MIT OpenCourseWare
http://ocw.mit.edu
HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis
Fall 2006
For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms.
HST.583: Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006
Harvard-MIT Division of Health Sciences and Technology
Course Director: Dr. Randy Gollub.
Final Exam
HST.583
December 18, 2006
Instructions:
There are 130 points on this exam, unevenly distributed through 7 problems.
Please immediately confirm that you have all 10 pages. This is a two-hour exam.
Read the whole exam first. Write legibly. Describe what you are thinking. Even if the
final answer is wrong, you will be given credit for your reasoning and approach to the
problem. Be efficient, assess what you can answer right away; divide your time so that
you can cover all the problems, allocating less time to the easiest parts. Don't spend
too much time on a single question. Try not to leave questions blank; we cannot
give partial credit without something written down.
Question 1.
a)
Image courtesy of D.S. Bolar.
In the above set, the left figure represents the original image. The middle figure displays
the image after discarding (high, low) frequency k-space information. The right figure
displays the image after discarding (high, low) frequency k-space information. Please
circle the correct bolded term. (2 pts)
b) From a k-space perspective (i.e. sampling in the frequency domain), how would you
increase spatial resolution? The field-of-view (FOV)? (4 pts)
To increase FOV, k-space samples should be closer together; FOV = 1/Δk
To increase spatial resolution, it is necessary to go further out in k-space; resolution = 1/2kMAX,
approximately
Question 2.
a) Describe experimentally how spatial SNR (SNR0) and temporal SNR (tSNR) can be
estimated (you did this in lab 5). (4 pts)
1
Cite as: Dr. Randy Gollub, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006.
(Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative
Commons BY-NC-SA.
Spatial SNR can be estimated by drawing an ROI in the tissue of interest and averaging to get
the mean signal intensity (SI). The noise standard deviation can be measured by drawing an
ROI in a large region of noise outside the brain. Dividing SNR/ noise std dev will give you an
estimate of SNR0. To estimate temporal SNR, first create a mean signal map by averaging
images across the time series, (i.e. average the time-series signal on a voxel-by-voxel basis).
Next, create a standard deviation map by taking the standard deviation of the time series signal,
again on a voxel-by-voxel basis. Divide the two to get a temporal SNR map.
b) Which parameter, SNR0 or tSNR, is more relevant for functional imaging? Why? (Hint:
think about fMRI statistics and relevant metrics of significance) (4 pts)
Temporal SNR is more important for fMRI, if our goal is to measure activation (typically using
the general linear model). There are several ways to think about it: one could note that
statistical significance (as measured by a t-statistic, for example) gets larger as the variance of
the error signal gets smaller or the effect size gets larger. I.e., for an equal amount of neural
activity during a stimulus, the measured effect size (i.e. change in signal intensity from baseline
to activation) will generally increase if the mean signal is larger at baseline, and the variance of
the error signal will decrease if the standard deviation of the signal is smaller.
c) Describe two ways to increase SNR0. Describe two ways to increase tSNR. (4 pts)
Three ways to increase SNR0: increase voxel size, decrease bandwidth, increase number of
measurements/ averages. tSNR is related to SNR0 (equation in lab 5 notes). Thus, you could
theoretically list the same two ways. Other practical ways to increase tSNR are to better restrict
head motion (e.g. use a bite bar), cardiac gate, or respiratory gate to address physiological
noise.
Question 2.
The deoxyhemoglobin dilution model predicts the following relationship between the BOLD
MRI signal and CBF (figure a), and has been supported experimentally:
From Hoge, R., et al. "Investigation of BOLD signal dependence on cerebral
blood flow and oxygen consumption: the deoxyhemoglobin dilution model."
Magnetic Resonance in Medicine 42 no. 5 (1999): 849-63.
Courtesy of Wiley-Liss, Inc., a subsidiary of John Wiley & Sons, Inc. Used with permission.
2
Cite as: Dr. Randy Gollub, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006.
(Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative
Commons BY-NC-SA.
a) As relative flow increases, the relative change in BOLD response approaches an asymptotic
limit. Describe from a physiological standpoint why this may happen. (4 pts)
The asymptotic limit could be the case where the blood is fully oxygenated – i.e. there is no more
deoxyhemoglobin to give rise to BOLD signal, since it has all been washed out. Thus, blood flow
can continue to rise and not affect the BOLD signal.
b) The plot depicted is known is one of many so-called “iso-contours”, in the sense that a
specific physiologic parameter remains approximately constant on this line. To which
parameter are Hoge et. Al referring? (3 pts)
CMRO2
Question 3
The figure below describes one of the proposed models linking the applied stimulus to the
measured output response.
a) Match the following responses to the corresponding boxes, by writing the appropriate letter in
each blank. Additionally, provide a brief justification for your choice in the space provided. The
explanation should consider features of the waveform.
a.
_b__ Neural response (3 pts)
Follows stimulus temporally, but also displays habituation
(i.e. signal slowly decreases).
b.
c.
d.
_c__ CMRO2 response (3 pts)
CMRO2 will rise as firing cells begin to metabolize and
start recovering neurotransmitter, etc. Note it does not rise
as much as blood flow (which allows discrimination from
d), since the CBF increases to a greater extent.
_e__ Deoxy-Hb response (3 pts)
f.f.
e.
e.
g.
From Buxton, R. B., et al. "Modeling the hemodynamic
response to brain activation." NeuroImage 23 supplement 1
(2004): S220-S233.
Courtesy of Elsevier, Inc.,
http://www.sciencedirect.com. Used with permission
Exhibits an initial rise, before CBF has caught up to
CMRO2, after which it drops (positive BOLD response).
After the response starts returning to baseline, it exhibits an
overshoot, since the dHB transiently increases, as CBV
takes longer than CBF to return to baseline.
_f__ CBV response (3 pts)
As blood flow increases, the compliant blood vessels
expand and support more blood (because of greater
pressure).
_g__ BOLD response (3 pts)
Our final response! It features the initial dip, poststimulus undershoot, and positive main response, from
which we detect activation.
3
Cite as: Dr. Randy Gollub, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006.
(Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative
Commons BY-NC-SA.
_a__ Stimulus (3 pts)
Freebee! Given in question as the initiating event.
It is a square function, corresponding to a bock
designed fMRI task.
_d__ CBF response (3 pts)
Increases in response to vasodilatory factors
released during cellular metab,which dilate
arterioles. We can distinguish CBF from CMRO2
because it is larger (see CMRO2 above)
b) Name some candidate signaling molecules that couple event b) to events c) and d), and briefly
describe the mechanism of action. (4 pts)
CO2, NO as factors released by metabolizing neurons and/or astrocytes; cause arteriolar
dilation to increase blood flow. Glutamate is a primary neurotransmitter released in synaptic
transmission, which stimulates glycolysis and leads to increased CMRO2 and CMRGluc.
c) Traditional fMRI is based on the fact that an increase in neural activity leads to an increase in
the BOLD signal. Describe a way to increase the BOLD signal that does not require an increase
in neural activity. Why does this method work? (4 pts)
Administer CO2; stimulates vasodilation and increased blood flow (see above), without much of
an increase in neural activity or CMRO2. Azetazolamide injetion is also an acceptable answer.
Question 4.
What are the trade-offs between using a FIR model and a gamma model? (4 pts)
The gamma model will likely be more efficient and provide more powerful inference when the
model closely matches the true hemodynamic response. The FIR model will be less
efficient/powerful but will be appropriate for a much wider range of response shapes and
durations. It is possible for the gamma model to miss a response that does not match. The FIR
model should be used when an a priori model of the hemodynamic response is not known.
4
Cite as: Dr. Randy Gollub, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006.
(Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative
Commons BY-NC-SA.
Question 5.
Consider the following experimental design in which there are 10 time points (Ntp=10)
collected with a TR=2s. During this collection, two types of stimuli are presented to the subject
(Nc=2). The data will be analyzed using an FIR model with a time window of 6 seconds
(TW=6s); the analysis will also include covariates for a mean offset and linear trend.
a. How many rows and columns will the design matrix have? (2 pts)
10 x 8: 10 rows for 10 ten time points. TW/TR = 3; so three columns per condition x 2
conditions = 6 columns for FIR. Plus two columns for constant detrending (one) and linear
detrending (two). So eight columns total.
b. Write out the design matrix given that stimulus type 1 is presented at t = 0, 2, 10, 14 sec, and
stimulus type 2 is presented at t = 6, 12, 18 sec. (4 pts)
Question 6.
a) List two (2) specific goals of using Common Coordinate Systems to analyze and/or interpret
fMRI data. (4 pts)
1) to improve accuracy of the localization of functional activation,
2) permit cross subject registration of multiple fMRI scans across subjects for group level
statistics
b) Briefly describe two examples of Common Coordinate Systems commonly in use today. (4
pts)
Talairach, MNI 305, spherical space
c) Given any specific Common Coordinate System, what are inherent limitations in the use of
that coordinate system for analyzing, interpreting and sharing neuroimaging data. (4 pts)
1) Need very clean data; i.e. will have poor results if starting data is noisy, poor resolution, has
artifacts, etc. 2) Spatial normalization often involves non-rigid body transforms on data sets,
thereby changing shape and size of individual voxels (i.e. stretching, shrinking, etc.). 3) Can be
difficult to identify anatomical regions in native space. Many other acceptable answers.
Question 7. (56 points total)
5
Cite as: Dr. Randy Gollub, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006.
(Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative
Commons BY-NC-SA.
Cortex
Striatum
Substania Nigra
Because of your stellar performance in HST.583, you have just been
awarded a prestigious post-doctoral fellowship award to work the
research lab of a Nobel Laureate professor at MIT and have been
given the task of implementing the lab’s first fMRI study. The lab
uses animal models to study central nervous system control of
movement. A simplified schematic of the neural network model that
has been developed in the laboratory over the past 20 years to
explain how the brain controls movement is shown in the adjacent
Figure. (Note: the Substantia Nigra, pars reticulata is located in the
midbrain- middle part of the brainstem).
Thalamus
The lab director is hugely enthusiastic about launching this new imaging initiative, and despite
her lack of imaging experience, on your first day in the lab she outlines the following proposal
for the work you will do in her lab. She wants you to conduct a pilot experiment to test her
hypothesis that in the human brain each of the four regions in the neural network shown in the
Figure will show increased fMRI signals during both imagined and real motor movements.
She has a very limited budget (she is used to doing behavioral experiments) and so tells you that
the pilot will be limited to scanning two (2) subjects and that this should be sufficient to generate
preliminary data for a grant as well as a good manuscript. Each subject will be scanned during
rest, during complex bilateral finger movements and during mental imagery of the same complex
bilateral finger movements. With the help of a collaborating cognitive scientist she has
determined that 10 minute long scans during which the subject performs an event related
experimental paradigm would be optimal. She proposes to repeat this paradigm 6 times (collect
6 identical scans) during the session.
She tells you that you will be using the new Trio TIM 3T scanning system at the Martinos
Center. You know that the Martinos Center has both a head coil and an occipital surface coil
available. However, she asks you to collect data using only the surface coil centered over the
back of the subject’s head.
For the functional scans she suggests using a T2-weighted EPI sequence, with TE=10ms,
TR=1000ms and flip angle 90 degrees and a TR of 1 second. She wants to collect 30 coronal
slices each 8 mm thick so she can have whole brain coverage.
For the anatomical scan she wants you to use a proton density image that has a high signal-tonoise ratio and can be acquired very fast (50 seconds) with high spatial resolution.
She is all excited about a new image analysis software package that allows the user to enter all
the experimental variables in the beginning, upload the scan data then press a button and it
returns (after a night of unspecified processing) statistical maps of the results.
Drawing upon the wisdom and knowledge you gained in HST.583, you take a deep breath and
prepare yourself to critically evaluate the decisions she has made.
6
Cite as: Dr. Randy Gollub, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006.
(Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative
Commons BY-NC-SA.
a) What is your opinion about using a cohort size of 2 subjects to test a hypothesis in an fMRI
study? What is your recommendation for the number of subjects to study and why? (4 pts)
Answer: fMRI data is noisy, signals are small and subjects highly variable. With too small of a
sample size, she may miss a real finding completely if the activations in regions are near
threshold for detection or if have much inter-subject variability in localization. This is especially
important for the smaller brain regions, such as the SNr and thalamus. A minimal sample size to
draw meaningful conclusions is typically 12-16 (anecdotally, for many fMRI studies). The actual
required sample size, however, required depends on several factors; specifically the expected
effect size and the desired power.
For 4 BONUS points:
b) What is your recommendation for how to best estimate an appropriate sample size?
Answer: Power analysis with effect size and standard deviation would be optimal, could use the
initial 2 subjects to help gain that info, but better to use a published study with similar design
and equipment.
c) What is your opinion about using an event related design for the initial study? Defend or
refute this choice and make your own recommendation giving your rationale. Include in your
recommendation a VERY specific description of your proposed paradigm(s). Be sure to cover
what the subject is instructed to do, how instructed, the timing, etc. Include a schematic
drawing. You will use this design to answer more questions below, so read ahead to be sure you
are including all necessary information. (14 pts)
Answer: First experiments typically begin with a block design to maximize power to detect
regional activation. She is proposing to spend 6 10 minute long scans doing a event related
paradigm. A less risky proposal would be to invest in a few block design trials to identify the
voxels of interest and then use the event related paradigm to look at the hemodynamic response
times of the components of the network. Also, she made no mention of parametrically varying
the motor task to allow a more robust detection of movement correlated activation. Such
variations could include the dimension of time (duration of movement), complexity, numbers of
fingers used.
A minimum of two event types must be specified; complex finger movement and imagined finger
movement and the duration of each event specified. Adequate time must be given for rest
(control condition). Each trial should be 1-5 sec long. We need plenty of trials to have statistical
power, so given 10 minutes scan could do about 100 trials per scan. Either spaced events spaced
about 16 sec or rapid presentation with 5-10sec with jitter. The number of trials needs to be
provided along with information about whether the events are being timed for a block, spaced
single trial or rapid event related analysis.
7
Cite as: Dr. Randy Gollub, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006.
(Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative
Commons BY-NC-SA.
To be able to average data across all scans, need to have stable performance of the task during
real movement so must practice prior to scans until achieve plateau performance. This also
indicates need to collect behavioral data to verify performance accuracy, speed etc. Otherwise,
learning/memory effects may confound results. This training will also help to equilibrate the
attention level of subjects and will help equilibrate the imagery component across subjects.
Keeping still for 10 minutes is difficult for some subjects; a larger number of shorter scans
(~5minutes) may yield better quality data with less motion artifact.
d) Do you agree with her choice of acquisition parameters for the anatomical image? For the
functional images (TE, TR, flip angle, slice thickness, number)? Why or Why not? If not, what
would you change and why? Are there additional acquisition sequences you recommend? If so,
specify the rationale for adding the scan and the acquisition parameters.
For the anatomical image: (3 pts)
What matters is good contrast between gray and white matter. Use a sequence that has high
spatial resolution and T1 contrast. PD does not. They should recommend an MPRAGE or
FLASH or SPGR type scan.
For the functional images:
1) The imaging sequence: T2-weighted EPI (3 pts)
We want BOLD contrast. The strongest BOLD contrast is obtained with T2* weighted
images, like gradient-echo EPI. Spin-echo EPI offers less susceptibility distortions but 5
times less BOLD sensitivity. So, I would start using the imaging method that is most
sensitive. Then, if I find that the activation could be in or close to an area where there are
strong susceptibilities, I'd try spin-echo EPI. But I would start with gradient-echo EPI.
Spiral is okay too.
2) Sequence parameters: TE (3 pts)
8
Cite as: Dr. Randy Gollub, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006.
(Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative
Commons BY-NC-SA.
For optimal T2* weighting I need TE~T2* from gray matter, which is about 30ms at 3T. If I
don't know this then I have to ask the physicist in charge of the magnet and/or check the
literature.
3) Sequence parameter: TR/flip angle (3 pts)
To have maximal signal in each image I would check that the flip angle is optimized for the
TR given. For this I need the T1 of gray matter at 3T. Again, literature or the physicist can
help me.
4) Sequence parameters: slices (thickness, number) (3 pts)
With the four a priori hypothesized Regions of Interest, I could reduce the number of slices
to cover just a certain area. (With fewer slices I will be less limited in my choice of TR.)
The hand representation in S1/M1 is on the lateral surface about 1/3 of the way from the top
of the brain, so the acquisition would need to include oblique axial slices though the middle
2/3 of the brain. I actually recommend whole brain imaging because it greatly improves
registration.
The thickness of the slices should be around 3 to 4 mm. Thicker slices will give higher SNR
but more partial volume effects and higher signal loss in brain areas with strong
inhomogeneity in the magnetic field (e.g., close to the sinuses). If the slices are too thin (say
less than 2mm) then the SNR will be low and so will be the ability to detect BOLD signal
changes.
If I don't have an a priori hypothesis, then I'd scan the whole head with the head coil.
Scanning a large number of slices will have an effect on the minimum TR. I'd have to check
the maximum number of slice per TR that are in agreement with the scanner hardware
limitations and safety rules. If the limitations are serious I might have to modify the
paradigm.
5) Additional sequence? (3 pts)
It might be useful to acquire a flow-weighted image to get an idea of the local vasculature in
areas of activation. This could be used to discard large BOLD effects coming from large
draining veins.
Given the inclusion of the SNr in the proposed network they might suggest adding some cardiac
gated acquisitions to improve our detection of activation in this region of the brain.
e) Do you agree with her decision to use the surface coil? Why or Why not? (4 pts)
Answer: The a priori hypothesis includes both cortical and subcortical brain areas and the plan
is to collect 30 slices through the brain. That requires use of the head coil. If only occipital
areas were of interest, surface coil might be more useful due to better CNR.
f) Finally, drawing another deep breath, you ask if she knows exactly what is done to the data by
the fMRI analysis program. After ascertaining that she has no appreciation of the complexities of
9
Cite as: Dr. Randy Gollub, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006.
(Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative
Commons BY-NC-SA.
fMRI signal processing, you endeavor to describe exactly how you propose to analyze this data
set.
Your written response can be a list of words or phrases, one per step followed by a phrase that
justifies the step. Include all pre-processing steps, statistical modeling methods and parameters.
For the statistical model, refer back to your experimental paradigm to specify each condition.
Include your contrasts and what specific hypothesis each will be used to test. (14 pts)
At minimum should have motion correction, spatial normalization, intensity normalization
preprocessing steps. May also include smoothing, noise estimation.
GLM should include nusiance terms such as linear drift, respiratory measures, etc. Event types
or conditions would include trials of rest (control condition), complex finger movement and
imagined finger movement. If parametrically varying any of them, then should be properly
specified. The contrasts for the statistical analysis would be: movement vs. rest (H0: movement
of the fingers activates the 4 ROIs), imagined vs. rest (H0: imagined movement of the fingers
activates the same 4 ROIs), and movement vs. imagined as well as a conjunction analysis (direct
investigation of the overlap in networks).
If two subjects- FIXED effects, otherwise MIXED or Random effects.
FILL IN BLANK FOR EXTRA CREDIT!
Top ten signs you've been scanning too much...
(Courtesy of Jody Culham, http://psychology.uwo.ca/fmri4newbies/ScanningTooMuch.html)
10. While pouring syrup on your Eggo waffles, you note that you missed a few voxels.
9. Your knowledge of brain anatomy exceeds your knowledge of geography. As in, "The
transverse occipital sulcus intersects the intraparietal sulcus near the level of the parieto-occipital
fissure" and "The Sahara is in Afghanistan, I think."
8. You have developed a rapid ritual for checking your body for metal that resembles the
macarena.
7. When you see drawings of brains in the popular media, you instantly decide whether or not
they are anatomically correct.
6. Friends wonder how you can run a four million dollar scanner and still fail to program a
VCR.
5. You suffer frequent left/right confusion and find yourself saying things like, "Make a left turn
at the lights... No, I meant a *radiological* left!"
4. At parties, you scope out people's subject-worthiness: "It was great talking to you. Say, what
are you doing Friday night?... Do you have any metal in your body?..."
3. Not only can you recognize the brains of your frequently-scanned co-workers, but also their
teeth from the bite bar impressions.
10
Cite as: Dr. Randy Gollub, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006.
(Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative
Commons BY-NC-SA.
2. When reminded of a special occasion, you remember it fondly because the scanner was free
all day long and you collected lots of good data.
1. __________________________________________________________________________
____________________________________________________________________________
THANKS FOR YOUR PARTICIPATION AND HAVE A GREAT HOLIDAY!!
- Randy & Div
11
Cite as: Dr. Randy Gollub, HST.583 Functional Magnetic Resonance Imaging: Data Acquisition and Analysis, Fall 2006.
(Massachusetts Institute of Technology: MIT OpenCourseWare), http://ocw.mit.edu (Accessed MM DD, YYYY). License: Creative
Commons BY-NC-SA.