Physics of MRI - Detailed
Magnetism is a property of matter that is a result of the orbiting electrons
in atoms. The orbiting electrons cause the atoms to have a magnetic moment
associated with an intrinsic angular momentum called spin. Spin will be
discussed in more detail a little bit further down. It's convenient to imagine
the electron spinning on its axis with the up and down orientations. However,
in reality the electron is not physically spinning!|
The body is largely composed of water molecules. Each water molecule has two
hydrogen nuclei or protons. MRI takes advantage of the high prevalence of hydrogen
in the body and the magnetic properties of the proton in a hydrogen atom. Hydrogen
atoms induce a small magnetic field due to the spin of this atom's proton.
When a person goes inside the powerful magnetic field of the scanner, the
magnetic moments (the measure of its tendency to align with a magnetic field)
of some of these protons changes, and aligns with the direction of the field.
The magnetic field in an magnetic resonance imaging (MRI) scanner is
generated by surrounding a coil of wire with super cooling fluids (liquid
helium and liquid nitrogen) lowering the temperature to about 10°K (-263°C
or -441°F). Electrical current in the coil moves very fast creating the
extremely large magnetic field.
Magnetic field strengths are measured in units of gauss (G) and Tesla (T).
One Tesla is equal to 10,000 gauss. The earth's magnetic field is about 0.5
gauss. The strength of electromagnets used to pick up cars in junk yards is
about the field strength of MRI machines (1.5 to 2.0T). The
in MRI refers to the main magnetic field and is measured in Tesla (T). The
majority of MRI systems in clinical use are between 1.5T and 3T. Altering the
field strength will affect the Larmour frequency at which the protons precess.
The protons placed in a magnetic field have the interesting property in that they
will absorb energy at specific frequencies, and then re-emit the energy at the
same frequency. To measure the net magnetization in a brain scan, a coil can be
placed around the head can be used to both to generate electromagnetic waves and
measure the electromagnetic waves that are emitted from the head in response.
Proton density (PD) is the concentration of protons in the tissue in the form
of water and macromolecules (proteins, fat, etc). The T1 and T2 relaxation
times define the way that the protons revert back to their resting states
after the initial RF pulse. The most common effect of flow is loss of signal
from rapidly flowing arterial blood.
So when the patient is first placed in the static magnetic field that the machine
creates, MRI takes advantage of that high prevalence of hydrogen in the body and the
magnetic properties of the proton in a hydrogen atom. Hydrogen atoms induce a small
magnetic field due to the spin of this atom's proton. Hydrogen protons within the
patient's body will then align to the magnetic field which is typically 30 to 60 thousand
times stronger than the magnetic field of the earth.
A radio frequency (RF) pulse is then emitted from the scanner, tuned to a specific
range of frequencies at which hydrogen protons precess. This results in some of
the hydrogen protons being "knocked" 180° out of alignment with the static magnetic
field and being forced into phase with other hydrogen protons. The echo time refers
to time between the application of RF excitation pulse and the peak of the signal
induced in the coil and is measured in milliseconds.
As the energy from the RF pulse is dissipated, the hydrogen protons will return
to alignment with the static magnetic field. The MRI signal is derived from the
hydrogen protons as they move back into alignment with the magnetic field, and
fall out of "phase" with each other. The actual process is much more complicated,
but is broken down into T1 relaxation and T2 decay. The MRI signal is then broken
down and spatially located to produce images.
A MRI is an image from a scanner that actually measures "magnetic resonance."
A strong magnetic field is placed across the tissue along the direction of
the bore of the magnet and is referred to as
The magnetic moments within the tissue will tend to align towards
although because of molecular vibrations and collisions, they will remain mostly
randomly distributed. After some time, the magnetic moments will reach an
equilibrium with a small amount favoring the direction of
While magnetic resonance can apply to a large number of different atoms (or even
molecules), in clinical MRI we are looking at the magnetic moments of the hydrogen
nuclei (protons), in the tissue. Hydrogen is used, once again, because it has a very
high abdundance in the body, among other characteristics.
Nuclei have an intrinsic quantum property called spin. When a magnetic field
is imposed on the nucleus of an atom, this nuclear spin will orient itself
according to this field, and so our z-axis can now be the direction of the
magnetic field, for convenience.
In classical physics, a rotating object possesses a property known as angular
momentum. Angular momentum is a form of inertia, reflecting the object's size,
shape, mass, and rotational velocity. It's typically represented as a vector (L)
pointing along the axis of rotation.
Spin is a quantum mechanical intrinsic property of elementary particles. It's very
difficult to imagine this property, and the notion of actual rotation can be
somewhat helpful. However, it's wise to separate this notion of a spinning particle
from the quantum mechanical property we call spin. Although spin is a form of angular
momentum, an elementary particle with spin doesn't mean it's rotating; particles with
spin simply have spin. For example, although an electron has mass, it's indicated
to be a "point particle", occupying no volume of space at all.
How can we imagine an electron rotating? Diagrams and explanations of spin and
its consequences can help, but we must be careful not to confuse quantum mechanical
(quantized angular momentum) and classical (rotating particle) explanations of MRI.
Atomic and subatomic particles posses a corresponding property known as spin or
spin angular momentum. Protons, neutrons, whole nuclei, and electrons all possess
spin and are often represented as tiny spinning balls. Although inaccurate, this
isn't a terribly bad way to think about spin as long as you don't take the analogy
Several key differences should be recognized:
The spin of a nucleus can be compared to a gyroscope.
||The particle is not actually spinning or rotating.
||Spin, like mass, is a fundamental property of nature
and doesn't arise from more basic mechanisms.
||Spin interacts with electromagnetic fields whereas
classic angular momentum (L) interacts with gravitational fields.
||The magnitude of spin is quantized, meaning that it
can only take on a limited set of discrete values.
In MRI, we are looking at the behavior of millions and millions of proton-magnets.
The net direction of their moments is referred to as the net magnetization vector M.
In equilibrium, since more protons are pointing along
M points in the direction of
This direction is typically referred to as the z-axis. There is no net polarization
in the x- or y-axes. However, the protons actually rotate round that axis (known
as precession), so that any one particular proton at any moment in time will be
pointing in some direction in the xy plane.
The simplest version of an MRI sequence involves a so-called 90° pulse. This
pulse of energy is exactly enough to rotate the protons 90°, so the net
magnetization is rotate from the z-axis, parallel to
into the xy-plane. At that point, Mz, the magnetization along
Note that you can put in less energy to give a rotation of less than 90 degrees,
which is often used in gradient-echo sequences. Alternatively, you may want to
employ a 180° pulse to 'flip' the M vector into the -z direction; this pulse
is twice as long (or strong) as the 90° pulse and is used for inversion
Nuclei precess around the magnetic field for essentially the same reasons
that tops or gyroscopes precess around a gravitational field:
||Both gyroscopes and nuclei possess angular momentum.
For the gyroscope, angular momentum results from a flywheel rotating
about its axis. For the nucleus, angular momentum results from an
intrinsic quantum property (spin).
||Momentum is also sometimes called inertia. Objects
possessing momentum have a tendency to maintain their motion unless
acted upon by an external force, like a speeding truck has a great
deal of (linear) momentum and can't easily be induced to change its
speed or direction. Angular momentum behaves similarly, conferring
on the nucleus or gyroscope a strong resistance to changing its
orientation or direction of rotation.
||Static gravitational and magnetic fields create a
torque or "twisting force" acting perpendicular to both the field
and the direction of the angular momentum. The gyroscope or nucleus
doesn't "tip over" but is instead deflected into a circular path
perpendicular to the field.
||The resultant circular motion is called precession.
Precession occurs at a specific frequency denoted either by ωo
(called the angular frequency, measured in radians/sec) or fo
(called the cyclic frequency, measured in cycles/sec or Hz). Since 2π radians = 360° = 1 cycle (revolution), angular
and cyclic frequencies can easily be converted by the equation:
ωo = 2 π fo
||The precession frequency of a gyroscope is a function
of the mass and shape of the wheel, the speed of wheel rotation,
and the strength of the gravitational field. The precession
frequency of a nucleus is proportional to the strength of the
and the gyromagnetic ratio (γ), a particle-specific
constant incorporating size, mass, and spin. This is embodied in the
famous Larmor relationship, given by the equation:
fo = γ * Bo
The spin is represented by the arrow. Notice the tip of the arrow precesses similar
to the top of the gyroscope. This spin allows absorption of a photon of frequency νL,
which is dependent on the strength of the magnetic field applied to the nulceus. The
applied magnetic field is the direction that the photons axis will align to when it's
Resonance and Larmor Frequency
Protons in a magnetic field have a microscopic magnetization and act like
tiny toy tops that wobble as they spin. The rate of the wobbling or precession
is the resonance or Larmor frequency (νL). In the magnetic field of an MRI scanner
at room temperature, there is approximately the same number of proton nuclei
aligned with the main magnetic field
as counter aligned. The aligned position is slightly favored, as the nucleus
is at a lower energy in this position. For every one-million nuclei, there
is about one extra aligned with the
field as opposed to the field. This results in a net or macroscopic magnetization
pointing in the direction of the main magnetic field. Exposure of individual
nuclei to RF radiation (B1 field) at the Larmor frequency causes
nuclei in the lower energy state to jump into the higher energy state.
In magnetic resonance, the Larmor frequency and is determined
by the gyromagnetic ratio γ of the particular magnetic moment (in this case, we
are looking at the hydrogen nucleus, and γ = 42.58 MHz/T):
νL = γ
Where νL is the frequency,
γ is the gyromagnetic ratio γ/(2π) in units of hertz per tesla (Hz/T),
is the magnetic field.
Now if a really high magnetic field is present, this precession is in the RF
portion of the spectrum. The atoms are placed in a non-uniform magnetic field.
The nuclei of these atoms will have a different Larmor frequency of spin as a
result of the equation above. As the RF electromagnetic radiation is sent
through the patient, the atomic nuclei in the body will absorb the energy.
This absorption of energy causes nuclei to change the direction of their spin.
You can intuitively understand this with the model shown above.
If you transmit energy into the system at the resonant frequency, you can
change turn protons away from pointing along
After some time, these protons will "relax" and give off energy to return
to the lower energy state. This energy will be given off at the same frequency,
and it's this signal that we measure.
On a macroscopic level, exposure of an object or person to RF radiation at the
Larmor frequency, causes the net magnetization to spiral away from the
field. In the rotating frame of reference, the net magnetization vector rotate
from a longitudinal position a distance proportional to the time length of the RF
pulse. After a certain length of time, the net magnetization vector rotates 90°
and lies in the transverse or x-y plane. It's in this position that the net
magnetization can be detected on MRI. The angle that the net magnetization vector
rotates is commonly called the 'flip' or 'tip' angle. At angles greater than or
less than 90° there will still be a small component of the magnetization that
will be in the x-y plane, and therefore be detected.
The recovery of longitudinal magnetization is called longitudinal or T1
relaxation and occurs exponentially with a time constant T1. The loss of phase
coherence in the transverse plane is called transverse or T2 relaxation. T1 is
thus associated with the enthalpy of the spin system, or the number of nuclei
with parallel versus anti-parallel spin. T2 on the other hand is associated
with the entropy of the system, or the number of nuclei in phase.
When the RF pulse is turned off, the transverse vector component
produces an oscillating magnetic field which induces a small current in the
receiver coil. This signal is called the free induction decay (FID).
The RF signal has a frequency equal to the unique resonant frequency of the
nuclei, the Larmor frequency. Once the RF signal is turned off, three basic
||Absorbed RF Energy is Emitted
Nuclei that have absorbed the radio frequency energy will not remain in
their excited state for a long time. They return to their initial state,
emitting a radio frequency signal to their surroundings. These signals are
picked up by detectors that are placed all around the body. The signals are
then compiled using Computed Tomography (CT) techniques into an image. The following
two nuclear processes are used to assemble a MRI.
When a nucleus absorbs a photon at its Larmor frequency, its spin state
changes. However the nucleus will not stay in this state. It will return
to its original state after emitting a photon. The time it takes to do this
is called the spin-lattice relaxation time, and is given by the constant T1.
Another type of relaxation used in MRI is spin-spin relaxation. Because the
magnetic field varies, the nuclei's Larmor frequency will vary. Since they
spin at different frequencies, the nuclei will gradually end up out of phase,
or spin at different times. MRIs use the loss of signal due to the phase-difference
between these nuclei to assist in creating the image.
The various types of MRI scans that are used (most commonly the T1-weighted scan
and the T2-weighted scan) measure this relaxation time differently. Computer
programs translate the data into cross-sectional pictures of the water in human
tissue. The layer of myelin that protects nerve-cell fibers is fatty and
therefore repels water. In the areas where the myelin has been damaged by MS,
the fat is stripped away. With the fat gone, the area holds more water, and
shows up on an MRI scan as either a bright white spot or a darkened area
depending on the type of scan that is used. Gadolinium (gd) can be injected
intravenously to further enhance the sensitivity of the T1-weighted MRI scan.
MRI image contrast is influenced by several characteristics of tissues and other
materials including: T1, T2 and T2* relaxation as well as spin density, susceptibility
effects and flow effects. Relaxation is the process in which spins release the energy
received from a RF pulse.
T1 and T2 relaxation rates affect the SNR in an image. Improvement in the SNR is seen
when the TR is increased significantly to about 3 to 5 T1 times. Changing the TR time
will also affect the T1 weighting of the image and the acquisition time. T1 weighting
occurs in a short TR spin echo sequence because of incomplete recovery of longitudinal
The T1 relaxation time, also known as the spin-lattice relaxation time, is a measure of how
quickly the net magnetization vector (NMV) recovers to its ground state in the direction of
The return of excited nuclei from the high energy state to the low energy or ground state
is associated with loss of energy to the surrounding nuclei. Nuclear magnetic resonance
was originally used to examine solids in the form of lattices, hence the name "spin-lattice"
relaxation. Two other forms of relaxation are the T2 relaxation time (spin-spin relaxation)
and T2* relaxation.
A MRI sequence produces signal from all the tissue in the scanner that's within
the transmit/receive coils. Without a means of spatial localization, all you would
get is a single number for the entire body. Drs. Lauterbur and Mansfield discovered
a way to separate signal from different parts of the body. In order to understand
how they did it, and how MR scanners work, you need to understand magnetic gradients.
While the main magnetic field of the scanner
can't change, additional smaller magnetic fields can be added with changing
electrical fields. If you remember physics classes, a changing electrical
field produces a magnetic field which is the basis of electromagnets. Each MR
scanner has 3 sets of spatial encoding electrical coils to produce magnetic
fields in the x, y, and z directions. These coils can be adjusted to produce
not a constant field but a gradient, in other words a magnetic field that
changes in strength depending on your position.
These magnetic fields are much weaker than
and vary linearly across the x, y, or z direction. They can even be turned on
in combinations to create a linear gradient in any arbitrary direction in space.
Now that we have gradients, we can separate different parts of anatomy by frequency.
We will start with the simplest type of separation: the imaging slice. Remember that
protons only exchange energy efficiently if the frequency of the energy matches their
precession frequency. Thus, the 90° and 180° pulses must be sent at the Larmor
frequency of the proton. We can combine this with gradients to select a slice of the
body to image.
By turning on the magnetic field gradient, the protons at each position in the body
experience a slightly different magnetic field - slightly more or less than
Thus, we get a gradient of precession frequencies along the body that differ. By
then altering the frequency of our 90° and 180° pulses, we will excite different
protons. The magnetic field gradients are close to the order of several hundredths
of a percent over a couple centimeters, so an extremely small frequency change will
move the position for the next image slice.
The scanner can select the particular slice to image by turning on the slice-select
gradient and then altering the frequency of the excitation pulses (90, 180, and any
inversion pulse) to match the frequency at the desired slice position. Protons not
in the slice will not get excited since their Larmor frequency will not match the
frequency of the pulse, thus they won't efficiently receive energy from the pulse.
In order to understand how to determine spatial localization within a slice (frequency
and phase encoding) we need to look at the Fourier transform. Fourier, a French
mathematician, realized that all signals, or oscillating functions, can be represented
as a combination of simple sine and cosine waves. Each sine and cosine corresponds to
a particular frequency in the signal. High frequencies correspond to rapidly changing
features, while low frequencies (including zero, a constant signal) correspond to
slowly changing features in the original signal. Fourier devised a method for transforming
a signal in time, such as music, into the set of frequencies that compose it, and this
is known as the Fourier transform.
The MRI Measurement consists of the following:
||Alignment of the protons in the body with the large
magnetic field of the MRI scanner. After a few seconds in the scanner
the protons in the patient are aligned with the magnetic field.
||A RF pulse is used to tip the protons
out of alignment with the scanner's magnetic field.
||Once out of alignment the magnetic moment of the hydrogen
protons can be measured as they rotate past measurement coils (loops
of wire) inducing an electrical current.
||The protons are pulled back into alignment with the main
magnetic field decreasing the measurable signal. The rate at which this
occurs determines the T1 properties of a tissue. If the protons in a
tissue return to alignment faster than all other tissues then this
tissue will be brightest on a T1-weighted scan.
||While rotating the protons gradually become out of phase
with one another decreasing the measurable signal. The rate at which
this dephasing occurs determines the T2 properties of a tissue. If the
protons in a tissue remain in phase with one another longer than all
other tissues then this tissue will be brightest on a T2-weighted scan.
||A proton density (PD) scan minimizes both T1 and T2
contrast to produce an image in which brightness is determined by the
number of protons in a voxel.
The contrast on the MRI can be manipulated by changing the pulse sequence
parameters. A pulse sequence sets the specific number, strength, and timing
of the RF and gradient pulses. The two most important parameters are the
TR and the TE. The TR is the time between consecutive 90° RF pulse. The TE
is the time between the initial 90° RF pulse and the echo.
Two controls determine tissue contrast: TR (repetition time) and TE (echo time) of
||Repetition time (TR) is the time from the application
of an excitation pulse to the application of the next pulse or the
time between successive RF pulses. A long repetition time allows
the protons in all of the tissues to relax back into alignment
with the main magnetic field. A short repetition time will result
in the protons from some tissues not having fully relaxed back
into alignment before the next measurement is made decreasing
the signal from this tissue. It determines how much longitudinal
magnetization recovers between each pulse. It's measured in
||Echo time (TE) is the time between the application
of RF excitation pulse and the peak of the signal induced in the
coil. A long echo time results in reduced signal in tissues like
white matter and gray matter since the protons are more likely to
become out of phase. Protons in a fluid will remain in phase for
a longer time since they are not constrained by structures such
as axons and neurons. A short echo time reduces the amount of
dephasing that can occur in tissue like white matter and gray
matter. It's measured in milliseconds.