In this introduction to MRI we will be describing some of the concepts that explain the basis
for generating an MRI image, from the fundamentals of how an MR signal is produced, how this
signal can be spatially encoded, and how image contrast can be manipulated. In this
presentation we start by introducing the nuclear spin, an essential property of nuclei that
gives rise to the MR signal. Atoms are comprised of a nucleus and its orbiting electrons.
All nuclei are composed of a number of particles, the most important being positively charged
protons and neutrally charged neutrons. The nuclei of all elements in the periodic table
are made up of protons with varying numbers of neutrons, with most elements having isotopes
that have the same number of protons but differing numbers of neutrons.
Protons have a charge equal but opposite to the electron and neutrons are overall neutral but have distributed charge.
The proton and neutron are both spinning and so contribute to the angular momentum of the
nucleus. We find that a nucleus has spin if it contains an odd number of protons, or if
there is an odd number of neutrons, but if the number of protons and neutrons are both
even, then the nucleus will have zero spin. It is this property of nuclear spin that is
essential for a nucleus to give rise to a magnetic resonance signal. Since the average
human body is approximately 60% water and water is made up of two protons and one oxygen
atom, by far the most abundant spins within the body are water protons, and it is these
nuclei that we usually detect in a MRI scan. For this reason we will refer only to the
simple proton as the nuclear spin from now on. As a spinning charged particle, the proton
generates a magnetic moment and this moment has a direction that is along the axis of
rotation of the spin. It is the behaviour of these magnetic moments that we observe
during a MRI scan. In the absence of environmental influences the isolated magnetic moment is
free to rotate and its axis fluctuates in random directions -- it has no preferred
orientation. What happens then with a collection of spins -- remember that their magnetic
moments have direction and so we treat them as vectors and can calculate the net result
of a large number of magnetic moments such as we have in the body. We start with a smaller
number, say 5 spins which are randomly fluctuating in space -- so the sum of these vectors will
give rise to a net magnetic moment of some size and direction. If we increase the number
to say 50, then we expect the sum of the vectors in 3 dimensions to get smaller and so for
very large numbers of spins as we have in the body, the net magnetic moment will reduce
to virtually zero due to the random orientation of the vectors. So what happens if we place
our sample of spins into a magnetic field? Well, just as small bar magnets experience
the force of the earth's magnetic field and align themselves along the field as in
a compass, the nuclear spins will be forced to align along the direction of the applied
magnetic field. You will notice that the magnetic moment does not point exactly in the direction
of the field, but at an angle to it -- this is due to the angular momentum of the nuclear
spin. You will also see that the magnetic moment begins to rotate around the direction
of the field at that angle -- this is called precession, and the rate of precession, or
frequency, is known as the Larmor frequency. While the magnetic moments prefer to align
with the applied field, some may align opposing the magnetic field -- this orientation is
a higher energy state than when the spins align with the field. Planck's law tells
us that the frequency of the energy absorbed by the spins to make a transition from the
low energy level to the high energy level is directly proportional to the energy difference
between the levels. This frequency is the Larmor frequency mentioned earlier. Since
the energy difference is directly proportional to the applied magnetic field strength, we
know that the Larmor frequency is also determined by the field strength Bo. This relationship
is perhaps the most important principle in MRI and is called the Larmor equation. The
constant of proportionality gamma is known as the gyromagnetic ratio and it is a unique
characteristic of the nucleus involved. So how many spins are there in the two energy levels
at any one time? This is determined by the energy difference and the temperature of the
system, and is governed by the Boltzmann distribution which relates the number of spins in a level
to the total spins, the energy of that level and the temperature. We can use this relationship
to calculate the spin population difference between the levels at a particular field strength
and temperature. For example, for a sample of 1 million spins, in a field of 2 Tesla
and at 25 degrees Celsius, we can show that the excess number of spins in the low energy
level is only 7 --this is an indication that MRI is a relatively insensitive scanning method.
So to summarise, in the absence of a magnetic field, proton spins have no preferred direction,
are all of equal energy. And when a field is applied, proton spins align either with
or against the field direction and the energy difference of these states is proportional
to the field strength Bo. The relative spin populations and the Larmor frequency are therefore
also directly proportional to the field strength. So we can now represent the magnetic moments
in the presence of a field as a collection of vectors, some pointing up, fewer pointing
down and they precess about the direction of the magnetic field, which we say is in
the z-direction. The rate of this precession is the Larmor frequency.
When we do an MRI scan, we are detecting the total average of all of the magnetic moments, which is simply
the sum of all the spin vectors and we refer to this as the net magnetization vector. The
net magnetization vector points along the z-axis at equilibrium, and its magnitude is
proportional to the population difference between the two energy levels. The signal
we obtain in the MRI image is determined by the fate of this magnetization vector during the scan.