Download MR Cha2 Basic Physics

M R I Physics
Course
Jerry Allison Ph.D., Chris Wright B.S.,
Tom Lavin B.S., Nathan Yanasak Ph.D.
Department of Radiology
Medical College of Georgia
M R I Physics course
Chapter 2
Basic Physical Properties
Magnetism
&
Resonance
The “M” and “R” in MRI.
Magnetism
“Magnetized” objects exert forces of
repulsion or attraction on one
another,
resulting from electric currents.
3
Magnetic Properties
• All substances are magnetic (to various
degrees).
• Magnetic susceptibility is the ability of a
substance to become magnetized.
Q: If all substances are magnetic, do all substances
have “electric currents” running in them?
A: We’ll examine this question shortly…
4
Magnetic Properties (continued)
External field is applied  object becomes
magnetized, according to susceptibility.
Most standard materials fall into one of these classes
(defined by the susceptibility):
• Diamagnetic
• Paramagnetic
• Super-paramagnetic
• Ferromagnetic
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Magnetic Properties
(continued)
• Diamagnetic - develop a small magnetic field in
opposition to an applied field (and have a small
negative magnetic susceptibility).
• Non-Magnetic - very weakly diamagnetic
No field
applied
Field
applied
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Magnetic Properties
(continued)
• Paramagnetic-develop a small magnetic field in
alignment with an applied field (and have a small
positive magnetic susceptibility).
• Super-paramagnetism is ascribed to small
particles of iron oxide that can be used as MRI
contrast agents.
No field
applied
Field
applied
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Magnetic Properties
(continued)
• Ferromagnetic - strongly paramagnetic Fe, Co,
Ni, Gd. Magnetism induced by an applied
magnetic field may be retained. Ferromagnetic
substances have a strong positive magnetic
susceptibility.
No field
applied
Field
applied
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Magnetic Properties
(continued)
• Stainless Steel: can be ferromagnetic
(exterior surface of the downtown VAMC)
or non-magnetic (most surgical steel)
depending upon the particular alloy (Fe, Cr,
Ni, Mn). Fortunately, most (not all)
surgical appliances (staples, clips, etc.) are
an alloy that is non-magnetic.
9
Induced Magnetism
• A ferromagnetic substance in an applied
magnetic field will develop a magnetic field
hundreds of times as strong as the applied
field. A spherical iron ball at a distance of
1.6 m from a 1.0 T unshielded magnet will
experience equal attractive forces from
gravity and the magnet. This phenomenon is
the basis for the “projectile hazards” in
MRI.
10
Induced Magnetism (continued)
• An electrical conductor wrapped around a
ferromagnetic iron rod induces a very useful
magnetic field when an electric current is
flowing: Electromagnets, Transformers,
and Motors have iron cores. The induced
field is much larger than the magnetic field
created by the current flow in the conductor.
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Magnetism in Our World
Magnetic fields are all around us:
• Average field in Milky Way: 5x10-6 Gauss
• Average field in Solar Wind: 5x10-5 Gauss
• Average field at Moon: 1x10-2 Gauss
• Average field at Jupiter: 2x104 Gauss
1 Tesla = 10,000 Gauss = 1x104 Gauss
1 T = 10,000 G
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Magnetism in Our World
(continued)
• The Earth’s magnetic field is 0.5 - 1.0
Gauss at 15° with axis of Earth’s rotation.
• A 1.5 Tesla (15,000 Gauss) field is 15,000
to 30,000 times greater than the Earth’s
magnetic field.
13
Origins of Magnetism
• “Stationary” electrical charges have an
electric field (“E-field”).
• “Moving” electrical charges develop a
magnetic field (“B-field”).
• The basis for ALL MAGNETISM is the
motion of electrical charges.
14
Relationship of E- and B-fields
Stationary
observer
of
stationary
charge
sees Efield
E
B
E`
Stationary observer of moving
charge also sees B-field
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Relationship of E- and B-fields
Because of the inseparability of electric charges
and magnetism, we refer to these phenomena
in general as “Electromagnetism”.
Phenomena of stationary charges 
“Electrostatics”
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Remember: an accelerating or decelerating point
electric charge radiates electromagnetic radiation.
“Acceleration” of electrons
as they are deflected by the
nucleus of a tungsten atom
in the target produces
Bremsstrahlung photons
for diagnostic x-ray
applications.
tungsten target on
X-ray tube anode
high speed electron
Bremsstrahlung
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photon
Electric Fields
(in this case, an “electrostatic field”)
“Stationary” Point Electrical Charges
-
+
Electric Field Lines (arrows) represent
the direction of the fields
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Origins of Magnetism (continued)
• The “right hand rule” describes the
direction of the magnetic field relative to
the direction of movement of electric
charges.
Thumb: direction
of positive charges
Fingers: direction
of magnetic field
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Magnetic Fields
A moving point electric charge develops a magnetic field
+
Movement of a positive
particle into the page
+
Movement of a positive
particle out of the page 20
Magnetic Fields
A moving point electric charge develops a magnetic field
-
-
Movement of an electron
out of the page
Movement of an electron
into the page
21
Direction of magnetic field depends on:
1) particle charge, and 2) direction of motion.
Movement of a positive
particle out of the page
+
+
Movement of a positive
particle into the page
--
Movement of an electron
out of the page
-Movement of an electron
into the page
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Topology of B-field
B
E`
Charges moving in
straight lines form
circular field.
B
Charges moving in a circle form a
linear field in the center of circle.
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Magnetic Properties
Q: If all substances are magnetic, do all
substances have “electric currents”
running in them?
Let’s examine this question…
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All Observable Matter is Composed
of
Subatomic
Particles
electrons
-
mass = ~0.0005 amu
charge = -1 electrostatic unit(esu)
protons
mass = ~1.0 amu
charge = +1 esu
+
neutrons
mass = ~1.0 amu
charge = neutral
25
Nucleons (or protons, neutrons) are
composed of charged “quarks”
Proton
2 Up quarks (+2/3 esu) and 1 Down
quark (-1/3 esu) = +1 esu net charge
Neutron
2 Down quarks (-1/3 esu) and 1 Up
quark (+2/3 esu) = no net charge
-
+
+
+
-
-
+
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Magnetic Properties
Subatomic particles have a
property called “spin”.
They behave as if they are
spinning on their axis.
So, let’s think about little
regions on the surface of
the particle, shown as
boxes.
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Magnetic Properties
Each box contains charged
particle material.
Therefore, as the particle
rotates, the boxes act like
moving charges. So, our
particle behaves like a
collection of currents, and
we generate a magnetic
field.
B
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Spinning of the subatomic particles generates a magnetic
field, called a “magnetic moment” or “magnetic dipole”.
Electron magnetic moment
Proton magnetic
moment
+
-
Neutron magnetic
moment
For both protons and neutrons, the spinning of the charged
quarks produces the magnetic moment. So, although the
neutron is electrically “neutral”, its spinning quarks give it
a magnetic moment.
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Magnetic Properties
Q: If all substances are magnetic, do all
substances have “electric currents”
running in them?
A: Yes, at the subatomic level. But the
currents are a result of particle “spin”.
30
Resonance
Stimulated oscillation at the
natural or normal frequency
31
A Classical demonstration using tuning forks:
Tuning Fork 1
Tuning Fork 2
(( ))
(( ))
E
D
E
F
Sound waves from tuning fork 1 stimulate a non-vibrating
tuning fork 2, with same resonant frequency, to
RESONATE. It will absorb and give off energy readily at
this frequency.
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Tuning Fork 1
(( ))
Tuned string
(( ))
The same is true of a guitar string tuned to the
frequency of the tuning fork. But, if you detune the
string, it will (essentially) not resonate anymore.
33
Resonance (cont.)
In MRI, resonance relates to the stimulation of
proton magnetic moments (hydrogen nuclei) by
RF energy of the appropriate resonant frequency.
So, the protons will readily absorb and release RF
energy at this frequency.
The resonant frequency is “tunable” by the strength of the
magnetic field in which the protons are spinning, as we
shall see in a later lecture.
34
Radio Frequency Energy
• (RF) - oscillating magnetic and electric fields (I.e.,
“electromagnetic” fields) having frequencies between 3
kilohertz (kHz) and 30 Gigahertz (GHz).
• Examples
– Radio waves(AM: 535-1605 kHz; FM: 88-108 MHz)
– MRI (21,43,64,128 MHzprotons in 0.5,1T,1.5T,3T;
lower for spectroscopy)
– Cellphones (824-848 MHz)
– TV transmission (50-900 MHz; Ch.2-4  54-72 MHz)
– Microwave Ovens (2.45 GHz)
– Radar (3-30 GHz)
35
Radio Frequency Energy
In MRI, magnetic fields oscillating at the
appropriate resonant frequency are used to
stimulate nuclei to either absorb energy or
to release energy (spin flip transitions;
phase coherence).
36
Summary
• All magnetism originates in the movement
of electric charge.
• Magnetic susceptibility describes to what
extent a material increases or decreases an
applied magnetic field.
• Resonance: periodic stimulation at the
natural frequency can cause energy
exchange.
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