Subsections

• 4.2.1 Magnetic Resonance (MR)
• 4.2.2 Magnetic Resonance Imaging (MRI)
• 4.2.3 Functional MRI
  • 4.2.3.1 Early Brain Research
  • 4.2.3.2 Functional Neuroimaging
  • 4.2.3.3 Functional MRI

4.2 Background

4.2.1 Magnetic Resonance (MR)

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

$$\notag \omega_{0} = \gamma B_{0}$$

where $\omega_{0}$ is the Larmor frequency, $\gamma$ is the gyromagnetic ratio, and $B_{0}$ is the strength of the applied magnetic field.

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 $42\,$MHz per Tesla. A Tesla is a measure of the strength of the magnetic field ($B_{0}$) with one Tesla equal to $10{,}000\,$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 $3\,$Tesla. The resulting Larmor frequency is about $126\,$MHz; for comparison a kitchen microwave oven operates at about $2450\,$MHz.

Some values of the constants $\gamma$ for other atomic species can be found at http://www.stat.cmu.edu$/\!\sim$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 $180\,$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 $B_{0}$ field at the Larmor frequency ( $\omega_{0}$). 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]).

4.2.2 Magnetic Resonance Imaging (MRI)

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.

Figure 4.2: This figure (redrawn from [31]) is a schematic showing how slice selection takes place

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 $xy$-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 ($z$-direction). In this manner, each $xy$-slice of the tissue is subjected to a slightly different magnetic field strength. If the linear gradient at $z$ is equal to $azB_{1}+B_{0}$, then the Larmor frequency at $z=1$ becomes $\omega_{1}$, where:

$$\notag \omega_{1} = \gamma (aB_{1} + B_{0})\,.$$

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 $\omega_{1}$, only slices of interest will be excited and imaged. This same principle can be used to define spatial locations in the $xy$ 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 ($T_{1}$), and transverse relaxation time ($T_{2}$). The amount of time that it takes for the longitudinal magnetization of the tissue to return to $63\,{\%}$ of its original value after an rf pulse is applied is denoted $T_1$, and the time that it takes for the transverse magnetization to return to $37\,{\%}$ of its original value after the applied rf pulse is denoted $T_2$.

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 $T_1$ and $T_2$ properties. This process is also known as weighting or contrasting, and images are usually $T_1$-weighted, $T_2$-weighted, or proton density weighted. For example, short TRs and TEs lead to $T_1$ weighted images, because at this time the differences due to the $T_1$ tissue properties will be the most apparent. In $T_1$ weighted images, the intensity of bone tissue is typically bright while fluids are dark.

On the other hand, to achieve the best contrast using $T_2$ properties, a long $T_R$ and a long $T_E$ are used. In $T_2$ weighted images, bone tissue is dark and fluid areas are light. Proton density weighting is achieved by using a long $T_R$ and a short $T_E$. 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].

4.2.3 Functional MRI

4.2.3.1 Early Brain Research

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.

4.2.3.2 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 $100{,}000$ 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]).

4.2.3.3 Functional MRI

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].

Figure 4.3: Model of brain activity and fMRI data

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 $1\,$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.