Atomic nuclei spin like gyroscopes. When placed into a magnetic field, atomic nuclei that are affected by magnetism (those having an odd number of protons or neutrons or both) align their axis of rotation with the magnetic field. Like a gyroscope the axis of rotation itself rotates; this rotation is called precession. Each nucleus precesses within the magnetic field. The frequency of this precession, the Larmor frequency, is proportional to the strength of the magnetic field, with the constant of proportionality being determined by the gyromagnetic ratio of the atomic species. The relationship can be described by the Larmor equation
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Hydrogen is currently the most widely used element for MR imaging
because of its abundance in biological tissue and the strength of the
emitted signal. Hydrogen atoms have a gyromagnetic ratio of
approximately
MHz per Tesla. A Tesla is
a measure of the strength of the magnetic field (
) with one
Tesla equal to
gauss. For reference, one-half gauss
is roughly the strength of the earth's magnetic field. An MR scanner
that is used for functional imaging has a typical field strength of
Tesla. The resulting Larmor frequency is about
MHz;
for comparison a kitchen microwave oven operates at about
MHz.
Some values of the constants for other atomic species can be
found at
http://www.stat.cmu.edu
fiasco/index.php?ref=reference/ref_constants.shtml
As the nuclei of the hydrogen atoms precess within the magnetic field,
the atoms will either line up along the field or against it (that is,
the atoms will line up at either 0 or
degrees). The
strength of the magnetic field and the energy state of the system
affect the number of atoms that line up accordingly. Then, while the
atoms precess in a steady-state fashion within the magnetic field,
a pulse of energy is injected into the system in the form of
a transient radio-frequency (rf) pulse perpendicular to the
field at the Larmor frequency (
). This rf pulse excites
the atoms at their resonant frequency, causing them to tilt out of
alignment with the magnetic field.
As these excited atoms return to equilibrium within the magnetic field they emit rf energy which is collected by an antenna and receiver. Their return to steady-state is known as relaxation, and the signal that the atoms emit is known as the free-induction decay (FID) signal. The FID signal reflects the distribution of hydrogen atoms in the tissue and is used to construct images (see, e.g., [3]).
As described, the basic theory of MR can be used to create images based on the distribution of hydrogen atoms or protons in the tissue sample. Other types of atoms can also be imaged. In these cases, the applied rf pulse must be applied at the Larmor frequency of the atoms of interest in the tissue sample.
In order to create images using MR, an FID signal must be encoded for each tissue dimension, and certain considerations must be made to recognize spatial information in the tissue sample from which the FID signals are being recorded. As outlined above, the resonant frequency at which the atoms must be excited to flip them is dependent on the magnetic field strength. Thus, by adjusting the magnetic field strength at certain locations in the tissue and sending rf pulses at the corresponding resonant frequency, only atoms at the location of interest will be excited. In this manner, spatial information can be resolved.
To aid in the understanding of this principle, consider slice
selection through a sample of tissue. As shown in Fig. 4.2,
the object under consideration (in this case a person) is placed with
the -slice axis perpendicular to the magnetic field. A linear
magnetic field gradient is then applied in a direction parallel to the
bore of the magnet (
-direction). In this manner, each
-slice of the
tissue is subjected to a slightly different magnetic field strength.
If the linear gradient at
is equal to
, then the
Larmor frequency at
becomes
, where:
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The magnetic field strength along each slice of the tissue is now
slightly different, so the resonant frequency for each slice of the
tissue will be slightly different. By adjusting the rf pulse to
correspond to
, only slices of interest will be excited
and imaged. This same principle can be used to define spatial
locations in the
plane as well. The interested reader should refer,
for example, to Buxton's 2002 book Introduction to Functional
Magnetic Resonance Imaging: Principles & Techniques.
The signal intensity from the tissue is a function of the density of
hydrogen atoms or protons in the tissue. The more protons in the
tissue, the greater the FID signal, and the higher the intensity
value. Because different types of tissues vary in their proton
density, tissue contrast can be achieved in the
images. Contrast also depends on the tissue specific parameters,
longitudinal relaxation time (), and transverse relaxation time
(
). The amount of time that it takes for the longitudinal
magnetization of the tissue to return to
of its original
value after an rf pulse is applied is denoted
, and the time that
it takes for the transverse magnetization to return to
of
its original value after the applied rf pulse is denoted
.
The imaging parameters of TR (time of repetition of the rf pulse) and
TE (time of echo before FID signal is measured) can be varied to
achieve the maximum contrast for the tissues of interest by
considering their and
properties. This process is also
known as weighting or contrasting, and images are usually
-weighted,
-weighted, or proton density weighted. For
example, short TRs and TEs lead to
weighted images, because at
this time the differences due to the
tissue properties will be
the most apparent. In
weighted images, the intensity of bone
tissue is typically bright while fluids are dark.
On the other hand, to achieve the best contrast using
properties, a long
and a long
are used. In
weighted
images, bone tissue is dark and fluid areas are light. Proton density
weighting is achieved by using a long
and a short
. With
this type of weighting, areas that have the highest proton density are
the brightest. These areas would include the cerebral
spinal fluid (CSF) and gray matter. Again, see [3] for details; a statistical approach is given in
[18].
The mysteries of the human brain have perplexed researchers for many centuries. Early ideas about brain functioning date at least as far back as the second century to Galen (and even earlier), who associated imagination, intellect, and memory with brain substance. The notion that the brain consisted of functionally discrete areas did not become an accepted idea until the nineteenth century with the work of Franz Joseph Gall ([12]). Ensuing research involved examining the relationships between the location of brain lesions and deficits and/or changes in behavior as a way to attribute brain function to structure. Although the technique was effective, this method for studying the brain was not without limitations. Since that time, however, the field of neuroscience has grown because of the development of new methods to explore the human brain in its living working state. These new techniques have been given the general term functional neuroimaging.
Functional neuroimaging is the term applied to techniques that can map
the activity of the living working brain in space and time.
Non-invasive approaches to this mapping have included
electrophysiological measurements and metabolic measurements.
Techniques to measure the electrophysiological signals include the
electroencephalogram (EEG) and the
magnetoencephalogram (MEG) (National
Research Council, 1992). These methods are thought to record
(a weighted integral of) the actual neural activity that is taking
place in the brain. Although both EEG and MEG have excellent temporal
resolution, in their most common form the measured output signals are
an integration of activity from many possible unknown sources.
Furthermore, for EEGs these integrated signals are only realized after
being filtered through layers of blood vessels, fat, and bone. On the
other hand, MEG generally only measures the component of the magnetic
field which is perpendicular to the surface of the skull. Both
methods typically record only a few hundred different locations;
a typical functional MRI study measures the signal at
locations or so. Thus, the spatial resolution of both EEG and MEG is
quite poor. Source localization is a research area devoted to trying
to map the locations at which these signals originate, but this has
proven to be a very difficult task.
Functional neuroimaging measurements also include Positron Emission Tomography (PET) and fMRI. Both of these techniques have good spatial resolution, but unlike EEG and MEG they record responses to changes in blood flow rather than the direct neural activity. Because of this, these techniques have relatively poor temporal resolution.
PET imaging is carried out by labeling molecules of compounds of interest with positron-emitting isotopes. Isotopes that are often used include Carbon-11, Nitrogen-13, or Oxygen-15. These labeled modules are termed ''probes'' or ''tracers''. The tracers are distributed in the brain according to their delivery, uptake, metabolism, and excretion properties. As these isotopes decay they emit a positron and a neutrino. The neutrino cannot be detected, but each positron collides with an electron and is annihilated. The annihilation converts the electron and positron from mass into energy in the form of gamma rays. These gamma rays are then detected by the scanner. PET can provide excellent measures of metabolic activity of the brain under conditions of normal and abnormal functioning and has therefore been a highly useful tool in studying brain activity. However, one of the main disadvantages of PET is that it requires the injection of ionizing radiation thereby limiting its use for human subject populations ([4]).
Functional MRI uses the same principles as MRI, but it is based on the idea that the magnetic state of the hemoglobin in the bloodstream is dependent on whether or not oxygen is bound to it. Deoxygenated blood is paramagnetic, meaning that the unpaired heme groups cause it to have more magnetic susceptibility than it does when oxygen is attached to the heme groups. In fact, the magnetic susceptibility of blood has been shown to vary linearly with blood oxygenation; see, [45], [3], [47], or [50].
When neurons in the brain are used, their metabolic demands increase. This begins with an increase in local glucose consumption and leads to an increase in local cerebral blood flow. However, for reasons that are unclear, the increase in cerebral blood flow exceeds the increase in metabolic consumption of local oxygen. Therefore the ratio of oxygenated blood to deoxygenated blood increases in the local blood vessels. The change in this ratio of oxygenated blood to deoxygenated blood leads to changes in the local MR signal. Modulations in the MR signal due to this phenomenon can be detected by the scanner and are known as Blood Oxygen Level Dependent (BOLD) contrast. BOLD contrast is currently the main basis of fMRI; see, e.g., [48], [34], [39], [3], or [47].
Several informational limitations are imposed by fMRI that should be considered when carrying out a neuroimaging study. Leading these is the fact that fMRI is an indirect measure of brain activity, and its exact physiological mechanism is not known. A model of the interface between actual brain activity and the fMRI signal is shown in Fig. 4.3. Also, the measured activity obtained with fMRI can include many types of local brain cells because the activation that is measured is essentially a combination of all the ''brain activity'' in the area. Information is thus blurred during fMRI, since the resolution is based on the ''smallest measurable vascular unit.'' Finally, as mentioned earlier, fMRI has poor temporal resolution; see, e.g., [48].
In spite of these limitations, fMRI has many advantages over
previously used methods for studying the brain. fMRI has much better
spatial resolution than EEG or MEG. In fact, although the activity is
lumped into small regions, these regions can provide accuracy in the
range of
mm or so. Next, and perhaps most importantly, fMRI does not
require the use of ionizing radiation. This allows it to be used
experimentally for many different subject types and under many
different types of situations. Other benefits include the fact that
the data can be collected fairly easily, and analysis tools are
becoming more readily available as the field grows.