Download Magnetic Resonance Imaging

Magnetic Resonance Imaging
Glenn Pierce, King’s College London, Department of Physics
Introduction
The spins in thermal equilibrium are distributed among the two
states according to the Boltzmann distribution. The ratio of the
nuclei in the spin-down state to the spin up state is given by
Edward Purcell and Felix Bloch were both awarded the Nobel
Prize in 1952 for their independent discovery of Nuclear
Magnetic Resonance also known as NMR.
In 1971 Raymond Damadian showed that the nuclear magnetic
relaxation times of tissues and tumours differed. This allowed
magnetic resonance to be used for the detection of disease.
Nd
e
Nu
hγB
2 pkT
The upper and lower energy spin states are almost equally
populated with only a very small excess in the lower energy
state. It is only measurable because of large number of
hydrogen nuclei in organic tissue.
Spin
The force that acts upon the dipole is proportional to the
strength of the field in which it is placed and the magnitude
of the moment. The proton has a large magnetic moment and
has a strong tendency to align with an external magnetic
field.
Fig. 1 Shows how
hydrogen nuclei
align themselves
along or against an
external magnetic
field.
Nuclei have the property of spin. Spin is a fundamental
intrinsic property of particles. The spin of an electrically
charged particle which moves creates a magnetic moment.
The hydrogen nucleus is the most important nucleus in the
field of NMR as the proton has a large magnetic moment and
has a strong tendency to align with an external magnetic field.
It is also highly abundant in the water and fat of the human
body.
Hydrogen nuclei magnetic moments are randomly oriented in
the absence of an external magnetic field and are considered to
have a net magnetization of zero.
Once hydrogen protons are placed in the presence of an
external magnetic field these alignments are quantized. In the
case of protons two alignments are possible. They will
orientate parallel or anti-parallel to the field. This is shown in
figure 1.
Figure 2 shows the energy separation between the two spin states of
the nuclei in a magnetic field. It shows that spin states which are
orientated towards being parallel with the magnetic field are in a
lower energy state than those states that are anti-parallel to the
magnetic field.
Fig 2 shows the energy
differerence for hydrogen
nuclei that are aligned in
opposing directions in a
magnetic field. As the
magnetic field strength
increases so does the energy
separation between states.
Precession
If the particles were perfect dipoles the particle moments
would all line up with the external field to minimise the
energy. However, In the case of nuclei with spin, the
randomly orientated dipole moments precess around the
axis of the magnetic field.
The angle between the external field and the spin axis of
the particle depends simply upon the initial spin axis
before the external field is applied. The rate at which this
precession occurs is known as the Lamor relationship and
is given by the equation
T1 Process
When the system is in equilibrium the net magnetization
vector aligns with the direction of the applied magnetic
field. This is known as the equilibrium magnetization. If
the system is exposed to energy of a frequency equal to the
energy difference between the spin states the net
magnetization can be changed. The energy absorbed by a
nucleus must exactly equal that defined by the Lamor
frequency. After the net magnetization is changed it will
eventually return to its equilibrium value. For a nucleus to
transition from the high energy state to that of the low
energy state a discrete amount of energy has to be
transferred to the lattice of the sample. The energy
difference between the low and high energy states results
in a greater probability of transition to the low energy
state. The time constant which describes how the
longitudinal magnetization returns to equilibrium is called
the spin lattice relaxation time, also known as T1
relaxation time or longitudinal relaxation. The rate at
which the relaxation occurs is given by
M0 1 e
If the particle absorbs the energy corresponding to the Lamor
frequency the nuclei can undergo a transition between the
two energy states. A particle in the lower energy state that
absorbs a photon can undergo transition to the higher energy
state. Therefore the energy corresponding to the Lamor
frequency is equal to the difference between the two energy
states of the system.
In clinical MRI, is typically between 15 and 80 MHz for
hydrogen imaging and thus the frequency of the photon is in
the radio frequency (RF) range. This is the resonance in MRI.
Due to T1 and T2 relaxation, it is possible differentiate between
various tissues in the body. Various tissues have different T1
and T2 values. For example due to the slow molecular motion
of fat nuclei, T1 relaxation occurs more rapidly than water
nuclei. This is due to the fact that water nuclei do not give up
their energy to the lattice as quickly as fat due to the high
kinetic energy of the water molecules. Figure 6 shows two MRI
images, one shows a T1 weighted image and the other T2
weighted.
Fig 4 shows the
T1 recovery for
two different
tissues. Tissue
A is shown to
return to the
equilibrium
magnetism faster
than tissue B.
Here beta is the magnetic field and gamma is the
gyromagnetic ratio that depends on the type of
nucleus.
Fig 3 shows the
precession of a
proton at an
angular velocity w
around an external
magnetic field B.
Tissue Contrast
t
T1
ω γΠ²0
Ï…
2 π 2 π
If the Lamor frequency is negative then the precession is
clockwise when looking against the magnetic field as show
in figure 3. For a positive Lamor frequency the direction of
precession is in the anti clockwise direction.
Fig 5 shows the T2
decay rate for two
different tissues.
The fat sample here
is shown to have a
faster T2 decay
rate than
cerebrospinal
fluid.
T2 Process
T1 and T2 processes occur at the same time. As stated when
an external magnetic field is applied to a sample the nuclei
will precess around the external field. After an radio
frequency pulse, hydrogen nuclei will be spinning in unison
or in-phase with each other. As the magnetic fields of all the
nuclei interact with each other, energy is exchanged
between those nuclei. As each of the nuclei is experiencing
a slightly different magnetic field and rotates at its own
Larmor frequency an exponential decrease or decay in
transverse magnetization occurs. This process is know as T2
relaxation or spin-spin relaxation as the decay is the result
of the exchange of energy between spinning hydrogen
nuclei, as T2 decay occurs, the MR signal dies out.
Fig 6 shows two images. The first is a T1 weighted image that
is used to compare T1 relaxation times between tissues. The
second is T2 weighted that is used to compare T2 relaxation
times between tissues.
Literature cited
Basic Priciples of MRI, Margaret M King,
http://www.erads.com/mrimod.htm, Last accessed 11-06-04
Malcolm H. Levit. Spin Dynamics Basics of Nucler Magnetic
Resonace. John Wiley and Sons, 1998.
Acknowledgments
I would like to thank Alan Michette for allowing me to
undertake the course "Xrays and Imaging" at Kings College.