
small current loop and
generating magnetic
moment .



+

+

+

J

The proton also
has mass which

generates an
angular
momentum
J when it is
spinning.

Thus proton “magnet” differs from the magnetic bar in that it
also possesses angular momentum caused by spinning.


Magnetic Moment
B

B
I

L

L
F

F = IBL
Force

W

= IBLW =
IBA
Torque


max

  


sin


Angular Momentum
J = m=mvr
J
m
v

r


The magnetic moment and angular
momentum are vectors lying along the
spin axis

 =J



 is the gyromagnetic ratio
 is a constant for a given nucleus

Vectors and Fields

•

Magnetic field B and magnetization M are vectors:
–
–
–
–

Quantities with direction as well as size
Drawn as arrows ....................................
Another example: velocity is a vector (speed is its size)
Vector operations:
dot product AB cos
cross product AB sin

• Magnetic field exerts torque to line magnets up in a
given direction
– direction of alignment is direction of B
– torque proportional to size of B [units=Tesla, Gauss=10–4 T]


How do protons interact with a
magnetic field?
• Moving (spinning) charged particle
generates its own little magnetic field
– Such particles will tend to line up with external
magnetic field lines (think of iron filings
around a magnet)

• Spinning particles with mass have angular
momentum
– Angular momentum resists attempts to change
the spin orientation (think of a gyroscope)


[Main magnet and some of its lines of force]

[Little magnets lining up with external lines of force]


Ref: www.simplyphysics.com



Net Magnetization

Bo

M

Bo
M c
T


Net magnetization
• Small B0 produces small net magnetization M
• 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 of antiparallel versus parallel protons is roughly 100,000
to 100,006 per Tesla of B0


The Energy Difference Between
the Two Alignment States
 E = 2 z Bo
 Eh 
/2
known as larmor frequency
/2= 42.57 MHz / Tesla for proton


Resonance frequencies of common nuclei


To measure magnetization we
must perturb it
• Need to apply energy to tip protons out of
alignment
– aligned with magnetic field is lowest energy
– aligned opposite magnetic field is next lowest
energy state

• Amount of energy needed depends on
nucleus and applied field strength (Larmor
frequency)

Basic Quantum Mechanics Theory of MR

The Effect of Irradiation to the Spin
System
Lower
Higher