Bai giang MRI

Contents:
Huynh Thanh Nhan
Introduction
Theory basis
The basis of experiments
Summary
Magnetic resonance
Magnetic resonance is a phenomenon found in magnetic systems that
possess both magnetic moments and angular momentum.
Magnetic resonance is an analytical technique based on a property of
matter called spin.
Magnetic resonance techniques include:
Magnetic resonance imaging (MRI),
Nuclear magnetic resonance (NMR),
Electron spin resonance (ESR),
Electron paramagnetic resonance (EPR).
Magnetic resonance techniques are generally non-invasive and non-destructive.
What is the magnetic resonance?
MRI is used by clinicians to produce tomographic images of
the inside of the human body. MRI is also used by scientists
to study materials as it is a non-destructive imaging technique.
NMR is used by scientists to study the structure and dynamics
of molecules.
ESR and EPR are used by scientists to study structure and reactions of free radicals.
Magnetic resonance technique applications
A system such as a nucleus may consist of many particles coupled together so that in any given state, the nucleus possesses a total magnetic moment  and a total angular momentum J. Two vectors may be taken as parallel
 = J

where  is a scalar called the “gyromagnetic ratio”

In quantum theory, we have
J = I

where I stands for a dimensionless angular momentum operator.
The basis of magnetic resonance
As an external magnetic field is applied, this field produces an interaction energy of nucleus of amount -H.

The Hamiltonian: H = - H
H = -H0Iz in the z-direction,
and E = H0m with m = I, I-1, ….-I (2I + 1 values)
To satisfy the conservation of energy,
 = E
E is the energy difference between the initial and final nuclear Zeeman energies.
 is an angular frequency
For producing magnetic resonance, an alternating magnetic field is applied perpendicularly to the static magnetic field, and is written by
H pert= -H0x Ixcost
Consequently, the allowed transitions are between levels adjacent in energy, giving
 = E = H0
or  = H0
On the other hand, for a particle with mass m and charge e moving in a circular path of radius r with period T
J = mvr = m.2r2/T
While the magnetic moment is  = iA, because i = (e/c)(1/T),
we have  = er2/cT, then deducing  = e/2mc.
Experiments
Schematic arrangement of apparatus for an electron paramagnetic resonance experiment in the microwave region.
Conclusion
With a large masses have low ’s, a factor of 1000 lower  for nuclei than for electrons.
We can change  by changing Ho, but in most cases it is advantageous to use as large a magnetic field as possible.
The electronic systems have a resonance in the microwave frequency region.
The nuclear systems have a resonance in the radio frequency region.
Thanks for your attention!