fMRI Methods Lecture4

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fMRI MethodsLecture4 Single subject analyses
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T2
Static main field
Excitation pulse
Spin phase
Transverse magnetization
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T2 T2T2
After 900 spin presses in-phase
T2
Includes ratio of oxy/deoxy blood
DEPHASING
T2
T2
Temporary and permanent on a timescale of 100ms
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T2 T2T2
T2 is far stronger than T2 and governs T2
decay. Most importantly T2 relaxation
(de-phasing) is reversible because it is caused
by permanent local magnetic inhomogeneities
(e.g. main and gradient magnetic fields, amount
of deoxygenated blood, tissue composition,
etc). T2 relaxation (de-phasing) is
non-reversible because it is caused by
temporary random spin-spin interactions (random
push and shove by neighboring spins). Extent of
spin-spin interactions depends on tissue
structure.
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Spin echo sequence
Reverse the order of spins and refocus the
magnetization.
Magnetization will not refocus to the original
strength.
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Spin echo sequence
The 180 pulse will refocus only the de-phasing
caused by T2 relaxation (permanent
inhomogeneities). Remaining relaxation/de-phasin
g is due to T2 relaxation.
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HRF linear shift invariant system
Stimulus
HRF
HRF
Time Invariance
Scaling
Additivity
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Convolution
Multiply each timepoint of the neural response by
a copy of the HRF
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Block design
We can build a model of the expected neural
activity and the ensuing hemodynamic changes.
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Temporal summation
Importance of block length and inter stimulus
interval when dealing with temporal summation.
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Correlation maps
Correlate the fMRI time-courses in each voxel
with the hemodynamics model
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General linear model
Determine the strength of the modeled neural
response
predictor
beta
data
residuals


error
a1

We want to find a1 that will minimize the error
term (best fit).
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Projection
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Projection
64,000 voxels
predictor
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Multiple predictors
Separate column in the design matrix for each
condition.
design matrix
beta
data
residuals


error
a1 a2

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Explaining variability
Every fMRI time-course has certain variability
What causes the fMRI to vary across time?
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Explaining variability
Were decomposing the variability into components


a1 a2
error

var(data) var(a1x1) var(a2x2) var(error)
The variance in the data equals the summed
variances of the components used to explain it.
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Estimating confidence
var(data) var(a1x1) var(a2x2) var(error)
F statistic can be translated into a p value
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Estimating confidence
t b/sqrt(var(res)pinv(modelmodel'))
T statistic can be translated into a p value
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Baseline/Rest
Beta values depict the scale of the response as
compared with baseline.
data
A small beta means that the hemodynamic activity
varied little between baseline and stimulation
period.

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Contrasts
Are there brain areas that respond more to faces
than to objects?
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Contrasts
Compute the betas for each voxel and identify
voxels where they differ significantly.
Objects
Faces
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Contrast significance
Beta 1
Beta 2
Translate the t value to a p value to assess
statistical significance chance of making a type
I error (false positive) is below 5 (p value lt
0.05).
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T test
The significance of a t value depends on the
number of samples degrees of freedom.
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Elaborate contrasts
Compare responses across multiple conditions
Gets funky!
Sad
Angry
Happy
Funny
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Statistical parameter maps
Paint the voxels by the statistical significance
of the p values
Around 64,000 voxels in a standard fMRI scan.
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Multiple comparisons
Using the same statistical test repeatedly on
independent samples, increases the likelihood of
type I errors (false positives).
If we assign a pair of random beta values to each
of the 64,000 voxels, 3,200 of them (5 of the
sample) will show a significant difference...
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Bonferroni
One option is to lower the p value for each
comparison so that the cumulative p value is
0.05. Bonferroni correction p/n
Using this correction would mean lowering the
significance threshold to 0.05/64,000 7.8
10-7
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Random field theory
Voxels are not independent random variables,
neighboring voxels are highly correlated. So the
Bonferroni method over estimates the number
independent statistical tests. The actual number
of independent tests depends on how spatially
correlated the voxels are. This can be determined
using Gaussian random fields num_independent_te
sts num_voxels / V3 V is the
full-width-half-maximum of the estimated
gaussian describing how smooth (spatially
correlated) the data is
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Cluster thresholding
Reduce the number of independent tests by working
on voxel clusters of a given size. Number of
expected false positive voxels in 1010
slice 0.05 100 5 Number of expected false
positive neighboring voxel pairs 0.05 0.05
360 0.9 Number of expected threesomes 0.05
0.05 0.05 520 0.06 P 1 (1 pc)nc
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False discovery rate
Made in Israel!
Estimates the number of false positives (type I
error) given the data.
total of voxels
Want to keep this lt 0.05
The solution depends on the number of significant
voxels and the level of their significance.
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False discovery rate
Lets say that we found 500 significant voxels (p
lt 0.05) before correcting for multiple
comparisons. We sort only the significant
voxels by their significance Then we find the
largest k such that Lets say we have the
following values P(1) 0.00003 1/5000.05
0.0001 P(2) 0.00008 2/5000.05 0.0002 P(3)
0.00014 3/5000.05 0.0003
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Beware of statistical thresholding
Threshold is always arbitrary!
From looking at these maps you dont know how big
the difference between betas really is or
anything about the actual responses
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Beware of statistical thresholding
Strong response?

fMRI response
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Regions of interest
Select the voxels of interest and average across
them to get a single time-course per ROI. Run
same GLM analysis to estimate betas per ROI.

fMRI response
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Beware of circularity
Is it informative that theres a significant
difference between the betas in this ROI?

fMRI response
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Regions of interest
We can now compare how neural populations in a
certain ROI respond under different experimental
manipulations. For example, we can correlate
response and reaction time.
Response amplitude
Reaction time
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Event related design

• Block design is very limiting
• Issues of attention (predictability, novelty)
• Temporal summation
• Break down a task into different temporal
  components
• There are many experimental situations where you
  want to measure neural responses to brief events
  (e.g. memory encoding, motor control, spatial
  attention).

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Event related design
Sparse event related design
Regular event related design
Will work as long as our predictors are
independent Random/Counter-balanced order,
jitter.
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Event related design
Jitter random temporal spacing of trials
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Event related design
Solve a GLM just like before
design matrix
beta
data
residuals


error
a1 a2

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Deconvolution
In a simple sparse event related design
So far weve been building a design matrix that
contains a single predictor constraining the
solution to the predefined HRF. Only had one
free parameter to fit
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Deconvolution
Build a design matrix with several
predictors/columns corresponding the consecutive
time-points of the response.


error
a1 a2 an

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Deconvolution
Jittering is particularly important for
de-convolution
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Deconvolution
We can scale this to deconvolve the responses of
multiple conditions (large models with many
columns)


a1 a2 an
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Deconvolution
Finally we can put error bars on the beta weights
as before
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Deconvolution
There is a price to enlarging the model (adding
predictors) Noise Constraining the model with
a canonical HRF gives a more robust solution, but
depends on the accuracy of the HRF used
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Trial triggered average
Cut out the trials from your time-course
Normalize each trial to its first two
samples The idea is that you expect the same
relative response in each trial.
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Trial triggered average
Inspired by ERP Jitter and randomness very
important Error bars are simply the standard
error of the mean
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Statistics on time-courses




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To the lab!
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Open a folder for your code on the local
computer. Try to keep the path name simple (e.g.
C\Your_name).Download code and MRI data
fromhttp//www.weizmann.ac.il/neurobiology/labs/
malach/ilan/lecture_notes.htmlSave Lab4.zip in
the folder youve created and unzip.Open
Matlab. Change the current directory to the
directory youve created.Open
Lab4_SingleSubjectAnalyses.m
Lab 4
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Matlab exercise email me the report as a word
document. The report should include answers,
figures, and the actual Matlab code used to
generate them (copy it into word).
Homework!