Download Solved Exam 1 for Brain Connectivity Mapping | PSY 2476 and more Exams Psychology in PDF only on Docsity!
Study Questions Brain Connectivity
Mapping
With Answers
Spring 2009 PSY 1054 (35986) and PSY 2476 (35987)
University of Pittsburgh, Psychology Department
Instructors Walter Schneider and Sudhir Pathak
Contact BrainConnectivityMapping@gmail.com
Webpage for class http://www.lrdc.pitt.edu/schneider/bcm-public/
These are study questions for the class. They are provided as a resource to people that would like a short
summary of key issues and methods for brain connectivity mapping. Note these are student generated. It
was a shared Google document.
Contributors
[DM] Derek Mockel, [JJ] Jeffrey James, [JP] Jeff Phillips, [KH] Katrina Han, [NC] Nadia Carter, [SB] Shane
Belin, [SP] Sudhir Pathak, [JP] Jessica Porter [SS] Sarah Schipul, [WS] Walter Schneider, [YL] Yanni Liu,
[BE] Bradley End, [KW] Kristine Wilckens , [VV] Vijay Venkatraman, [MM] Morgan Major [DS] Danielle
Stein
1. Introduction of Connetome based assessment
1.1. What is the human Connectome? [ws] According to Sporns "The connection matrix of the
human brain (the human ‘‘connectome’’) represents an indispensable foundation for basic and
applied neurobiological research". The Connectome is the division of cortical areas of the brain
(e.g., V1, V2) that have a common function and connective topology and the links between the areas.
The links can be both anatomical and functional. [MM] it is a structural description of the human
brain, a map of structural connection patterns.
1.2. What are the two pivotal challenges of Connectome Mapping?
[WB] The 2 challenges are: a) Follow fibers through crossings; b) Objectively quantify borders
based on anatomy.
1.3. Van Essen (1992) Distributed Hierarchical Processing in the Primate Cerebral Cortex
1.3.1. How might brain connectivity vary in representation areas and control areas? [ws] This
was covered more in the lecture than the readings. The reading described the visual system
which is a representation system. The visual system has an hierarchical connectivity for both
bottom up and top down information flow with greater connectivity between close neighbors. In
the lecture there was a brief mention of domain general control areas including anterior
cingulate cortex/pre-supplementary motor area (ACC/ pSMA), dorsolateral prefrontal cortex
(DLPFC), inferior frontal junction (IFJ), anterior insular cortex (AIC), dorsal pre-motor cortex
(dPMC), and posterior parietal cortex (PPC)
1.3.2. Identify brain areas with high connectivity and comment on why that might be the
case. (Van Essen 1992) [ws] In the representation areas there is high connectivity to near
neighbors (e.g., V1-V2) and very low connectivity between modalities (e.g., V1-A1). This is
likely due to the local feedfoward and backward necessary to interpret the stimulus.
1.3.3 What is a visual hierarchy? How many visual areas were identified? What are the basic
specializations seen? [ws] There is high connectivity in the local neighborhood of the regions.
Van Essen reports 32 areas show visual responsiveness with 302 connections between areas..
There are a variety of specializations including spatial object and location (what/where) and
motion (see Figure 3).
1.3.4. How an anatomy be used to determine the direction of flow of information? [ws] Van
Essen reports 32 areas show visual responsiveness with 302 connections between areas..
There are a variety of specializations including spatial object and location (what/where) and
motion (see Figure 3).
1.3.5. Distinguish feedfoward, lateral, and feedback connections. How do their connective
layers differ? [ws] See Figure 5 differences between ascending, descending, and lateral
projections. Each has a different pattern. (F) Forward pattern terminate layer 4; (C)
Collumner pattern equal density to all layers; (M) multilayer avoids layer 4;. Forward
projections start from superficial layers feeding to layer 4 (S-F pattern) and superior and lower
(56) projections back to layer 4. Lateral connections are have the columnar connection
pattern. Feedback have a B-M (backward multilayer) pattern and I-M patter (Inferior
multilayer).
1.4. Sporns (2005) Human Connectome: A Structural Description of the Human Brai n.
1.4.1. What is a parcellation scheme and why is this an obstacle to understanding brain
science?
[sb]A parcellation scheme is a scheme or definition used to delineate or separate brain areas
from one another. It is an obstacle to understanding brain science because there is not a
universally accepted parcellation scheme for human brain regions. This also presents an
obstacle to forming the human connectome, which would greatly advance brain science.
1.4.2. What steps does Sprons suggest it will take to create a human Connectome? Which of
these steps are possible now?
[sb]There are 5 main steps for creating the human connectome.
Step 1: Diffusion-weighted imaging and probabilistic tractography of thalamocortical tracts
and corticocortical pathways. Currently possible.
1.5.5. Be able to understand Table 1 and Figure 1 and discuss the non-uniformity in the table
and its meaning.
In table 1, the numbers correspond to different types of connections. Connections
coded as ‘0’ are either projections which have been explicitly tested for and found absent of
connections which are not presently known. Connections coded as ‘1’ are one-way projections
and connections coded as ‘2’ are reciprocal. The structure in figure 1 was derived by
submitting the proximity matrix in Table 1 to non-metric multidimensional scaling using
ALSCAL.
1.5.6. Is the spatial position in the brain a good predictor of connectivity? Are there
exceptions?
Yes, the spatial position in the brain is a good predictor of connectivity. There are
exceptions. MT is distinguished topologically by its one-way projections to frontal cortex area
46and to the frontal eye fields (FEF).
1.5.7. What is the model of 2 streams with reconvergence mean? Notes it picks up a large
amount of the variance (r
The model of 2 streams with reconvergence is a two-dimensional configuration in
which the hierarchical model is dimension 1 and the two treams model is dimension 2. The
model represents dichotomization and reconvergence and accounted for almost three quarters
of the variability in Fig. 1.
2. MRI structural imaging (2a) , functional MRI (2b)
2.1. What is Resonance? [MM] Resonance is the tendency of a structure or material to oscillate at
maximum amplitude at a certain frequency.
2.1.1. What will happen if you put Hydrogen Proton in Magnetic field?
[JP] This will the change the spin so that some of the hydrogen protons will point up and some
down. They will become alligned thus allowing them to be measured outside of the body.
2.1.2. How “Child’s spinning top” is similar to Hydrogen Proton?
[JP] The precision axis is perpendicular to the force. Hydrogen protons spin just like a spinning
top. When a magnetic field is introduced they spin with a larger radius. The nuclei are not
always the same position but they rotate or precess like gyroscopes around the direction of the
field.
2.2. What is Lamer Equation?
[JP] It determines the resonance frequency. This equation gives the frequency of the RF signal
which will cause a change in the nucleus spin energy level. As a proton tries to realign with the main
magnetic field, it will emit energy at the Larmor frequency. By varying the magnetic field across the
body with a magnetic field gradient the corresponding variation of the Laramor frequency can be
used to encode the position.
.2.2.1. From where Radiofrequency energy come from?
[SS] It comes from the RF pulse given off by the scanner used to excite proton spins. The
angle and timing of the pulse are set by the user.
2.2.2. What is Gyromagetic ratio? What is the value for hydrogen proton?
[WB] Gyromagnetic ratio is a ratio between charge and mass, which is constant for a
given nucleus. The value of the gyromagnetic ratio for hydrogen proton is 42.58 MHz/T.
2.3. What is T1 and T2 relaxation and Contrast?
T1: longitudinal relaxation time
Occurs after the application of a 180 degree RF pulse, where the magnetization vector is
inverted. Then a recovery process occurs.
Tissue-specific time constant for protons, is a measure of the time taken to realign with the
external magnetic field. The T1 constant will indicate how quickly the spinning nuclei will
emit their absorbed RF into the surrounding tissue.
Starting from zero magnetization in the z direction, the z magnetization will grow after
excitation from zero to a value of about 63% of its final value in a time of T1.
T2: transverse relaxation time and pertains to the decay process.
Dependent on the amount of TE in milliseconds. (TE time of echo).
This occurs after a short waiting period (TE/2), in which a 180 degree pulse in a spin echo is
applied and an echo is formed.
2.3.1. At what point T1 and T2 contrast is maximum?
[JP] 63%
2.3.2. What affect cause T2 relaxation?
[BE] T2 relaxation is caused by the random interaction of 2 excited spins which results in a loss
of phase coherence (transverse relaxation)
The phase encoding gradient is a magnetic field gradient that allows the encoding of the
spatial signal location along a second dimension by different spin phases.
The phase encoding gradient is applied after slice selection and excitation (before the
frequency encoding gradient), orthogonally to the other two gradients.
The spatial resolution is directly related to the number of phase encoding steps (gradients).
2.10. What is k-space?
[JP] The k-space is a temporary memory of the spatial frequency information in two or three
dimensions of an object; the k-space is defined by the space covered by the phase and frequency
encoding data.
2.11. Describe in detail about what SNR is? How it can be calculated? [MM] it is the signal to
noise ratio defined as the ratio of a signal power to the noise power corrupting the signal. It
compares the level of a desired signal to the level of background noise. The higher the ratio, the less
obtrusive the background noise is. It can be calculated by (Asignal/Anoise)^2.
2.12. What is dicom, analyze and nifti format?
[JJ] These are three commonly used neuroimaging formats. Dicom is often the standard scanner
output and includes the header and data in one file. ANALYZE has the header and data in separate
files (.hdr/.img). NIFTI is an update of the ANALYZE format that usually combines the header and
data into one file (.nii/.nii.gz), but sometimes may keep them separate as in ANALYZE.
2.13. Basic Connectivity
2.14. What is functional and structural connectivity? Name some technique to measure
them.
[JJ] Functional connectivity is the temporal correlation between spatially remote
neurophysiological events. fMRI tasks are often used to explore this type of connectivity. Structural
connectivity refers to the network of physical connections (synapses) between sets of neurons and the
strength of these connections. DTI and DSI examine this type of connectivity.
2.15. Why functional and structural connectivity are same?
[JJ] Areas of the brain that exhibit temporal correlation are thought to be physically connected in
some manner.
2.16. What is effective connectivity?
[JJ] Effective connectivity describes the information flow between two neuronal groups. Specifically,
it looks at how a set of neuronal groups can causally affect the firing of other neuronal groups.
2.17. FMRI Basic
2.18. What is fMRI? How is different than MRI?
[WB] fMRI is a neuroimaging technique that uses standard MRI scanners to investigate changes in
brain functions over time.
With fMRI it is possible to study not only what the brain looks like, but also how the brain works
while MRI is mainly used for structural imaging. Operationally, functional MRI differs from
conventional MRI in two basic respects. First, it is tailored to be sensitive to contrasts in blood flow
and/or oxygenation that reflect neural activity. Second, it is typically conducted with special
hardware that permits the very rapid variation of the magnetic field gradients that are needed to
create images. This permits much more rapid acquisition of whole-brain volumes than is
conventionally done in MRI.
2.19. What is the BOLD response, what is the temporal profile?
[WB] BOLD is short for Blood Oxygenation Level Dependent. It refers to a general method of MRI
for detecting changes in the signal that are caused by the varying concentration of
deoxyhemoglobin, locally, in the blood near a part of the brain.
The BOLD hemodynamic response rises to a peak over 4-5 seconds, before falling back to baseline
(and typically undershooting slightly).
2.20. What does fMRI measure?
[WB] fMRI measures the amount of deoxygenated hemoglobin in the venous blood. Under normal
conditions, oxygenated hemoglobin (Hb) is converted to deoxygenated hemoglobin at a constant rate
within the capillary bed. But when neurons become active, the vascular system supplies more
oxygenated hemoglobin than is needed by the neurons, through an overcompensatory increase in
blood flow. This results in a decrease in the amount of deoxygenated hemoglobin and a
corresponding decrease in the signal loss due to T 2
- effects, leading to a brighter MR image.
2.21. What is the slow frequency response of on fMRI signal?
2.22. What is the tradeoff between block, fast event, and slow event related designs?
[SS] Block designs present blocks of items within a condition and analyze them all as one item.
Event-related designs present items individually so you can analyze individual items. Slow event-
related designs have a long interstimulus interval to allow the hemodynamic response to go down.
Fast event-related designs have a jittered (randomized length) interstimulus interval. Block designs
give you more power in less time, but you cannot track the timecourse of activation for a single item
because the HR does not go down between items. Slow event-related designs let you analyze each
item but it takes a lot of time to get enough items for good power. Fast event-related designs also let
you analyze each item and with less overall time, but the findings may not be as reliable.
2.23. How neural activity is correlated to fMRI signal?
[SS] The neural activity is strongly correlated with the fMRI signal.
2.24. What is active state? And one can measure spatial location of different activity?
[SS] Active state is when a participant is engaged in a task. One can isolate activity related to a
specific component of the task by comparing one condition to another condition which is similar and
only varies in that specific component.
2.25. Savoy, R (1999) Functional Magnetic Resonance Imaging (fMRI)
Solution: If the movement is not too great in amplitude or not too rapid, there are
algorithms available in most fMRI data
analysis packages that are adequate to detect the motion and transform the data in
an attempt to compensate for the effects of that motion
2.25.4. What is the typical size and timecourse of the BOLD response?
2.25.5. How do you produce a colored activation map?
[NC] (See Figure 4.) After preprocessing, comparison of the values of the functional
MR images collected during different experimental conditions are
used to generate a statistical map. Middle gray represents little difference
between the two experimental conditions in question; bright regions occur
where the first condition elicited much stronger MR signal than the second
condition; darker regions occur where the first condition elicited much
weaker MR signals than the second condition. In order to combine information
from the statistical map with the higher resolution structural images, two
transformations are applied to the statistical map. First the gray-scale intensities
used to represent the statistics are mapped into a color scale. Second,
a threshold is applied so that statistical values are within a user-defined range
close to zero are mapped to transparency. This permits the combining of
the two maps by overlaying the color map on top of the structural map
2.25.6. What are the benefits and problems of averaging across brains?
[NC]Problems: Real brains are not rigid transformations of one another
Benefits: When the abbreviated form of the Talairach transformation is
performed (brain is scaled as a whole as opposed to piecewise linear
portions for each hemisphere) comparisons are faster and simpler to
implement
2.25.7. How does a rigid body motion correct for movement? What movement effects does it
not correct for?
2.25.8. Be able to explain how all the graphs in figure 6 could be obtained and what they mean.
2.25.9. Very briefly describe an applications of fMRI in the study of one of the topics of
retinotopy, attention, emotion and affect, surgery, pharmachology, eurological/psychiatric
disorders, and dyslexia.
[NC] Pharmacology application: The good spatial resolution and moderate temporal
resolution of fMRI makes it well-suited to identifying
which functional brain systems a drug influences. Studies of the action of
clinically and socially significant drugs have revealed specific
patterns and locations via fMRI
2.26. Pooley (2005). Fundamental physics of MR Imaging
2.26.1. What is the longitudinal direction and the transverse plan for spin effects?
[YL]The direction parallel to the main magnetic field B0 is the longitudinal direction.
For typical superconducting cylindrical-bore
magnets, longitudinal direction corresponds to the head-foot direction. The plan
perpendicular to the longitudinal direction is called
transverse plane or x-y plane.
2.26.2. What is precession of the of atom spin?
[YL]If we place spinning protons in a strong magnetic field, the force from the magnetic
filed interacts with the spinning protons and
results in precession of the protons
2.26.3. What are T1 and T2 of grey, white and CSF and how might imaging be tuned to
maximize contrast?
[YL]T1 is a characteristics of tissue and is defined as the time that takes the longitudinal
magnetization to grow back to 63% of its final value.
Different tissues have different rate of T1 relaxation. White matter has a very short T1 and
relaxes rapidly. CSF has a long T1 and relaxes
slowly. Grey matter has an intermediate T1 and relaxes at an intermediate speed. If an
image is obtained at a time when the relaxation
curves are widely separated, T1-weighted contract will be maximized.
T2 is also a characteristics of tissue and is defined as the time that is takes the transverse
magnetization to decrease to 37% of its starting issue.
White matter has a short T2 and diphase rapidly. CSF has a long T2 and dephases slowly.
Gray matter has an intermediate T2 and dephases
intermediately. If an image is obtained at a time when the T2 relaxation curves are widely
separated, T2-wighted contrasts will be maximized.
2.26.4. What is spin echo. Be able to explain what is occurring in figure 18.
2.27. Jacobs (2007) MR Imaging: Brief overview and Emerging applications
2.27.1. How does MRI localize the information from the signal to create a structural image?
[DM]The key to MR localization is the Larmor frequency ( ω = γBB 0
). Application of a
different magnetic field causes the protons in a particular
location to spin with a particular frequency. Also, another magnetic field can cause
protons of a particular location to have a particular
phase. ALSO, another magnetic field selects a slice of tissue to be excited. The
combination of frequency (x direction), phase (y direction),
and slice selection (z direction) assigns every voxel in 3D space with a particular
combination of (x,y,z) / (frequency, phase, slice). When
the signal returns to the RF coil reading the signal, it can determine 3D location based
on the frequency, phase, slice.
2.27.2. How does slice selection work? What is B o
and the slice selection gradient.
[DM]The slice selection gradient (Gz) is just like the other gradients. The way that a
particular thickness of slice of tissue is chosen is via
filtering the return signal. In other words, the gradient is applied, say values from 0T to
5T, and when the RF coil excites the protons it
only excites within a bandwith, say 2.1T to 2.2T. Therefore, protons that are located
within 2.1T to 2.2T in the 0T to 5T gradient are excited.
B
refers to the main magnetic field while the RF pulse of a particular bandwith is the
B
field.
2.27.3. How does frequency encoding and phase encoding work?
[DM]The frequency gradient encodes the protons to make a complete spin in a certain
amount of time. Each proton at a certain point in the frequency
gradient will make one complete turn in a different amount of time. Phase encoding
refers to where the direction of the spin "starts". For instance,
if your finger is the vector of the spin direction flat on a table, one proton's spin will
start pointing away from you while another spin starts pointing
at you. In reference to the cartesian plane, the spin pointing away from you has 90
degree phase while the spin point at you has 270 or -90 degree
phase (Assume 0 degrees is to your right). Even if these two protons spin at the same
speed, their spins will be pointing in a different direction at any
point in time.
2.27.4. Be able to explain figure 4-6.
[DM]Figure 4 shows the frequency component of MR signal acquisition. One notices
that along the gradient (diagonal line in the box) a different frequency
is returned. S(f1) has a low frequency because it is at the wearkest gradient spot while
S(f3) has the highest frequency because it is located at the strongest
magnetic gradient position.
Figure 5 shows the phase component of MR signal acquisition. As the gradient is
applied across the brain, different phases (phi) on the cartesian plane are
encoded in the proton spins.
Figure 6 accurately depicts the T2 curve as the exponential decay of the echos returned
from the tissue. However, T1 does not seem to be correct in this figure.
One should expect T1 to be a decaying signal, not an augmented signal. Also, the curve
does not appear to be measuring any return signal, but is in fact a curve fit to
space. See another paper for a better figure of T1.
2.27.5. Explain how collecting data in k-Space allow parallel imaging of all the molecules in a
slice?
[DM]The Y-axis of K-space is determine by the phase encoding of a particular voxel,
determined by the equation: k Y
= γ (G phase encode
· t phase encode
). The idea behind
parallel imaging is to increase the number of RF coils and therefore decrease the
number of phase encoding steps. This reduction in phase encoding steps leads
to "gaps" in the k-space map. These empty spaces are mathematically estimated using
B
sensitivity profiles and basis sets.
2.27.6. Provide an example of use of T1 and T2 contrast. Be able to explain the top row of
Figure 7, how are each of the scan different and how do the expose different things (note some
of this is covered in week 3)?
[DM] Deciding whether to use T1 or T2 weighted imaging depends solely on what you
wish to see in your image. T1 makes fatty tissue bright and fluid (water) dark,
while T2 makes fluid (water) bright, fatty tissue intermediate, with solid being the
darkest. In a simple case, if you wish to highlight the CSF space, T2 would trump T1,
while if you wish to view the white matter in the brain T1 would be better.
Figure 7, particularly the top row, exploits the pros and cons of T1, T2, DWI, and ADC
imaging. T1 and T2 fail to pick up new ischemia due to a stroke in the right
occipital lobe while DWI makes it hyerintense. The ADC map shows hypointensity in the
new ischemia of the right occipital lobe and slight hyperintensity at the left
temporal lobe.
2.28. Rykhlevskaia, (2007) Combining structural and functional neuroimaging data
for studying brain connectivity: A review
3.3. Does fiber tracks calculate from fiber tractography is same as neural axons?
[sb] No, as the resolution is not high enough to show individuals axons. The calculated tracks are
fiber bundles.
3.4. What is Tensor of order 2?
[sb] Tensor order of 2 is a matrix of m x m.
3.5. Explain in brief about Eigen Value Decomposition? [MM] It is the factorization of a matrix
into canonical form, whereby the matrix is represented in terms of its eigenvalues and eigenvectors.
3.6. What are Eigen Vector and Eigen Value? [MM] given a linear transformation A, a non-zero
vector x is defined to be an eigenvector of the transformation if it satisfies the Eigenvalue equation
Ax=λx for some scalar λ. The scalar λ is called an eigen value of A corresponding to the eigenvectorx for some scalar λx for some scalar λ. The scalar λ is called an eigen value of A corresponding to the eigenvector. The scalar λx for some scalar λ. The scalar λ is called an eigen value of A corresponding to the eigenvector is called an eigen value of A corresponding to the eigenvector
x. After finding eigenvalues, it is possible to find eigenvectors.
3.7. What is principle Eigen Vector?
[JJ] It is the eigen vector which points in the direction of greatest anisotropy (associated with the
eigenvalue λx for some scalar λ. The scalar λ is called an eigen value of A corresponding to the eigenvector 1
3.8. What is Fractional Anisotropy?
[JJ] FA is a measure reflecting directional organization of the brain. It essentially reduces the shape
of the tensor into one number.
3.8.1. What does a Voxel with FA 0.0, 0.5, 1.0 represents?
[JJ] FA value of 0.0 represents a voxel with purely isotropic diffusion (spherical), 0.
represents planar diffusion, and 1.0 represents purely anisotropic diffusion (linear).
3.9. What is mean diffusivity?
[JJ] Mean diffusivity is a scalar measure of the total diffusion within a voxel.
3.10. What does Cl, Cp, Cs mean?
[JJ] C
l
, C
p
, and C s
are measures of anisotropic diffusion as proposed by Westin et. al.
C
l
is linear anisotropic diffusion where λx for some scalar λ. The scalar λ is called an eigen value of A corresponding to the eigenvector 1
is much greater than λx for some scalar λ. The scalar λ is called an eigen value of A corresponding to the eigenvector 2
and λx for some scalar λ. The scalar λ is called an eigen value of A corresponding to the eigenvector 3
(λx for some scalar λ. The scalar λ is called an eigen value of A corresponding to the eigenvector 2
≈ λx for some scalar λ. The scalar λ is called an eigen value of A corresponding to the eigenvector3).
C
p
is planar anisotropic diffusion where λx for some scalar λ. The scalar λ is called an eigen value of A corresponding to the eigenvector 1
≈ λx for some scalar λ. The scalar λ is called an eigen value of A corresponding to the eigenvector 2
and are much greater than λx for some scalar λ. The scalar λ is called an eigen value of A corresponding to the eigenvector 3
C
s
is spherical isotropic diffusion where λx for some scalar λ. The scalar λ is called an eigen value of A corresponding to the eigenvector 1
≈ λx for some scalar λ. The scalar λ is called an eigen value of A corresponding to the eigenvector 2
≈ λx for some scalar λ. The scalar λ is called an eigen value of A corresponding to the eigenvector 3
3.10.1. Why you get signal loss if you apply magnetic gradient is particular direction?
3.11. Be able to draw out the pulse sequence for diffusion imaging and explain how a
defused atom provides a different signal than an non moving atom. Be able to explain how the
gradients are used to select the slice and measure the net diffusion.
3.12. What do you understand by b-value? How you can change b-value by change
scanner parameters? List all parameters that are involved.
[WB] The b-value is the contrast “knob” in a diffusion experiment and is varied in magnitude and in
a specified number of directions. b value is proportional to the product of the square of the gradient
strength and the diffusion time interval.
We can change b-value by change the gradient strength or the diffusion time interval.
3.13. What is q-space and how it is analogues to k-space? [MM] K-space measures
XxYxZ locations and Q-space measures Xx Yx Z. Q space measures displacement and each dot
equals a 3-D image, you use a constant vector and rotate different gradient directions for single
shell.
3.14. What is FA for corpus callosum (approximately)?
[WB] Close to 1.
3.15. What assumption we make for probability density function of water molecule in
case of DTI?
[WB] DTI makes the assumption that probability density function of water molecule is zero-mean
trivariate Gaussian distribution.
3.16. In order calculate Diffusion Tensor how many parameters you need to assume?
What assumption you made while doing that?
[WB] There are 6 free parameters to assume.
A 3-by-3 tensor matrix D has 9 parameters. By assuming the symmetry of the tensor D, there are
only 6 parameters to assume, which are elements of the symmetric three-by-three matrix D. To fit the
six free parameters, we need a minimum of six A(q) with independent q, one measurement with q = 0
for normalization.
3.17. Explain what is Fiber tractography? What parameters you are going to decide
before doing fiber tractography?
[WB] DWI provides quantitative measures of the molecular motion of water in 3D space. This
information can be utilized to study the orientation of anisotropic tissues by traversing a continuous
path of greatest diffusivity from an initial set of seed points. These techniques are known as fiber
tractography.
Before doing fiber tractography, we should decide the measured diffusion tensor for each voxel and
also derive the scalar measures to characterize the isotropic (trace) and anisotropic (e.g. fractional
anisotropy) portion of the tensor to yield the direction of preferred diffusion in each voxel.
3.18. What will happen with diffusion profile, if you increase b-value?
[WB] Increasing the b-value increases the contrast between slow and fast diffusing water molecules
and works better on crossing fiber problem.
3.19. Why DTI will not work in certain part of brain for example pons?
[WB] Because there are many fibers densely packed in the pons and also many of these fibers cross
each other.
For deterministic fiber tracking, confidence intervals can be displayed for the principle
eigenvector at each voxel.
3.20.4. What is the crossing fiber problem?
[SS] The crossing fiber problem results from the inadequacy of the tensor model to characterize
fiber orientation when there is more than one fiber population within a voxel. The Gaussian
tensor model assumes a unimodal displacement probability distribution, which is not true of
voxels in which multiple fibers are present.
3.20.5. What is the distance normalization problem?
[SS] The distance normalization problem is encountered by probabilistic algorithms. They
produce maps in which the likelihood of a voxel being connected to a seedpoint decreases as
you get further away from the seedpoint, suggesting a decrease in ‘anatomical connectivity’.
However, fibers that do not branch off into other fibers should lose no information along the
pathway. Therefore the ‘functional connectivity’ of the pathway should be uniform along the
entire course of a single fiber.
3.21. Hagmann (2006) Understanding diffusion MR imaging techniques: From
scalar diffusion tensor imaging and beyond.
3.21.1. What is the displacement distribution?
[BE] The displacement distribution is a statistical concept used to describe erratic motion by
molecules during diffusion. The displacement distribution describes the proportion of molecules
that undergo a displacement in a specific direction and to a specific distance.
3.21.2. What are the six dimensions of a diffusion image?
[BE] The six dimensions of a diffusion image are the result of the combination of the p (or
position vector [x,y,z]) with the r (or displacement vector [x,y,z]). Thus the six dimensions come
from the three dimensions of the p vector and the three dimensions of the r vector.
3.21.3. What is an orientation distribution function (ODF)?
[BE] An orientation distribution function is like a deformed sphere whose radius in a given
direction is proportional to the sum of the values of the diffusion probability density function in
that direction. These values are color coded according to direction (red=x, blue=y, green=z)
3.21.4. What is q-space? How does it change as you add more directions?
[BE] Q-space is analogous to k-space, in that the concept remains the same, though the
coordinate system contains three axes (3D) and the coordinates are defined by vector q. A
single pulsed gradient SE produces one diffusion-weighted image that depicts the diffusion-
weighted signal intensity of q for every brain position. Multiple gradients and directions can be
used to determine hundreds of values for every brain position, which is decoded into an image
using a Fourier transform.
3.21.5. Why might you sample diffusion at different time intervals?
[BE] Increasing the diffusion-time interval produces and image with better directional
resolution but a lower signal-to-noise ratio. The time interval can be tweaked to provide the
ideal blend of directional resolution and signal-to-noise ratio.
3.21.6. What is the b value proportional to?
[BE] The b value is proportional to the product of the diffusion time interval and the square of
the strength of the diffusion gradient.
3.21.7. How is the diffusion tensor represented? Be able to show the what the tensor matrix
values would be for key diffusion spaces (sphere, disk, tube).
[BE] The diffusion tensor is represented as a 3x3 matrix that characterizes diffusion in 3D
space. It can also be represented as eigenvectors with corresponding eigenvalues which
describe the diffusion rate in the x, y and z axes. λx for some scalar λ. The scalar λ is called an eigen value of A corresponding to the eigenvector1 and λx for some scalar λ. The scalar λ is called an eigen value of A corresponding to the eigenvector2 (similar) >>> λx for some scalar λ. The scalar λ is called an eigen value of A corresponding to the eigenvector3 then planar/disc
shaped diffusion. If all are significantly different then anisotropic diffusion. If λx for some scalar λ. The scalar λ is called an eigen value of A corresponding to the eigenvector1>>> λx for some scalar λ. The scalar λ is called an eigen value of A corresponding to the eigenvector2 then
cigar shaped diffusion. If all are about equal then isotropic/sphere like diffusion.
3.21.8. Where does the diffusion model fail to follow fibers?
[BE] It fails in regions where several fiber populations aligned along intersecting axes cross. It
cannot map several diffusion maxima at the same time.
3.21.9. What is the difference between DTI and DSI? What are the advantages and
disadvantages of each?
[BE] DTI has a limited number of applied diffusion gradients and degrees of freedom and
thus is unable to resolve fiber crossings. DSI is not predictated on any particular hypothesis
concerning diffusion and thus is able to resolve fiber crossing and diffusion probability density
functions.
DTI: Advantages: Short acquisition time, some post processing required, provides
information about diffusion orientation and anisotropy, examination well tolerated by patients,
adequate hardware abilities readily available. Disadvantages: Hypothesis based, does not
provide accurate map of complex bier architecture, tractography results are vulnerable to
severe artifacts.
DSI: Advantages: Principle based, hypothesis free, practically validated, accurate depiction
of fiber crossings w/ specific angular resolution, maps entire field of diffusion increasing
possibility of quantitation, provides diffusion tensor information. Disadvantages: Hardware
requirements are high, acquisition time is comparatively long, whole brain studies not tolerable
for patients
3.21.10. What is q-ball imaging? (be able to understand table 1 & 2).
[BE] Q-ball imaging can account for multiple crossings of fibers within a voxel due to its
assumption that compartments inside voxels are a set of straight, thin pipes with impermeable
walls, with diffusion only in the length of the pipe. The data are reconstructed using the Funk-
Radon transform to produce high-resolution images of ‘fiber pathways’
3.22. Vilanova (2000) An introduction to visualization of diffusion tensor imaging
and its applications.
3.22.1. Know the differences of fiber kissing, crossing, and diverging.
