**Appendix A. Setting Up an fMRI Scanning Session**

\[*This will be adapted from my handout in the June 1998 workshop*.\]

**Appendix B. Safety Issues in MRI**

\[*Consult with Tom Prieto*\]

**Appendix C. Glossary**

Some of these terms are not used in this book, but are defined here to
help in reading the fMRI literature.

*[Acoustic Noise]{.underline}*

When electrical current flows through a wire that is embedded in a
magnetic field, there is a force on the wire that is perpendicular to
both the magnetic field and to the direction of the current flow. This
force tends to move the wire and whatever it is attached to. If the
current flow is reversed, the force will point in the opposite
direction. The currents in gradient coils are large (about 100 Amperes)
and they are embedded in large magnetic fields. In echo-planar imaging
(EPI), the gradient currents are switched back and forth in direction
about 1000 times per second. This produces a large alternating
in-and-out force on the gradient coil structure, right at typical
acoustic frequencies. The resulting vibration of the gradient coil is
transmitted to the air and is audible, often painfully so.

*[Acronyms]{.underline}*

MRI physicists love acronyms. It seems that an imaging method isn't
complete until a funny- or profound-sounding acronym has been attached
to it. Some examples:

DUFIS Dante UltraFast Imaging Sequence

RAGE Rapid Acquisition with Gradient Echoes

FLAIR FLuid Attenuated Inversion Recovery

*[Adiabatic RF Pulse]{.underline}*

This type of RF excitation pulse is used when precise slice selection is
important. They work particularly well when the B~1~ field is not
uniform in intensity. The technique requires a longer time (20--30 ms,
vs. 2--4 ms for normal RF pulses), which means that more radio­frequency
energy is deposited into the subject with each transmission. This effect
means that the repetition time (TR) with adiabatic pulses must be longer
to keep the total SAR at safe levels. For this reason, adiabatic pulses
are only used when necessary. One application is to slice selective 180°
(inversion) pulses, which are hard to design accurately using simpler
methods.

*[ADC \[Apparent Diffusion Coefficient\]]{.underline}*

Water molecules diffuse amongst themselves due to thermal motion. The
self-diffusion coefficient (symbol: *D*) measures the rapidity of this
mixing. *D* can be measured using MRI, since H­~2~O molecules that move
will carry their protons into regions with different magnetic field
strengths, and so cause greater signal dephasing. However, what is
really measured is the amount of H­~2~O molecular mixing averaged over a
voxel volume. Such mixing also occurs due to microscopic flows (as in
capillaries), which increases the measured value of *D* over its true
value. For this reason, the *D* that is measured with MRI in tissue is
usually called the apparent diffusion coefficient (ADC).

In a layered medium, water molecules can diffuse more easily in some
directions than in others. In the brain, water diffuses more easily down
myelinated axonal fiber tracts than across them. This preferential
diffusion can be detected using MRI, and promises to provide a method to
trace white matter tracts noninvasively *in vivo*. Diffusion imaging has
also proved useful in assessing cerebral damage due to stroke.

*[ADC \[Analog to Digital Converter\]]{.underline}*

This device converts the voltage detected in the RF receive coil to
numbers for storage in a computer. One number is measured in each
sampling interval (usually 1--10 μs) for the duration of the readout
window; the number of bits used to measure the voltage is called the
sampling depth of the converter (usually 12--16 bits). This collection
of numbers through time is then broken into frequency and phase
components to reconstruct the actual image.

*[Aliasing]{.underline}*

Time series data is acquired in discrete steps, almost always uniformly
spaced in time. The underlying processes are occurring in continuous
time, being made up of components at all frequencies. Discretely sampled
data cannot distinguish between all these frequency components. Denote
the sampling time step by ∆*t*. Then continuous time frequencies *f* and
*f*+(∆*t*)^−1^ cannot be distinguished in the sampled data; for example,
cos(0⋅*t*) and cos(2π*t*/∆*t*) are identical at all times *t*=*n*⋅∆*t*
for integer* n* (both are equal to 1 for all *n*). This confusion of
frequencies is called aliasing. Aliasing is the source of wraparound
when the image FOV is smaller than the object being scanned. Aliasing
also makes it difficult to separate high frequency heartbeat-related NMR
signal changes from low frequency activation-related NMR signal changes,
since the ∆*t* for fMRI tends to be several seconds (e.g., ∆*t*=4 s
means that frequency aliasing occurs for frequencies above 0.25 Hz;
heartbeat-related signals at 1.0--1.1 Hz will be aliased with signals in
the range 0.0--0.1 Hz, which is the typical low frequency range of fMRI
measurable activations).

*[Amplifiers]{.underline}*

An MR scanner contains many things called amplifiers. The gradient
amplifiers produce the electrical current to run through the gradient
coils (about 100 Amperes). The RF amplifier produces the radiofrequency
waves transmitted to the RF coil, used to excite the magnetization. The
RF receiver contains several amplifiers to boost the received NMR signal
up to a level where it can be detected by the analog to digital
converter.

It is important to understand that the actual numbers in the MRI voxels
do not represent an absolute measurement. The entire RF receiver
amplification system is designed to boost the NMR signal to a standard
voltage range for digitization. This goal is accomplished by changing
the receive amplifier gain to get the signal to the right level. The
amplifier gain may be set by the scanner operator, or may be set
automatically by the scanner software at the start of the scanning
session. In either case, it is unlikely to be the same on two different
days. Even if the amplifier gain were set consistently, the strength of
the NMR RF signal is somewhat dependent on the exact position of the
subject's head and body relative to the RF receive coil, even for whole
body coils. As a result of these complications, the BOLD effect is
usually quoted in "percent signal change", indicating that the voxel
values rise 3% (say) above the resting baseline during an active task.
Analyzing the results relative to the baseline removes the issue of the
inter-session variability in NMR signal amplification.

*[Angiography \[MRA\]]{.underline}*

This term refers to a set of MRI techniques that are designed to allow
detection of blood vessels. All such techniques rely on changes that
occur in the NMR signal when the H­~2~O protons are flowing rather than
standing still (or just diffusing). Vessels smaller than about 1 mm in
diameter cannot be detected reliably with MRA techniques. The term
"venography" is sometimes used when MRA methods are applied to detection
of veins.

*[Arterial Spin Labeling \[ASL\]]{.underline}*

About 70% of the H­~2~O molecules that enter a cerebral capillary diffuse
through tiny pores and end up in the brain parenchyma (water in the
brain diffuses back to replace the water in the capillaries). If the
water in the base of the brain were labeled, then the blood in the major
arteries would flow up to the capillaries and most of it would exchange
to the parenchyma. Detection of this label would provide a measure of
the amount of tissue perfusion, since there is relatively little water
"leakage" from larger vessels in the brain. Positron emission tomography
(PET) works by using ^15^O labeled water as a radioactive tracer. ASL is
an MRI technique where magnetization inversion is used to provide the
labels; a slice-selective RF 180° pulse at the base of the brain flips
the magnetization over. When these protons reach the parenchyma, their
magnetization will be different from those protons that were not
inverted. The resulting difference in the NMR signal can be used to
estimate the amount of water that was transported from the base of the
brain to the cerebral tissue.

There is a number of different imaging methods used for ASL, including:
EPISTAR \[**???**\], FAIR \[**???**\], and QUIPPS \[**???**\]. The main
drawback to all ASL techniques is the relatively small signal change
that survives after all the magnetization processing that takes place.

*[Artifact]{.underline}*

This is a catch-all term used by MRI physicists to denote anything that
corrupts or distorts an image. Anything that affects the static magnetic
field, the RF magnetic field, or the subject in the scanner is likely to
affect the image. In some cases, artifacts can be used to measure
interesting physiological or physical properties. For example, the
self-diffusion coefficient *D* of water increases with temperature; this
artifact is one way to map temperature *in vivo* using MRI (it's
accurate to about 1° C).

*[Asymmetric Spin Echo (ASE)]{.underline}*---see Gradient Echo

*[Axial]{.underline}*

An axial slice is a horizontal section; it is as if one were looking at
the brain from the top. It is important to realize that images are often
displayed with the subject's left on the right side of the image---this
is the radiological convention.

![](media/image1.png)

Figure C.1. [Left]{.underline}: axial slice. [Middle]{.underline}:
coronal slice. [Right]{.underline}: sagittal slice.

These images are extracted from a T1-weighted SPGR 3D volume acquired at
1.5 Tesla.

*[B~0~]{.underline}*

This is the mathematical symbol for the main magnetic field; the units
are Tesla or Gauss (typical values for fMRI are 1.5--3 Tesla; a few 4
and 7 Tesla systems also are in use).

*[B~1~]{.underline}*

This is the mathematical symbol for the radiofrequency magnetic field
that is used to turn the magnetization away from being aligned in the
direction of B~0~. Typical values of B~1~ are 10^-5^ Tesla. B~1~ is
usually turned on for only a few ms at a time.

*[Balloon Model]{.underline}*

This is a mathematical-physiological model that attempts to explain
various features of the MRI-measurable hemodynamic response to neural
stimulation (see Fig. 3.3). Its salient feature is the explanation of
the post-stimulus undershoot as a pooling of deoxygenated blood in
venules that expanded during the stimulus (when the blood flow
increased), and that take some extra time to deflate to their resting
size after the stimulus and flow increase end \[**??? Buxton**\].

*[Bandwidth]{.underline}*

The mathematical concept of a pure single-frequency signal is
unachievable in the physical world; all real signals can be thought of
as a sum of single-frequency signals that are at different frequencies.
The bandwidth of a real signal expresses the range of frequencies that
are included in the signal. For example, a standard television signal in
the USA has a bandwidth of 4.3 MHz; that is, the smallest frequency
present in the signal is 4.3×10^6^ Hz smaller than the largest
frequency. The bandwidth of the NMR signal received in human brain
imaging usually ranges from 60 KHz to 250 KHz---this bandwidth is
determined by the gradient strength and the size of the subject.

*[BOLD \[Blood Oxygenation Level Dependent\]]{.underline}*

This acronym refers to the discovery that the NMR signal strength
received from a voxel containing blood depends on the amount of oxygen
in the blood \[**??? Thulborn, Ogawa**\]. This effect is the foundation
of fMRI, since blood oxygen level increases locally during neural
activity. The cause of the BOLD effect is the change in microscopic
magnetic field randomness as the iron atoms in blood hemoglobin
molecules bind to oxygen (decreasing magnetic field randomness, since
the susceptibility of oxyhemoglobin is the same as other soft tissue) or
become unbound from oxygen (increasing magnetic field randomness, since
the susceptibility of deoxyhemoglobin is different from other soft
tissue)---see Fig. 3.1.

*[Bore]{.underline}*

This term refers to the diameter of the main field magnet. For
whole-body human imaging, the bore size is usually 90--100 cm. The
actual usable space inside the magnet is usually smaller due to the
extra equipment inside the main magnet cylinder (i.e., shim, gradient,
and RF coils built into the walls).

*[Carrier Frequency]{.underline}*

This is the central frequency present in any real signal. In MRI, the
carrier frequency for the NMR signal transmitted to and received from
the protons is equal to 42.54 MHz times B~0~; at the widely used field
strength of 1.5 Tesla, this is about the same frequency as television
channel 4.

*[Chemical Shift]{.underline}*

The frequency at which a particular proton precesses is determined by
the magnetic field strength *at that proton*. The electrons surrounding
the protons may cause the externally imposed magnetic field (B~0~) to be
slightly altered at the atomic nucleus. The amount of this alteration
depends on the configuration of the electrons, and is different for
different hydrogen-containing chemical compounds. For example, the
methyl CH~3~ groups in fat molecules "see" a different magnetic field
than the H~2~O molecules of water, and so resonate at a slightly
different frequency. In NMR spectroscopy and spectroscopic imaging, it
is possible to use the chemical shift to detect the concentrations of
several different molecular species. (The chemical shift in frequency is
larger when B~0~ is bigger, which is one reason for the drive to ever
increasing magnetic fields.)

*[CNR \[Contrast to Noise Ratio\]]{.underline}*---see SNR

*[Coherence]{.underline}*

When dealing with several time-varying phenomena at the same time
(e.g., multiple measurements), the different time series are said to be
coherent if knowledge of one phenomenon at a given time helps to predict
the others at that time. This is a similar concept to correlation, but
coherence can also be calculated as a function of frequency. For
example, Biswal has shown that resting-state fMRI time series data from
the left and right primary motor cortex areas are coherent at low
frequencies (\< 0.1 Hz) and incoherent at high frequencies \[**???
Biswal**\].

*[Coil]{.underline}*

Magnetic fields are created by electric currents in coils of wire, and
are detected by the currents they generate in coils of wire. Gradient
coils are arrangements of wire designed so that when current is applied,
the resulting magnetic field strength varies spatially---in the *x-*,
*y*-, and/or *z*-directions. RF coils are used to transmit and receive
radiofrequency magnetic fields (exciting magnetization and detecting it,
respectively). For practical reasons, the RF coil must be inside the
gradient coil, since transmitting radio waves through a metal structure
to get to the subject can cause serious electrical problems. The RF coil
can also be thought of as an antenna that is tuned to operate at the
resonant frequency of the magnetization. In some situations, separate RF
coils are used for the transmitter and receiver.

Coils can be built into the bore of the scanner, so that they are not
readily visible. This type of coil is called a body coil, since the
subject's entire body goes inside them. Coils can also be smaller and
removable, and designed to fit over just a portion of the body. This
type of coil is called a local coil. If a local gradient coil is used,
then a local RF coil is needed for reasons explained above; however,
a local RF coil can be operated with the body gradient coil, if desired.

*[Complex Number]{.underline}*

A complex number is defined as any number of the form
$a + b \cdot \sqrt{- 1}$, where *a* and *b* are standard real numbers.
In the mathematical analysis of MRI physics, the separately measured I
and Q components of the raw NMR signal are usually combined into one
complex number, with *a*=I and *b*=Q. The reconstructed MR images
contain a complex number in each voxel, but the final output is usually
just the magnitude in each voxel: $\sqrt{a^{2} + b^{2}}$. Some imaging
methods also use the phase of the image values: $\text{tan}^{- 1}(b/a)$;
the phase is used in some forms of angiographic imaging and in measuring
the magnetic field.

*[Contrast]{.underline}*

This term expresses the concept of a difference in NMR signal strength
between two different types of tissue, or between the same tissue in two
different conditions. The flexibility of MRI allows different physical
and physiological properties to be enhanced with different imaging
methods. Some examples of important contrast are:

T1 contrast Distinguishes gray and white matter in the brain (e.g., as
in Fig. C.1)

T2\* contrast Via the BOLD effect, distinguishes more and less neurally
active tissue

Flow contrast Used in MR angiography to emphasize moving tissue,
especially blood

*[Contrast Agent]{.underline}*

This is a chemical compound given to the patient in order to enhance the
NMR signal differences between tissue types. These agents work by
incorporating atoms that have a large intrinsic magnetic field
(e.g., iron, gadolinium, dysprosium). Water molecules near these agents
will experience a shift in the magnetic field, which will affect the T1,
T2, and/or T2\* relaxation time of the protons' magnetization. (One can
think of deoxyhemoglobin as an intrinsic contrast agent; hence the BOLD
effect.) Although the first fMRI experiment was done with a external
contrast agent \[**??? Belliveau**\], this type of experiment has not
been repeated often in humans. Contrast agents are mostly used for
detection of tumor and other pathologies; for these purposes, they are
used millions of times per year.

*[Convolution]{.underline}*

A relationship between functions of one of the forms below is called a
convolution:

$$\begin{array}{r}
r(t) = \int_{}^{}{h(t - q) \cdot s(q)\text{dq}\text{  or  }\int_{}^{}{h(t - q) \cdot s(q)\text{dq}}} \\
r(t) = \sum_{q = 0}^{T}{h(t - q)} \cdot s(q)\text{  or  }\sum_{q = t}^{T}{h(t - q)} \cdot s(q)\ \text{.}
\end{array}$$

*r*(*t*) is said to be the convolution of *h*(*t*) with *s*(*t*). This
type of relationship is often used to model the response *r*(*t*) of a
system to input stimuli *s*(*t*); the function *h*(*t*) is called the
system's impulse response function, and represents the output of the
system to a brief stimulus occurring at time *t*=0. If *r*(*t*) is
measured and *s*(*t*) is known, then the process of solving for *h*(*t*)
is called "deconvolution". For many systems, this is quite a sensitive
operation; one whose results can be strongly contaminated by noise or
slight changes in assumptions.

*[Coronal]{.underline}*

A coronal slice is a vertical section; it is as if one were looking at
the brain from the subject's front (see Fig. C.1).

*[Correlation Method]{.underline}*

This is the name of a widely-used method for detecting functional
activation from fMRI time series data. The technique is to find the
correlation coefficient between a user-specified time series that is
presumed to model the time course of neural response to the known
stimulus time course, and the NMR data time series from each voxel.
Voxels with a large correlation coefficient are presumed to be "active".
(See chapter 7 for more details.)

*[Crushers, Killers, and Spoilers]{.underline}*

When an RF pulse is transmitted into the subject, the usual intention is
create transverse magnetization in a certain slice and that has certain
properties. If there is any pre-existing transverse magnetization, it
will interfere with these goals. Crushers (etc.) are large bursts of
current applied to the gradient coils whose goal is to dephase any
existing transverse magnetization so that it won't interfere with the
transverse magnetization that is about to be created by a new RF pulse.

*[Degree of Freedom (DOF)]{.underline}*

A statistical term that (roughly speaking) measures the number of
independent random samples in the analysis of a set of measurements. If
the noise in each measurement is uncorrelated with all others ("white
noise"), then the number of degrees of freedom is the number of
measurements minus the number of parameters being fit in the analysis.
Given a fixed level of a statistical parameter (e.g., a *t*-statistic or
a correlation coefficient), the statistical significance of the
parameter becomes higher---the *p*-value decreases---as the number of
degrees of freedom increases. When the measurement noise is not white,
the number of degrees of freedom is sometimes adjusted (reduced) to make
the calculations of statistical significance be more correct.

*[Dephasing \[Destructive Interference\]]{.underline}*

The signal detected in the RF coil is the sum of all the signals emitted
from magnetized protons all over the brain. If these component signals
are positively coherent, then they will add up to a large value. If
these component signals are random, then they will tend to cancel out,
since about as many will be positive as are negative. At the moment
transverse magnetization is created, all its components are positively
coherent (in-phase). Since different regions of the brain will have
slightly different magnetic fields, their transverse magnetizations will
precess at slightly different frequencies. When enough time has passed,
all the component signals will be incoherent (out-of-phase) and no NMR
signal will be detectable (see Fig. 2.7). This process can be
accelerated by the application of crusher gradient fields, which will
enlarge the inter-regional magnetic field differences.

*[Diamagnetic]{.underline}*---see Susceptibility

*[Diffusion]{.underline}*

This term describes the concept of molecular motion due to random
thermal agitation (vs. motion caused by flow or other non-random
collective movements). In MRI, the most important diffusing substance is
water, which diffuses easily due to its low molecular weight.

*[Echo]{.underline}*---see Gradient Echo and Spin Echo

*[Eddy Current]{.underline}*

The magnetic fields from the gradient coil not only penetrate inwards to
include the subject, but also propagate outward. As they change in time,
these external gradient fields induce extra currents in the
superconducting coils of the main magnet (or in other nearby conductive
surfaces)---these are referred to as eddy currents. Eddy currents in
turn generate changes in the magnetic field back in the subject. These
changes are unwanted and interfere with the imaging process,
particularly with high speed imaging methods such as echo-planar imaging
(EPI), where the gradient fields are changing rapidly and continually.
The effects of eddy currents are smaller in large bore magnets, since
the distance between the gradient coil and the main coil is farther.
Another technique to reduce the effect of eddy currents is to build an
"anti-coil" (or "active shield") outside the gradient coil. This
anti-coil operates in parallel with the gradient coil and is intended to
produce an approximately opposite magnetic field at the main coil. The
main drawback to this active shielding approach is that the opposite
field also penetrates the subject, tending to cancel some of the
gradients needed for imaging.

*[EPI \[Echo-Planar Imaging\]]{.underline}*

This term describes a very fast method for acquiring NMR image data:
40--100 ms per 2D image. EPI requires a gradient power supply and
gradient coil combination that can be switched from positive to negative
currents repeatedly and very rapidly (unlike most other imaging
methods). Until relatively recently, this type of hardware was uncommon,
but since the advent of fMRI, EPI capabilities have become more usual
(but can still be expensive, particularly with whole body gradient
coils). EPI is the most widely used acquisition technique in fMRI due to
its high speed, which makes it possible to gather a whole brain volume
every 2--4 seconds.

*[Ernst Angle]{.underline}*

After an RF pulse is applied, the pre-existing longitudinal
magnetization is partly converted into transverse magnetization (the
detectable component). If the flip angle is θ, then the fraction that
remains as longitudinal magnetization is cos(θ) and the fraction that is
converted to transverse magnetization is sin(θ). If θ = 90°, then all
the longitudinal magnetization is converted into transverse
magnetization. One might think that this would give rise to the largest
possible NMR signal; however, this conclusion ignores the fact that many
RF excitations will be used and the important thing is to have a large
average signal over each separate readout. Suppose that the RF
excitations hit a particular slice very rapidly (i.e., TR is short).
Then the longitudinal magnetization that is the source of the transverse
magnetization will have little time to recover (T1 relaxation). If
θ = 90°, the result is that there will be little NMR signal to measure
at the second and subsequent readouts. Paradoxically, a smaller θ can
actually result in a larger signal in the later readouts, since each
time we are saving some longitudinal magnetization for later use. The
Ernst angle is the optimum flip angle for a given TR, in that it
produces the largest NMR signal over many RF pulse/readout combinations:
θ~Ernst~ = cos^-1^(*e*^−TR/T1^).

*[Excitation]{.underline}*

If left alone long enough (about 10 seconds), all the magnetization
created by the main field will be aligned with the direction of the main
field. In this condition (pure longitudinal magnetization), there is no
precession of the magnetization, and there is no NMR signal that can be
detected. The process of turning longitudinal magnetization to point at
an angle to the main magnetic field is called excitation. It is
accomplished by applying a tiny magnetic field (B~1~) perpendicular to
the main field and oscillating it at the same frequency that the
magnetization precesses at.

*[Fat Suppression]{.underline}*

The signal from protons in CH~3~ groups in fat is at a slightly
different frequency than the signal from protons in H~2~O. In MRI,
position is determined by frequency, so that the image of fat will be
somewhat displaced from the image of water. For most imaging methods,
this is unimportant, since the bandwidth of the methods is much larger
than this chemical shift. However, for EPI, the bandwidth in the
phase-encoding direction is so low that the fat appears displaced
several centimeters from its true location relative to the water. To get
good echo-planar images, it is necessary to suppress the NMR signal from
CH~3~ before the water signal is excited. This is done by using an RF
pulse with carrier frequency centered at the CH~3~ frequency and with a
bandwidth narrow enough to miss the H~2~O frequency. The result is that
the CH~3~ protons are excited to transverse magnetization, which is then
removed (completely dephased) with a crusher pulse.

*[FID \[Free Induction Decay\]]{.underline}*

After RF excitation, if the transverse magnetization is left undisturbed
(i.e., no gradients applied and no more RF), then the measurable signal
starts off large and will decay steadily to zero over an interval of
about 3⋅T2\*. "Induction" is the electromagnetic term for the current
induced in the RF receiving coil when the magnetization inside is
changing. "Free" refers to the unmanipulated nature of the
magnetization. In this situation, the recorded NMR signal is sometimes
referred to as an FID, although the term really refers to the process
rather than the result.

*[Field]{.underline}*

This term just refers to a physical quantity or parameter that is
defined at every point in a spatial region. For example, the magnetic
field created by the main magnet permeates space; its strength and
direction vary from point to point. This is why it is called a "field".
In contrast, the speed of a car is not called a field, since it is a
quantity that is attached to a single object.

*[Field Map]{.underline}*

In MRI, this term refers to an image whose voxel values are proportional
to the magnetic field intensity difference from B~0~ at each location.
The most common method for acquiring a field map is to acquire two
images with identical methods except for different TEs; the phase
difference between the complex numbers in the images yields the desired
field map (after a little post-processing).

*[FFT \[Fast Fourier Transform\]]{.underline}*

The FFT is a collection of clever algorithms for computing a digital
approximation to the Fourier transform quite rapidly. (If Cooley and
Tukey---inventors of the first FFT algorithm \[**??? Cooley**\]---got 1¢
royalty for each FFT performed, they would now own the world. Being
honorable mathematicians, they donated the algorithm to the world.)

*[FLASH \[Fast Low Angle ???\]]{.underline}*

This is a relatively rapid imaging method: about 600--1000 ms per 2D
slice (approximately 10 times slower than EPI). It has been used for
fMRI, but mostly at sites where EPI is not available. It is not
practicable to do whole brain fMRI with FLASH, since about 20 slices are
needed to cover the cerebrum, and about 50 images per slice are needed
to compute decent functional activation maps.

*[Flip Angle]{.underline}*

If left alone long enough (about 10 seconds), all the magnetization
created by the main field will be aligned with the direction of the main
field. When disturbed by an RF pulse, the magnetization will point in a
different direction. The angle between the magnetization before the RF
pulse and after the RF pulse is called the flip angle.

*[Fourier Transform]{.underline}*

The application of gradient fields after the excitation means that the
frequency of the signal emitted by the magnetization depends on its
location. The signal detected at the RF coil is the sum of all the
signals emitted from the excited tissue, so the recorded data will
contain a mix of frequencies. These data must be broken down into their
frequency components, each of which is then assigned to the appropriate
location in the final image. The mathematical operation that transforms
data recorded in time to their frequency components is called the
Fourier transform. For this reason, MRI is sometimes called a Fourier
imaging method, since the raw data do not comprise an image, but are the
Fourier transform of an image.

*[FOV \[Field of View\]]{.underline}*

This term denotes the physical size of the imaged region, which is
determined by the sampling rate in *k*-space, and thus is set by a
combination of the analog to digital conversion rate and the gradient
field strength. FOV can be specified at the scanner console directly
(the scanner computer determines the necessary physical parameters for
you). It is important to set the FOV to be large enough to encompass all
the tissue in the slices being imaged. If there is tissue outside the
FOV, it will *not* be unseen in the image. Instead, it will wrap back
around the other side of the image, and overlap with the desired tissue.
This happens when the sampling rate in *k*-space is too coarse, meaning
that the Fourier transform can't tell some frequencies apart. (This
frequency confusion effect is also called "aliasing".)

*[Frequency]{.underline}*

When a signal is oscillating periodically in time, the number of periods
it cycles through in a unit time is called the oscillation frequency.
The units of frequency are Hertz (cycles per second); KHz is the
abbreviation for 1,000 cycles per second; MHz is the abbreviation for
1,000,000 cycles per second. Some examples:

Respiration about 0.25 Hz

Heartbeat about 1.1 Hz

EPI gradients about 1000 Hz

RF signals 42.54 MHz per Tesla of B~0~ (for protons)

*[Frequency Encoding]{.underline}*

The measured NMR signal is the sum of all the signals emitted from all
the magnetically excited tissue. To be able to distinguish source
locations in the measured signal, the components are made to differ in
frequency by making the magnetic field strength vary with location. This
is called frequency encoding. The Fourier transform provides a way to
break the signal, measured as a function of time, into its different
frequencies. As a result, the magnitude of each frequency component can
be assigned to the location from which it originated (since the
relationship between frequency and position is known). This type of
spatial encoding only provides one dimension of the needed localization.
The other two dimensions are provided by phase encoding and by slice
selective excitation.

*[Fully Relaxed]{.underline}*

The condition that magnetization reaches when it is undisturbed by RF
pulses for an interval at least 5⋅T1 in length. The longitudinal
magnetization reaches its maximum value, and the transverse
magnetization goes to zero.

*[FWHM (Full Width at Half Maximum)]{.underline}*

This term is used to describe the shape of a point spread or impulse
response function. It is the distance (or time) between the points on
the function where the function value is half of its maximum. This
number describes the distance (or time) over which an impulse input
affects the output. This number is often taken to be the resolution of
the system, since two input impulses closer than the FWHM will be
blurred together in the output and will be indistinguishable.

![](media/image2.png){width="3.908333333333333in"
height="1.9833333333333334in"}

Figure C.2. Definition of FWHM for a sample response function.

*[Gauss]{.underline}*

An older unit for the strength of a magnetic field; 1 Gauss equals
10^-4^ Tesla. The Earth's magnetic field is about 0.5 Gauss (except near
the North and South magnetic poles). Abbreviation: G.

*[Gaussian Noise]{.underline}*

Noise whose sample values follow a Gaussian distribution. Separate
values of Gaussian noise do not need to be independent
(uncorrelated)---Gaussian noise should not be confused with white noise.

*[Ghosts]{.underline}*

In MRI, position is deduced from the frequencies and phases of the
detected NMR signal. Unmeasured imperfections in the scanning process
can cause the frequencies and phases of some components of the signal to
be corrupted. These components will then be reconstructed to the wrong
locations. These artifacts are usually faint, and so are called "ghost
images". Echo-planar imaging is particularly prone to ghosting,
especially if the magnetic field is poorly shimmed.

*[Gradient Echo]{.underline}*

The application of a gradient field to the subject will cause the
transverse magnetization to dephase, and the total NMR signal will decay
away. Reversing the direction of the gradient field (e.g., changing the
sign of G*~x~*) will cause the dephasing to be undone, and the NMR
signal will grow back. This effect is called a gradient echo. Imaging of
the NMR signal relies on reading out the signal strength during the
decay and/or echo intervals while gradient fields are applied. Gradient
echoes can be made to coincide with spin echoes---this is the normal
technique used in spin echo imaging. When a spin echo is created, but
the gradient echo used in image acquisition does not coincide in time
with the spin echo, this is called an asymmetric spin echo (ASE).

*[Gradient Field]{.underline}*

The precession frequency of the magnetization at location *x* is
proportional to the magnetic field strength B(*x*) at that location. By
making B(*x*) = B~0~ + G⋅*x* for some nonzero constant G, the frequency
depends on location *x*; this is the mechanism that allows the total NMR
signal to be separated into components that came from different
locations. The magnetic field G⋅*x* is called the *x*-gradient field.
For 3D imaging, gradient fields in the *y*- and *z*-directions are also
needed, so that the total static magnetic field imposed by the scanner
takes the form B(*x*,*y*,*z*,*t*) = B~0~ + G*~x~*(*t*)⋅*x* +
 G*~y~*(*t*)⋅*y* +  G*~z~*(*t*)⋅*z*. The strengths of the gradient
fields are determined by the amount of current sent into the gradient
coils. Typical values for the gradient strengths are 10 mT/m (= 1 G/cm).

*[Hard and Soft RF Pulses]{.underline}*

A "hard" RF pulse is one applied without magnetic field gradients turned
on. In this case, the resonant frequency of all the protons inside the
RF coil is the same, and they are all "flipped". This is also called
"whole volume excitation". A "soft" RF pulse is one that is designed to
keep to a narrow frequency band, and is applied at the same time a
magnetic field gradient is turned on. The result is that only some of
the region inside the RF coil is resonant with the RF pulse, and only
the magnetization inside the resonant region is affected by the RF pulse
(see Fig. 2.9).

*[Hematocrit \[Hct\]]{.underline}*

Volume fraction of the blood that is occupied by whole red blood cells.
It is often used as a indicator of blood oxygen carrying capacity.

*[Hemodynamic]{.underline}*

An adjective used to describe changes in blood flow, volume,
oxygenation, etc., in response to other physiologic events. Changes in
neural activity do not measurably influence the NMR signal, but these
type of changes in blood are visible in MR images, and can be caused by
neural activity---hence, fMRI.

*[Hemodynamic Response Function \[HRF\]]{.underline}*

Many fMRI data analysis methods explicitly or implicitly assume that the
NMR signal response to neural stimulation can be described by the
superposition of a basic response *h*(*t*) that starts at the instant of
stimulus. If two stimuli are separated by 3 s, then the model response
is *h*(*t*)+*h*(*t*−3). (Causality implies that *h*(*t*) = 0 for
*t* \< 0.) A popular model function is
*h*(*t*) = *t*^8.6^⋅*e*^−*t*/0.547^ \[**??? Cohen**\]. This function
reproduces the stimulus onset delay, the time to maximum response, and
the decay back to baseline reasonably well, and has the advantage that
it is easy to program (unlike the balloon model, say). The hemodynamic
response function is the temporal point spread function for the mapping
from neural stimulation to fMRI time series.

*[Hertz]{.underline}*---see Frequency

*[I and Q]{.underline}*---see Quadrature

*[Impulse Response Function]{.underline}*

The measured response of a system to an infinitesimally brief stimulus
(an "impulse"). When the stimulus is longer, the system's response is
modeled to be the sum (or integral) of time-shifted copies of the
impulse response function, each copy originating at the time of its
corresponding stimulus. This concept is the time-domain analog of the
point spread function.

*[Inversion]{.underline}*

If the flip angle of an RF excitation pulse is set to 180°, it is
sometimes called an inversion pulse. The effect is to turn longitudinal
magnetization upside-down; that is, to anti-align it with the main
magnetic field. Transverse magnetization is rotated 180° in the
transverse plane. These effects have a large number of uses in MRI,
including the generation of spin echoes.

*[Inversion Recovery \[IR\]]{.underline}*

Spin echoes are formed by first flipping the magnetization by 90°,
waiting, and then applying a 180° flip. Inversion recovery imaging works
in the opposite way: longitudinal magnetization is flipped by 180°, the
pulse sequence waits, and then a 90° flip creates transverse
magnetization, which is then used to form an image. During the 180°--90°
waiting period, the upside-down longitudinal magnetization will begin to
relax back to the aligned state. By choosing the wait time (TI)
properly, the resulting image can be very sensitive to the T1 values in
tissue (i.e., very T1-weighted). Also, since M~z~ migrates from negative
to positive, at some point in time it goes through zero. By choosing TI
appropriately, tissue with any given value of T1 can be completely
removed from the image. In brain imaging, this nulling is usually
applied to cerebrospinal fluid. A double inversion recovery method can
be used to remove two different values of T1; with this technique, it is
possible to make a gray matter only or a white matter only image of the
brain. \[**??? Redpath**\]

*[Isocenter]{.underline}*

This is the spot inside the magnet bore where the main magnetic field is
most uniform. If you are using a local gradient coil, it should be
centered around this location.

*[k-space]{.underline}*

"*k*" is the mathematical symbol used for coordinates in the Fourier
transform. For this reason, MRI physicists often refer to the raw data
as being acquired in *k*-space, which then must be transformed back to
"real-space" for image display.

*[Larmor Frequency]{.underline}*

This denotes the frequency at which transverse magnetization precesses
about the direction of the magnetic field. For magnetized protons, the
Larmor frequency is B ⋅ 42.54 MHz. The phrase "resonant frequency" is
used interchangeably with this term.

*[Localizer]{.underline}*

During a scanning session, it is necessary to prescribe the desired
slices in some way. A localizer is a quick 2D image taken perpendicular
to the plane of the desired images (e.g., if you are going to gather
axial slices, the localizer would be sagittal or coronal). From the
localizer, it is easy to pick out the anatomical coverage desired by the
subsequent image acquisitions.

*[Magnetic Field]{.underline}*

A magnetic field is defined by its effects on small magnets (or
magnetizable materials, such as iron): it tends to align magnets placed
in the field in a particular direction (see Fig. 2.1). The strength of
the field determines the torque that the test magnets experience; the
direction that the test magnets become aligned with defines the
direction of the magnetic field. In MRI, the total magnetic field is the
sum of many independently generated components: the main field, the
gradient fields, the RF field, and the complex inhomogeneous field
generated in the subject by susceptibility effects.

*[Magnetization]{.underline}*

Protons by themselves, as in a hydrogen nucleus, are slightly magnetic.
When immersed in a large magnetic field, protons tend to line up with
this field (see Fig. 2.2). As a result, water (H~2~O) in a magnetic
field becomes slightly magnetized. The term magnetization refers to the
amount of magnetism that is created at any given location; for example,
tissue with a higher density of water will have a larger magnetization.

Magnetization is a vector field: it has a strength and points in a
direction, and the strength and direction both can vary with spatial
location (see Fig. 2.3). The symbol for vector magnetization is **M**.
The component of magnetization that points along the main magnetic field
direction is called longitudinal magnetization (symbol: M~z~). M~z~ is
not directly detectable. The component of magnetization perpendicular to
the main magnetic field direction is called transverse magnetization
(symbol: M~xy~). M~xy~ is detectable, since it precesses rapidly about
the direction of B~0~; this produces a tiny rapidly changing magnetic
field, which induces a tiny rapidly changing voltage in the nearby RF
receive coil.

*[Magnetization Transfer \[MT\]]{.underline}*

To contribute to the directly measurable NMR signal, hydrogen nuclei
must be in molecules that vibrate and move rapidly (this effect is
called "motional narrowing"). For the most part, this mean H~2~O
molecules and CH­~3~ groups in fats; hydrogens in proteins and other
large molecules are too rigidly bound to contribute to the measured
signal---the result is that the T2 of protein protons is only about
10 μs, and their NMR signal decays away before it can be measured at
all. However, it is possible for such macromolecules to indirectly
influence the NMR signal. Their ^1^H nuclei still become magnetized.
When an H~2~O molecule come close to a protein, the magnetization state
of the water protons can exchange with the protein protons. The
magnetization of the protein protons is completely dephased, so when it
transfers to the water protons, it does not contribute to the NMR
signal. The magnetization of the water protons becomes completely
dephased within microseconds of exchanging to the protein protons. The
net effect is a diminishing of the NMR signal---the magnetization
transfer (MT) effect. The MT effect is normally not large, but can be
enhanced by using special RF pulses designed to flip the protein
protons' magnetization along with the water protons' magnetization. MT
imaging has not been used much in fMRI, but has some applications in
clinical scanning (e.g., detection of multiple sclerosis lesions).

*[Main Field]{.underline}*

This is the huge magnetic field produced by the superconducting
current---typical strengths for fMRI are 1.5--3 Tesla. Fields up to
about 0.3 Tesla can be produced by permanent magnets or currents in
normal resistive wire, but larger fields require such large currents
that superconductors are the only available technology. The symbol for
the main field is B~0~.

The main field magnetizes the protons in the tissue and creates the
magnetization. The main field also causes the magnetization to precess
(i.e., rotate, or spin) about the direction in which B~0~ points, at a
speed that is proportional to the main field magnitude (see Fig. 2.3).
The region inside the magnet where the main field is spatially uniform
is called the "sweet spot" of the system. The middle of the sweet spot
is the magnet's isocenter.

Spatial uniformity in the main field is important for (at least) three
reasons. The first is that frequency is used to encode spatial position,
by the application of magnetic field gradients. The relationship between
frequency and position must be known for this technique to work. The
second reason is that a nonuniform magnetic field would increase the
transverse relaxation rate (i.e., decrease T2\*), and so the NMR signal
would decay away faster. The third reason is that a larger range of
magnetic field strengths would mean that a larger range of frequencies
would be present. The NMR signal would have a larger bandwidth, which
would require enlarging the RF receiver bandwidth. That would in turn
increase the thermal noise level in the received NMR signal, which would
degrade the image quality.

*[Matrix]{.underline}*

In MRI jargon, the image acquisition matrix is the size of the *k*-space
grid on which the raw data are measured. The most common matrix used in
EPI has been 64×64. Normally, an image is reconstructed onto a grid that
is the same size as the acquisition matrix, but this is not necessary.

In mathematics, a matrix is a set of numbers that represents a linear
transformation of a vector; for example, rotation of coordinates can be
expressed using a mathematical matrix. This leads to the concept of
using matrix algebra to rotate image matrices---the same word having two
different meanings.

*[MRI \[Magnetic Resonance Imaging\]]{.underline}*---see Chapter 2

*[NEX \[Number of EXcitations\]]{.underline}*

If it takes *n* RF shots and readouts to get the data needed for one
image, one might want to acquire more data than are strictly necessary.
These redundant data can be used for signal averaging, which will reduce
the effects of noise on the final product. If 2⋅*n* excitations are used
where *n* could have sufficed, then the resulting method is said to have
used NEX=2. (The mathematics of Fourier transforms sometimes allows
½⋅*n* excitations to be used to reconstruct an image; in this case, the
jargon is NEX=½, even though there really is no such thing as half of an
RF excitation.)

*[NMR \[Nuclear Magnetic Resonance\]]{.underline}*---see Chapter 2

*[NMR Signal]{.underline}*

The RF signals emitted by all the transverse magnetization in the
subject are detected simultaneously by the RF coil; this is the total
NMR signal.

*[Noise]{.underline}*

This term denotes the components of a signal that interfere with the
detection of that part of the signal in which we are interested. In NMR,
the fundamental noise is the electronic thermal noise in the RF
detection system, and the electromagnetic thermal noise emitted by the
subject. These noise sources cannot be removed, and are what physicists
usually mean by the term "noise". In fMRI, the NMR signal changes
induced by the hemodynamic consequences of neural stimulation are the
signal component we wish to detect. Other NMR signal changes due to
respiration or the cardiac cycle can be considered "noise" in the
context of brain mapping.

*[Paramagnetic]{.underline}*---see Susceptibility

*[Partial Volume Effect]{.underline}*

A digital medical image is a collection of voxels, each of which has a
numerical value attached. The number stored for each voxel is an average
of some physical parameter over the voxel's volume. Since voxels are
relatively large (1 mm^3^ or larger) and brain tissue is so intricate,
most voxels will contain a mix of different tissue types; for example,
most "gray matter voxels" will contain some cerebrospinal fluid (CSF).
If the physical parameter of interest is only associated with gray
matter (e.g., blood), then the actual voxel value will not only depend
on the value of the parameter in the gray matter inside the voxel but
also on how much CSF is in the voxel. The tissue of interest in this
example only occupies part of the volume of the voxel---hence the name
of this effect. The partial volume effect makes it difficult to compare
voxel values in different locations, since it is usually impracticable
to know how much of a voxel volume is occupied by tissues of different
classes or in different physiological states.

*[Partition Coefficient]{.underline}*

A chemical in the blood will diffuse or be transported into the
parenchymal tissue, and vice-versa. When equilibrium is reached, the
concentrations in the blood and in the tissue may not be equal---the
chemical may have a greater affinity for blood or tissue. The ratio of
concentrations at equilibrium is called the partition coefficient. In
models of the hemodynamic response to neural stimulation, the partition
coefficient of oxygen is an important parameter. In models of contrast
agent imaging, the partition coefficient of the contrast agent is of
crucial importance.

*[Perfusion]{.underline}*

The amount of flow in capillaries, measured in milliliters per gram of
tissue per second. Since capillary flow is where most oxygen and
nutrients are delivered to brain tissue, measuring perfusion with
arterial spin labeling methods is thought to have the best spatial
localization potential for brain mapping, of all techniques based on
hemodynamic changes.

*[Phase]{.underline}*

The remembrance of frequency past. In a pure cosine function
cos(2πf*t*), the phase is 2πf*t*. In other words, frequency is the rate
of change of phase. Phase represents where (or when) some signal is
relative to some reference point.

*[Phase Encoding]{.underline}*

Frequency encoding can directly only encode one spatial dimension, since
frequency only has one dimension itself. Phase encoding uses the fact
the magnetization accumulates the frequencies to which it has been
exposed, and stores them as the magnetization's phase (the angle of
M~xy~ in the *xy*-plane). This phase can be measured in the NMR signal.
By arranging the M~xy~ phase so that it varies linearly in some
direction, it is possible to separate NMR signal components in that
direction, using the Fourier transform. Combining frequency encoding in
one direction and phase encoding in a perpendicular direction is what
makes 2D image formation practical.

*[Physiological Noise]{.underline}*

This is the term used for physiologically caused fluctuations in the NMR
signal that are not relevant to neural activation. Respiration and the
cardiac cycle are the two major components of this "noise". There is
also a very low frequency (≤ 0.1 Hz) component that may be related to
resting state fluctuations in neural activity.

*[Pixel]{.underline}*

A contraction of "picture element"; this term refers to the individual
component of a digital image. The numerical value associated with a
pixel defines the intensity of the image at the pixel's location.

*[Point Spread Function \[PSF\]]{.underline}*

The numerical value stored in a voxel is an average of the NMR signal
over a region. The average is not equally weighted at all locations or
in all directions. The PSF expresses the importance of each location in
the vicinity of the voxel to the single number in the image. In MRI, the
in-slice point spread function is usually proportional to
sin(π*x/*∆)⋅sin(π*y/*∆)/(*xy*), where *x* and *y* are the coordinate
distances measured from the voxel center and ∆ is the length of a voxel
edge. (∆ is determined by the amount of *k*-space that is covered by the
imaging pulse sequence.) The resolution of an image is determined by the
distance over which the PSF is significantly different from zero.

*[Precession]{.underline}*

Precession is the rotation of one axis about another axis; it is
illustrated in Figs. 2.3 and 2.4. In NMR, it refers to the motion of the
magnetization vector about the direction of the magnetic field vector.

*[Pulse]{.underline}*

MRI works by transmitting bursts of RF radiation into the subject to
create transverse magnetization from longitudinal magnetization, then by
sending bursts of current into the gradient coil to control the
frequency and phase of the transverse magnetization. Both types of
bursts are called "pulses", and the software that controls them is
called a "pulse program" or "pulse sequence".

*[Quadrature]{.underline}*

A time-varying signal that is at a pure frequency f can be represented
as a mixture of two components: cos(2πf*t*) and sin(2πf*t*). The first
is called the I (in-phase) component, and the second is called the Q
(quadrature) component. Both components of the NMR signal are measured.
By convention, I corresponds to the *x*-component of M~xy~ and Q to the
*y*-component.

*[Raw Data]{.underline}*

This term refers to the actual NMR signal recorded by the RF receiver
subsystem, as a function of time. The raw data must be reconstructed
(usually using the Fourier transform) to produce a useful image.

*[Readout]{.underline}*

This term refers to the time interval when the RF receiver is turned on
and the NMR signal emitted by the subject is actually digitized and
stored in the computer for reconstruction. The RF receiver cannot be
turned on during the RF transmit interval, since the transmit power is
vastly greater than the receiver is capable of handling. (See Fig. 2.10
for a sample of the sequence of events in a typical MRI pulse program.)

*[Reconstruction]{.underline}*

The process of turning raw data into a human-usable image.
Reconstruction usually includes computing the Fourier transform of the
raw data, and often involves several other calibration steps to adjust
for imperfections in the scanning process (e.g., unshimmable distortions
in the magnetic field, and slight timing errors in the gradient pulses).

*[Reference Waveform]{.underline}*

The correlation method of fMRI data analysis requires that the analyst
specify a function that specifies the shape of the expected time series
in activated voxels. This function is called the reference or ideal
waveform.

*[Refocusing]{.underline}*

When the magnetic field is not spatially uniform, the total NMR signal
decays away rapidly due to dephasing of the component signals from
different locations. The Hahn spin echo can restore some of this
dephasing, and so the measured NMR signal can be made to increase after
it decreases (see Fig. 2.8.). This effect is sometimes called a
refocusing of the NMR signal. If the dephasing was caused by
deliberately applied magnetic field gradients, then applying opposite
gradients will also refocus the NMR signal.

*[Registration]{.underline}*

This term refers to the process of adjusting an image to be aligned with
a "master" image. Image registration is commonly used in fMRI data
post-processing to (partially) correct for the effects of subject head
motion.

*[Relaxation]{.underline}*

This term describes the processes by which the magnetization returns to
its equilibrium state after being disturbed (usually by an RF pulse).
The restoration of longitudinal magnetization is sometimes called
"spin-lattice" relaxation, and the decay of transverse magnetization is
sometimes called "spin-spin" relaxation. Longitudinal magnetization is
restored by internal electromagnetic fluctuations of matter that occur
at the Larmor frequency. These fluctuations are caused by the thermal
agitation of water molecules near other magnetized molecules. Transverse
magnetization is destroyed by nonuniformities in the magnetic field,
which cause the phase of different protons to drift apart.
Nonuniformities occur on a microscopic scale due to variations in tissue
susceptibility. Contrast agents can increase these nonuniformities and
so increase the relaxation rates.

*[Resolution]{.underline}*

The spatial resolution of an imaging method is the smallest distance
apart two separate objects in the real world can be for them still to be
distinguished in the image. The resolution of a digital image cannot be
finer than the size of a pixel, but it can be coarser (consider
digitizing an out-of-focus photograph---no matter how finely you scan
it, you cannot get around the fact that the information needed for fine
resolution just isn't there). In MRI, spatial resolution is largely
determined by the gradient strength and by the readout time, and is
approximately equal to FOV/matrix size in the in-slice directions and is
equal to the slice thickness in the through-slice direction. It is
possible to reconstruct an MR image to a finer grid than the acquisition
matrix, but this does not increase the resolution of the result (but it
may improve the perceived visual quality).

*[RF \[RadioFrequency\]]{.underline}*

In NMR, RF refers to magnetic fields that oscillate at the Larmor
frequency of the protons. The most common use of the term RF is when
talking about the transmitted radiofrequency waves that are used to
excite the magnetization; however, RF can also refer to the received NMR
signal. RF is transmitted and received by special coils; the transmit
and receive coils may be identical or may be separate.

*[Sagittal]{.underline}*

A sagittal slice is a vertical section; it is as if one were looking at
the brain from the subject's left or right (see Fig. C.1). Sometimes the
term "parasagittal" is used instead.

*[SAR \[Specific Absorption Rate\]]{.underline}*

This term refers to the average rate at which the subject's tissue is
absorbing energy from the transmitted RF. To prevent heating of the
subject, MRI systems contain a safety interlock that will shut off the
RF if the scanner detects that too much power is being transmitted.
Methods to minimize power deposition include increasing TR and reducing
the flip angle. Unfortunately, power deposition goes up with RF
frequency, which means that scanning at higher B~0~ field strengths gets
closer to the edge of safety.

*[Saturation]{.underline}*

In virtually all imaging methods, numerous RF pulses are applied to the
subject in close succession. Before the first RF excitation is used, the
longitudinal magnetization M*~z~* is at its largest possible value. The
RF pulse converts this M*~z~* to transverse magnetization, which emits
the NMR signal that is manipulated to form the raw image data. When the
second RF excitation is applied to the same region and less time than
5⋅T1 has elapsed, M*~z~* will not have fully recovered to its peak
value. Thus, there will be less longitudinal magnetization to convert to
transverse magnetization, so the NMR signal will be weaker after the
second RF pulse than after the first. With repeated RF pulses, this
situation reaches an equilibrium condition, and the NMR signals will
level off at values somewhat less than the first readout gives. When
this equilibrium is reached, the longitudinal magnetization is said to
be saturated. In fMRI, the practical import is that the first few images
in a time series will be brighter and have a different quality than the
later images; these first images must be discarded in the data analysis.

Saturation is also used to mean the complete dephasing of transverse
magnetization by crusher pulses. This type of saturation is needed in
inversion recovery imaging, for example, since the 180° pulses will not
be perfect and will leave some residual transverse magnetization behind
which would interfere with the later readout if it were not saturated
(reduced to zero). These two meanings of the word are somewhat
different.

*[Shielding]{.underline}*

This term encompasses several schemes for restricting the reach of the
various electromagnetic fields used in MRI. The main magnet may be
shielded to keep its fringe field from interfering with equipment near
the scanner. The whole scanner room must be shielded to prevent outside
RF radiation from leaking in and corrupting the received NMR signal. The
gradient coil may be shielded to reduce the effects of eddy currents.
Electronic equipment placed in the scanner room may need to be shielded
to prevent interference with the scan. (If possible, electronics should
be placed outside the shielded scanner room and only have leads brought
in through the room's penetration panel.)

*[Shimming]{.underline}*

MRI uses frequency to encode spatial position. For this reason, it is
important to ensure that B~0~ is the same at all locations in the field
of view. The scanner main magnet is designed to make a very uniform
magnetic field. Putting a nonuniform object (such as a human being) into
the bore will cause the field to become nonuniform, due to the different
susceptibility of bone, air, and soft tissue. Shimming refers to the
process of adjusting the main magnetic field to make it as uniform as
possible. These adjustments are made by varying the electrical current
in a separate set of coils ("shim coils") which are just inside the
superconducting main magnet coils. Shimming is usually the first
operation done after the subject is made comfortable in the scanner. (In
mechanics, a "shim" is a thin slip of metal used to fill up a space or
force something into the right position. In the early days of NMR---long
before MRI---magnetic fields were adjusted by physically distorting the
main magnet coil with shims. Now it is all done electronically, but the
name has survived.)

*[Shot]{.underline}*

MRI physics slang for an RF excitation pulse. For example, EPI is
referred to as a "single-shot" imaging method, since it gets all the
data needed to reconstruct an image from the transverse magnetization
created by one RF excitation. FLASH is a "multi-shot" imaging method,
since it uses more RF excitations to get the data necessary for one
image.

*[Slice Selection]{.underline}*

Most MR imaging methods acquire images from 2D slices, rather than from
the whole 3D volume at once. Since the measured NMR signal comes from
all the excited protons inside the RF receive coil, a 2D image can only
be gathered if only a thin slice of the tissue is affected by the RF
excitation shot. This is done by combining an applied gradient field
with the transmitted RF radiation (see Fig. 2.9).

*[SNR \[Signal to Noise Ratio\]]{.underline}*

The signal strength is measured as the mean of the image voxel values,
averaged over voxels that are actually in tissue. The noise strength is
the mean of the image voxel values, averaged over voxels that are in air
(where there is no true NMR signal). SNR is the ratio of these values.
Images with SNR below 20 look very grainy.

A related concept is Contrast to Noise Ratio (CNR). The numerator for
CNR is the difference in mean voxel values between two different types
of voxels; for example, in fMRI, the contrast would be measured as the
mean change in voxel value with neural stimulation, averaged over those
voxels selected as "active". In this application, the noise value in the
denominator would usually be the average standard deviation of the time
series of voxels with no apparent activation. This would include the
effects of physiological noise.

*[Spectroscopy]{.underline}*

Most of the measurable NMR signal from tissue comes from H~2~O or CH~3~
protons, but there are a few other molecules that are present in large
enough concentrations and have long enough T2 relaxation times to be
"visible". In the brain, these species include glutamate,
N-acetyl-aspartate, lactate, and choline. The resonant frequency for the
^1^H nuclei depends on which compound it is in. If gradients are *not*
applied during readout, and the NMR signal is separated into frequency
components accurately, then each peak in the resulting spectrum can be
identified with a particular metabolite. The principal difficulty with
*in vivo* spectroscopy is that the NMR signals from non-water, non-fat
molecules are very weak, due to their low concentrations. Many
acquisitions are needed to get decent data---typically 20 minutes or
more for a single image. Voxels must be large (10--20 mm on a side).
Spectroscopic techniques have been applied to fMRI stimulation paradigms
in attempts to measure lactate production \[[Frahm]{.mark}\].

Spectroscopy is frequently done to detect ^31^P containing compounds,
instead of ^1^H containing compounds. Some information about phosphorous
metabolism can be obtained this way. To our knowledge, this type of
spectroscopy has not been applied to fMRI (yet).

*[SPGR \[SPoiled GRASS\]]{.underline}*

This is a true 3D image acquisition method, using phase encoding in two
dimensions and frequency encoding in the third. These type of images are
strongly T1-weighted, and are useful for anatomical localization since
they have strong gray-white matter contrast. Figure C.1 shows 3 slices
extracted from a SPGR data set, which took about 12 minutes to acquire.
MP-RAGE is another name for a similar imaging method.

*[Spin]{.underline}*

Spin is the quantum mechanical analog of angular momentum, and it is
what makes a nucleus be magnetic. For this reason, MRI physicists often
describe their specialty as "spin physics", and refer to the protons as
"spins". (By this logic, radiologists could be called "spin doctors".)

*[Spin Echo]{.underline}*

The transverse magnetization in each small region precesses at the rate
determined by the local magnetic field. These small components of the
NMR signal decay at a rate given by T2, but the overall NMR signal
decays faster since the component signals get out of phase with each
other. When an inversion RF pulse is applied, the phase relationships of
the regional magnetizations are reversed---what was behind get ahead,
and what was ahead gets behind. The result is that the component signals
will come back into phase (briefly), and the signal decay is partly
reversed. This effect was first described by Erwin Hahn
\[[Hahn]{.mark}\], and is called a spin echo (see Fig. 2.8). Spin echoes
are used in combination with gradient echoes in many forms of MR
imaging.

*[Static Field]{.underline}*

In NMR, magnetic fields are divided into two time scales: radiofrequency
(RF) fields which oscillate in time at a rate very near the Larmor
frequency, and static fields, which either do not change at all, or
oscillate in time at rates much slower than the Larmor frequency. In
EPI, the gradient fields oscillate about 1000 times per second (1 KHz),
but this is still slow relative to the precession rate, so the gradient
fields are considered to be static.

*[Stimulus Correlated Motion]{.underline}*

It is often observed that subjects in fMRI experiments move slightly
when an external stimulus is presented. The image changes caused by
these movements are highly correlated with the time course of the
stimulus, and thus will often have characteristics similar to the
expected hemodynamic response. The result of functional activation data
analysis will include a large number of false positives. These are most
pronounced at the edges of the brain, where the signal changes due to
voxel motion are largest. If an fMRI activation map shows activation
along a large portion of the edge of the brain, this is a certain sign
that the results are corrupted by stimulus correlated motion. Image
registration (realignment) can reduce the magnitude of this problem
significantly.

*[Susceptibility]{.underline}*

Most materials, when immersed in an externally created magnetic field,
will create a small extra magnetic field. The ratio between the
strengths of the substance-generated field and the external field is
called the susceptibility constant (denoted by μ). A diamagnetic
substance creates an extra field that subtracts (a little) from the
external field. Most soft tissue, including oxyhemoglobin, is
diamagnetic with μ ≈ −10^-7^. At a resonant frequency of 63
MHz---B~0~ = 1.5 Tesla---this corresponds to a frequency shift of
--6.3 Hz. However, deoxygenated hemoglobin is paramagnetic; that is, it
creates an extra field that adds to the external field, with μ ≈ +10^-7^
\[**???**\]. This difference in susceptibility is the origin of the BOLD
effect.

*[T1]{.underline}*

Left to itself (undisturbed by RF), the magnetization will return to its
equilibrium value, which is pointed along the direction of B~0~ and has
a magnitude denoted by M~0~. The time scale over which this relaxation
to equilibrium occurs for the longitudinal magnetization is denoted
by T1. Immediately after being disturbed by an RF pulse, suppose that
the longitudinal magnetization M~z~ has value *m*. Then at time *t*
after the RF shot, M~z~(*t*) = (*m*-M~0~)⋅*e*^-*t*/T1^+M­­~0~. T1 is about
500--1000 ms in the brain, and varies about 20% between gray and white
matter. The fact that T1 is so long means that it is normally better to
space RF shots to the same slice about a second apart, so that the
longitudinal magnetization has time to recover before being converted
again into transverse magnetization. This is one reason that 2D
multi-slice imaging methods are popular: while M~z~ recovers in one
slice, the other slices can be excited and have their signal acquired.
The reciprocal of T1 is called R1 (the longitudinal relaxation rate).

*[T2]{.underline}*

This symbol denotes the time scale over which the transverse
magnetization decays to zero (its equilibrium value) after an RF
excitation. Immediately after being disturbed by an RF pulse, suppose
that the transverse magnetization M~xy~ has value *n*. Then at time *t*
after the RF shot, M~xy~(*t*) = *n*⋅*e*^-*t*/T2^. T2 is about 120/B~0~
ms in the brain (B~0~ measured in Tesla). The reciprocal of T2 is
called R2 (the transverse relaxation rate).

*[T2\*]{.underline}*

As explained in Chapter 2, T2 actually denotes the time scale for decay
of the transverse magnetization signal *not* including the effects of
signal dephasing caused by magnetic field inhomogeneities above the
scale of 10 μm or so. If these effects are included, then the shorter
decay time is denoted by T2\*. In the brain, T2\* is usually about half
of T2. Changes in T2\* are the most pronounced consequence of the BOLD
effect; changes in T2 are also present, but are smaller (T2\* and T2
both increase with blood oxygen level). The reciprocal of T2\* is
called R2\*.

*[T2′]{.underline}*

T2′ measures the relaxation time scale difference between T2 and T2\*.
The formula is 1/T2′ = 1/T2\*−1/T2; or R2′ = R2\*−R2. This represents
the rate that the overall NMR signal is decaying due to dephasing caused
by microscopic magnetic field inhomogeneities.

*[TE \[Time of Echo\]]{.underline}*

TE measures the time from the RF excitation to the point where the total
NMR signal is largest (i.e., its components are most in-phase). In a
gradient echo image, the signal intensity in a voxel at location *x*
will be proportional to *e*^−TE⋅R2\*(*x*)^. If TE is much smaller than
the average T2\*, then all the voxels will be about the same intensity
no matter what R2\* is. If TE is much larger than the average T2\*, then
all the voxels will be nearly zero. For maximum sensitivity to changes
in R2\* (e.g., as caused by the BOLD effect), TE should be about equal
to the average T2\*. TE is controlled by the pulse program and the
scanner console computer (see Fig. 2.10).

*[Tesla]{.underline}*

The SI unit of magnetic field strength; one Tesla equals 10^+4^ Gauss.
Abbreviation: T.

*[TI \[Time of Inversion\]]{.underline}*

When an inversion RF pulse is used---as in a spin echo---TI denotes the
time between the RF pulse that excites the transverse magnetization and
the inversion RF pulse. In a spin echo pulse sequence, TE = 2⋅TI (see
Fig. 2.11).

*[TR \[Time of Repetition\]]{.underline}*

All MRI pulse sequences involve repeated RF excitations and readouts.
The time interval between excitation of the same tissue slice is denoted
by TR. If *N* slices are being acquired, then the time for acquisition
of each slice is TR/*N*. (This slice acquisition rate has no particular
name in the MRI lexicon.)

*[Transverse Magnetization]{.underline}*---see Magnetization

*[Undershoot]{.underline}*

The MRI measurable response to neural activation follows a complex time
course (see Fig. 3.3). Prior to the main signal rise, some laboratories
have observed a slight dip in the NMR signal---this phenomenon is called
the pre-undershoot (consumption of oxygen before perfusion increases is
the explanation usually proffered). After the main signal peak decays,
a post-undershoot is often seen (the balloon model is one explanation
for this effect).

*[Vector]{.underline}*

A vector quantity is something that has a magnitude and a direction;
a scalar quantity has only magnitude. For example, velocity is a vector,
and speed is a scalar. (If you are caught driving the wrong way on the
freeway, you should be given a velocity ticket, not a speeding ticket.)
Magnetic fields and magnetization are vectors.

*[Voxel]{.underline}*

Supposed to be an abbreviation for "volume element". We prefer to use
this as the name for an element of an MR image---rather than
"pixel"---since it serves as a reminder that the numerical values in the
image are averages over small 3D volumes. Typical voxel dimensions in
high-resolution images are 1×1×1 mm^3^; For high-speed fMRI, voxel sizes
of 3×3×3 mm^3^ are more common.

*[Weighting]{.underline}*

Approximately another term for "contrast". Usually prefixed with another
term indicating what physical or physiological parameter most influences
the voxel values in the image. For example, SPGR images are T1-weighted,
meaning that T1 differences between the tissue in different voxels has
the largest influence on the image. Functional images are T2\*- or
T2-weighted (for gradient and spin echoes, respectively), since these
are the parameters that are most strongly affected by the hemodynamic
changes consequent to neural stimulation.

*[White Noise]{.underline}*

Noise values that are completely independent---unpredictable---from time
to time (or place to place) are called "white". Mathematically, this is
equivalent to each frequency component of the noise having equal
variance. (The term comes from the properties of white light.) It is
also equivalent to saying that the separate noise values are
uncorrelated. A common error is to assume that white noise must be
Gaussian, which is a separate concept.

*[Wraparound]{.underline}*---see FOV

**Appendix D. The *AFNI* Software Package for fMRI Data Analysis**

*AFNI* is a collection of program written by one of the authors (RWC)
for fMRI data analysis. It is distributed freely over the Internet in C
source code format. Compiled versions for Linux systems are also
available. About 200 pages of documentation come with the system. At
this time, the Web address for accessing the *AFNI* package is
http://varda.biophysics.mcw.edu/\~cox/ .

*AFNI* refers both to the interactive program of that name, and to the
entire software package. The basic unit of data storage is the \"3D
dataset\", which consists of one or more 3D arrays of voxel values
(bytes, shorts, floats, or complex numbers), plus some control
information stored in a header file.

***AFNI* Built-in Interactive Functions**

Just the most obvious ones (much of the \"fun\" of *AFNI* comes from
finding the unobvious functions):

-   Switch viewing/analysis between many different datasets.

-   Image display in axial, sagittal, and/or coronal views (including
    multi-image montages).

-   Display of graphs (line and surface) of data extracted from image
    viewers.

-   Time series graphing of square regions from image viewers.

-   Linked image/graph viewing of multiple 3D datasets (e.g., linked
    scrolling through multiple brains).

-   Transformation to Talairach coordinates (12 sub-volume piecewise
    linear method).

-   Computation of activation maps using the \"correlation method\".

-   Color overlay of activation maps onto higher-resolution anatomical
    images (resampling of lower-resolution functionals is handled on the
    fly).

-   Interactive thresholding of functional overlays.

**Command Line Programs**

These programs are often used in batch processing scripts. Generally,
they take as input 3D *AFNI* datasets, and compute new 3D datasets as
output. The results can then be displayed or further processed with the
interactive *AFNI* program.

-   *to3d* --- Program to create a 3D *AFNI* dataset from image data.

-   *3dmerge* --- Program to average or otherwise merge multiple 3D
    datasets.

-   *3dttest* --- Program to do voxel-by-voxel *t*-tests on 3D datasets.

-   *3dANOVA*, *3dANOVA2*, and *3dANOVA3* --- This series of program
    performs 1-way, 2-way, and 3-way ANOVA tests across a collection of
    3D datasets, on a voxel-by-voxel basis.

-   *3dRegAna* --- Multiple linear regression across a collection of 3D
    datasets.

-   *3dFriedman*, *3dKruskalWallis*, *3dMannWhitney*, and *3dWilcoxon*
    --- This series of programs carries out various nonparametric
    statistical analyses across a collection of 3D datasets, on a
    voxel-by-voxel basis.

-   *3dDeconvolve* --- Multiple linear regression of a 3D time series,
    including linear deconvolution to find an ideal response vector for
    each voxel.

-   *3dNLfim* --- Nonlinear regression of a 3D time series. The
    nonlinear time series model functions can be anything programmable
    in C. Twelve sample model functions are supplied with the *AFNI*
    source code, including convolution with a gamma variate impulse
    response function.

-   *3dcalc* --- General purpose 3D dataset calculator program.

-   *3dTsmooth* --- Program to smooth voxel time series.

-   *3dfim* --- Implements the \"correlation method\" on a 3D time
    series.

-   *3dclust* --- Program to find clusters of above-threshold voxels.

-   *3dfractionize* --- Program to resample an ROI mask from one grid
    spacing to another.

-   *3dmaskave* --- Program to compute statistics of voxels selected by
    an ROI mask.

-   *3dpc* --- Program to compute principal components from multiple 3D
    datasets.

-   *3drotate* --- Program to rotate the volumes in a 3D dataset.

-   *2dImReg* --- Program to do 2D (slice-wise) registration of a 3D
    time series.

-   *3dvolreg* --- Program to do 3D volume registration of a 3D time
    series.

-   *3dIntracranial* --- Remove the \"scalp\" from a T1-weighted
    high-resolution anatomical dataset.

-   *3daxialize* --- Reorient the slices in a dataset to be in a
    standard axial order.

The following utility programs make certain tasks easier:

-   *3dTcat* --- Utility program to catenate multiple 3D time series
    files into one.

-   *3dbucket* --- Utility program to catenate 3D volumes into one big
    \"bucket\".

-   *3dbuc2fim* --- Utility program to extract 3D volumes from a
    \"bucket\" dataset.

-   *3dhistog* --- Utility program to extract a histogram of a 3D
    dataset.

-   *3dinfo* --- Utility program to print out information about a 3D
    dataset.

-   *3drefit* --- Utility program to edit the header information about a
    3D dataset.

-   *3dTSgen* --- Utility program to generate random 3D time series
    datasets from nonlinear model equations; used for testing *3dNLfim*
    and other analysis codes.

-   *AlphaSim* --- Simulates noise-only 3D time series and activation
    detection therefrom, in order to estimate the probability of false
    positives. Used when analytical estimates for this *p*-value are
    unavailable.

-   *adwarp* --- Resample a functional dataset to the Talairach
    coordinate grid defined by an anatomical \"parent\".

-   *waver* --- Utility program to generate an \"ideal\" response
    function for use with the correlation method (or other regression
    analyses).

-   *float_scan* --- Utility program to scan a floating point file for
    illegal values (Infinity and NaN).

-   *2swap*, *4swap*, and *24swap* --- Utility programs to swap byte
    pairs and quads; used when transferring data between computers with
    different CPU architectures.

-   *RSFgen* --- Generates random stimulus timeseries functions.

-   *cdf* --- Calculates thresholds and *p*-values for various
    statistical distributions.

**Interactive *AFNI* Plugins**

Plugins are a way to add interactive functionality to *AFNI* without
modifying the core software. There is a 40 page programming manual to
aid in the creation of new plugins.

-   *plug_clust* --- Interactive version of *3dclust*.

-   *plug_copy* --- Make a copy of a dataset (useful for subsequent
    editing/drawing).

-   *plug_deconvolve* --- Interactive version of *3dDeconvolve*.

-   *plug_delay_V2* --- Hilbert transform estimation of time delay in
    active voxels.

-   *plug_drawdset* --- Draw values into a dataset (used to create ROI
    masks).

-   *plug_edit* --- Interactive version of *3dmerge* (voxel value
    editing functions).

-   *plug_imreg* --- 2D (slice-wise) image registration.

-   *plug_lsqfit* --- Interactive linear least squares regression on
    time series data.

-   *plug_maskave* --- Interactive version of *3dmaskave* (statistics
    from an ROI).

-   *plug_nlfit* --- Interactive nonlinear least squares regression on
    time series data.

-   *plug_power* --- Power spectrum estimation from a 3D time series.

-   *plug_realtime* --- Real-time image acquisition, registration, and
    activation maps. (Program *rtfeedme* is used to simulate real-time
    imaging, and will transmit images into this plugin in lieu of a
    scanner.)

-   *plug_render* --- Volume rendering of 3D datasets, with color
    functional overlay. (Particularly useful in conjunction with
    *3dIntracranial*.)

-   *plug_stats* --- Compute some voxel-by-voxel statistics of a 3D time
    series.

-   *plug_tag* --- Put \"tags\" into a dataset, as markers for points of
    interest.

-   *plug_volreg* --- Interactive version of *3dvolreg* (volume
    registration).

-   *plug_reorder* --- Reorder a 3D+time dataset; useful for analysis of
    \"event-related\" FMRI data.