MRI Lectures
• Disclaimer: This material is not novel, but is
collected from a variety of sources on the
web.
Principle of MRI (1)
• Certain atomic nuclei behave like a spinning top
– behave like small magnets
• Under normal circumstances
– the body is not magnetic
– the hydrogen nuclei within the body point into all
directions randomly
– the net magnetic field strength (magnetization) = 0
• When we place an ensemble of nuclei with spin
in a strong magnetic field
– the nuclei tend to align themselves with the magnetic
field
Fonar
The MRI Operating Room:
Fonar OR 360
• Magnet Specs
Field Strength: 0.6 Tesla
Operating Frequency: 25.5
MHz
Patient Gap: 19 inches
Patient Access: 360
degrees
Treatment Room Specs
Standard 8-foot ceiling
Width: 14 Feet
Length: Unlimited
GE
Hitachi
Hitachi
Philips: 3T MRI
Principle of MRI (2)
• This alignment occurs
– the nuclei prefer to be in a state with the lowest
energy
– 00 K ↑all nuclei align themselves to the external
magnetic field
• At room temperature
– the nuclei also possess thermal energy
• external magnetic field
– 0.1 tesla
excess 1/106
– 1 ml H20 = 3 x 1022 molecules ~1017 hydrogen
atoms aligning parallel to the magnetic field
Spin Alignment
EM Radiation
• While the nuclei are under influence of the
external magnetic field
– pulse of electromagnetic radiation are beamed into
the tissue
• EM radiation is characterized by
– an electric and a magnetic component
– the magnetic component of the EM radiation exerts a
force on the magnetic nuclei
• When the magnetic component of the EM
radiation has a direction perpendicular to the
external magnetic field
– cause the magnetization to precess around the
direction of external field
Larmor Frequency
– in such a way
• the angle between the direction of the magnetization
and the external field will increase linearly with time
– only happen when the EM radiation has a
certain frequency
• the frequency is proportional to the strength of the
external magnetic field
• gyromagnetic ratio
• characteristic for the element (isotope)
• the range of radio frequencies 2 to 50 MHz
Precession of Magnetization
Principle of Gamma Camera
A Scintigram of the Lungs
Principle of ECG-gated
Scintigraphy
Rotating Gamma Camera
• The Distribution of Energy
• The distribution functionThe density of
states
The Maxwell-Boltzmann Distribution
• The MaxwellBoltzmann
distribution is the
classical
distribution
function for
distribution of an
amount of energy
between identical
but distinguishable
particles.
•
http://hyperphysics.phy-astr.gsu.edu/
• Besides the presumption of distinguishability, classical statistical
physics postulates further that:
• There is no restriction on the number of particles which can occupy
a given state.
• At thermal equilibrium, the distribution of particles among the
available energy states will take the most probable distribution
consistent with the total available energy and total number of
particles.
• Every specific state of the system has equal probability.
• One of the general ideas contained in these postulates is that it is
unlikely that any one particle will get an energy far above the
average (i.e., far more than its share). Energies lower than the
average are favored because there are more ways to get them. If
one particle gets an energy of 10 times the average, for example,
then it reduces the number of possibilities for the distribution of the
remainder of the energy. Therefore it is unlikely because the
probability of occupying a given state is proportional to the number
of ways it can be obtained.
Torque on a Current Loop
• Magnetic Dipole
Moment µ = i A
• External magnetic
field B
• Magnetic Moment
Torque
Precession of Spinning Top
• Gyromagnetic Ratio γ
• Larmor Frequency ω
• ω=γB
• h is Planck's Constant (equal to 6.626 x 10-34 J
s;
• ms = gs mB ms.
• ms is called the spin magnetic moment, gs is the
spin gyromagnetic ratio, mB is the Bohr
magneton and ms is 1/2 or -1/2 (the spin of the
electron divided by h). Of these numbers, only the
Bohr magneton has physical units. Its value is mB
= e h / 4 p me = 9.274 * 10-24 Am2
• Nuclear Magnetic Moments
• The nuclei of atoms contain protons and neutrons. Since a neutron is electrically
neutral, you might expect it to have no magnetic moment. In fact, it has a magnetic
moment of -9.6624 * 10-27 Am2. How can this be?
• Protons and neutrons are made up of smaller elementary particles called quarks.
The force which binds the quarks together is called the strong force. It acts like a
spring whose spring constant gets stronger as the distance between the quarks
increases, so they are never seen alone. The quarks come in six flavors, which have
been dubbed up, down, charm, strange, top and bottom.
• The proton is made of 2 up quarks and 1 down quark, and the neutron is made of 1
up quark and 2 down quarks. The up quarks have an electrical charge of 2e/3, while
the down quarks have an electrical charge of -e/3. All have spin quantum numbers of
1/2 or -1/2. This means that while the neutron is electrically neutral, it still has
spinning charges within, and hence can have a nonzero magnetic moment.
• By the same token, the nucleus of all atoms have spin, since they are collections of
spinning protons and neutrons. The nuclear magnetic moment of a particular atom
is
• g mN I. Here the gyromagnetic ratio has a different value for each atom, which
depends not only on the species but on its immediate environment as well, and the
nuclear magneton mN = e h / 4 p mp = 5.0501 * 10-27 Am2, where mp is the mass
of a proton. I is the nuclear spin; the spin quantum number for a nucleus can be any
number in the set {I, I - 1, I - 2, ..., -I + 2, -I + 1, -I}.
Spin Up vs Spin Down
• ∆E=2µB
• Nuclei that are of
interest in MRI:
•
•
•
•
•
•
•
1H - 42.58 MHz/T
2H - 6.54 MHz/T,
31P 17.25 MHz/T,
23Na 11.27 MHz/T,
14N - 3.08MHz/T,
13C - 10.71 MHz/T,
19F - 40.08 MHz/T.