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 exter

nal magnetic field– pulse of electromagnetic radiation are beamed into th

e 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 radiati

on has a direction perpendicular to the external magnetic field– cause the magnetization to precess around the directio

n 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 Maxwell-

Boltzmann 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.