Single session analysis using FEAT

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Single session analysis using FEAT

• David Field
• Thanks to.
• Tom Johnstone, Jason Gledhill, FMRIB

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Single session or first level FMRI analysis

• In FMRI you begin with 1000s of time courses,
  one for each voxel location
• Lots of preprocessing is applied to maximise
  the quality of the data
• Then, each voxel time course is modelled
  independently
• the model is a set of regressors (EVs) that vary
  over time
• the same model is applied to every voxel time
  course
• if (part of) the model fits the voxel time course
  well the voxel is said to be active

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Plan for today

• Detailed look at the process of modelling a
  single voxel time course
• The input is a voxel time course of image
  intensity values and the design matrix, which is
  made up of multiple EVs
• The GLM is used to find the linear combination of
  EVs that explains the most variance in the voxel
  time course
• The output is a PE for each EV in the design
  matrix
• Preprocessing of voxel time courses
• this topic probably only makes much sense if you
  understand 1) above, which is why I am breaking
  with tradition and covering this topic second
  rather than first
• Implementing a single session analysis in FSL
  using FEAT (workshop)
• Note There is no formal meeting in week 3 of the
  course, but the room will be open for you to
  complete worksheets from today and last week
• at least one experienced FSL user will be here to
  help

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Preprocessing.
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• The BET brain extraction option refers to the 4D
  functional series
• This will not run BET on the structural
• Normally turn this on
• Brain extraction for the structural image that
  will be used as the target for registration has
  to be performed by you, before you use FEAT to
  set up the processing pipeline

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• On the Misc tab you can toggle balloon help
• Balloon help will tell you what most of the
  options mean if you hover the mouse over a button
  or tickbox
• But it gets annoying after a while
• If progress watcher is selected then FEAT opens a
  web browser that shows regular updates of the
  stage your analysis has reached

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Motion Correction MCFLIRT

• Aims to make sure that there is a consistent
  mapping between voxel X,Y,Z position and actual
  anatomical locations
• Each image in the 4D series is registered using a
  6 DOF rigid body spatial transform to the
  reference image (by default, the series mid
  point)
• This means every image apart from the reference
  image is moved slightly
• MCFLIRT plots the movements that were made as
  output

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MCFLIRT output
Head rotation
Head translation
Total displacement
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The total displacement plot
displacement is calculated relative to the volume
in the middle of the time series
Relative displacement is head position at each
time point relative to the previous time point.
Absolute displacement is relative to the
reference image.
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The total displacement plot
Why should you be particularly concerned about
high values in the relative motion plot?
The first thing to do is look at the range of
values plotted on the y axis, because MCFLIRT
auto-scales the y axis to the data range
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Slice timing correction
Each slice in a functional image is acquired
separately. Acquisition is normally interleaved,
which prevents blending of signal from adjacent
slices Assuming a TR of 3 seconds and, what is
the time difference between the acquisition of
adjacent slices?
A single functional brain area may span two or
more slices
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Why are the different slice timings a problem?

• The same temporal model (design matrix) is fitted
  to every voxel time course
• therefore, the model assumes that all the voxel
  values in a single functional volume were
  measured simultaneously
• Given that they are not measured simultaneously,
  what are the implications?
• Consider two voxels from adjacent slices
• both voxels are from the same functional brain
  area
• this time the TR is 1.5, but the slice order
  differed from the standard interleaved procedure,
  so there is a 1 sec time gap between acquisition
  of two voxels in the adjacent slices that cover
  the functional brain area

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• Blue line real HRF in response to a brief event
  at time 0

Blue squares intensity values at a voxel first
sampled at 0.5 sec, then every 1.5 sec thereafter
(TR 1.5)
Red circles intensity values at a voxel from an
adjacent slice first sampled at 1.5 sec, then
every 1.5 sec thereafter (TR 1.5)
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These are the two voxel time courses that are
submitted to the model
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The model time course is yoked to the mid point
of the volume acquisition (TR), so there will be
a better fit for voxels in slices acquired at or
near that time.
These are the two voxel time courses that are
submitted to the model
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Slice timing solutions

• Any ideas based on what was covered earlier?
• Including temporal derivatives of the main
  regressors in the model allows the model to be
  shifted in time to fit voxels in slices acquired
  far away from the mid point of the TR
• But,
• this makes it difficult to interpret the PEs for
  the derivatives do they represent slice timing,
  or do they represent variations in the underlying
  HRF?
• and, you end up having to use F contrasts instead
  of t contrasts (see later for why this is to be
  avoided if possible)

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Slice timing solutions

• Any ideas based on what was covered earlier?
• Use a block design with blocks long enough that
  the BOLD response is summated over a long time
  period
• But,
• Not all experimental stimuli / tasks can be
  presented in a block design
• So,
• another option is to shift the data from
  different slices in time by small amounts so that
  it is as if all slices were acquired at once
• this is what the preprocessing option in FEAT
  does

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Shifting the data in time - caveats

• But if the TR is 3 seconds, and you need to move
  the data for a given slice by, e.g., 1 sec, you
  dont have a real data point to use
• get round this by interpolating the missing time
  points to allow whole voxel time courses to be
  shifted in time so effectively they were all
  sampled at once at the middle of the TR
• But
• Interpolation works OK for short TR, but it does
  not work well for long TR (gt 3 sec?)
• So this solution only works well when slice
  timing issues are relatively minor
• There is a debate about whether to do slice
  timing correction before or after motion
  correction
• FSL does motion correction first
• some people advise against any slice timing
  correction
• Generally, if you have an event related design
  then use it, but make sure you check carefully
  with the scanner technician what order your
  slices were acquired in!

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Temporal filtering

• Filtering in time and/or space is a
  long-established method in any signal detection
  process to help "clean up" your signal
• The idea is if your signal and noise are present
  at separable frequencies in the data, you can
  attenuate the noise frequencies and thus increase
  your signal to noise ratio

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AAAAAAAVVVVVVVRRRRRRRAAAAAAAVVVVVVVRRRRRRR
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AAAAAAAVVVVVVVRRRRRRRAAAAAAAVVVVVVVRRRRRRR
Time
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Raw data
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After low pass filter
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Very low frequency component, suggests that high
pass filter also needed
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Low and high frequencies removed
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Setting the high pass filter for FMRI

• The rule recommended by FSL is that the lowest
  setting for the high pass filter should be equal
  to the duration of a single cycle of the design
• In an ABCABCABC block design, it will be equal to
  ABC
• If you set a shorter duration than this you will
  remove signal that is associated with the
  experiment
• If you set a higher duration than this then any
  unsystematic variation (noise) in the data with a
  periodic structure lower in frequency than the
  experimental cycle time will remain in voxel time
  courses
• In complicated event related designs lacking a
  strongly periodic structure there is a subjective
  element to the setting of the high pass filter

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Setting the high pass filter for FMRI

• Do not use experimental designs with many
  conditions where the duration of a single
  experimental cycle is very long
• e.g. ABCDEABCDE, where ABCDE 300 seconds
• setting the high pass to 300 sec will allow a lot
  of the low frequency FMRI noise to pass through
  to the modelling stage
• Furthermore, the noise can easily become
  correlated with the experimental time course
  because you are using an experimental time course
  that has a similar frequency to that of FMRI
  noise
• In any signal detection experiment, not just
  FMRI, you need to ensure that the signal of
  interest and noise are present at different
  temporal frequencies

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Low pass filter?

• As well as removing oscillations with a longer
  cycle time than the experiment, you can also
  elect to remove oscillations with a higher cycle
  time than the experiment
• high frequency noise
• In theory this should enhance signal and reduce
  noise, and it was practiced in the early days of
  FMRI
• However, it has now been demonstrated that
  because FMRI noise has temporal structure (i.e.
  it is not white noise), the low pass filter can
  actually enhance noise relative to signal
• The temporal structure in the noise is called
  temporal autocorrelation and is dealt with in
  FSL using FILM prewhitening instead of low pass
  filtering
• in another break with the traditional structure
  of FMRI courses temporal autocorrelation and
  spatial smoothing will be covered after t and F
  contrasts

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After preprocessing and model fitting

• You can now begin to answer the questions you set
  out to answer.

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Which voxels activated in each experimental
condition?

• In the auditory / visual stimulus experiment, how
  do you decide if a voxel was more activated
  during the visual stimulus than the baseline?
• If the visual condition PE is gt 0 then the voxel
  is active
• but gt 0 has to take into account the noise in the
  data
• We need to be confident that if you repeated the
  experiment many times the PE would nearly always
  be gt 0
• How can you take the noise into account and
  quantify confidence that PE gt 0?
• PE / residual variation in the voxel time course
• this is a t statistic, which can be converted to
  a p value by taking into account the degrees of
  freedom
• The p value is the probability of a PE as large
  or larger than the observed PE if the true value
  of the PE was 0 (null hypothesis) and the only
  variation present in the data was random
  variation
• FSL converts t statistics to z scores,
  simplifying interpretation because z can be
  converted to p without using deg of freedom

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Why include effects of no interest in the model?

• Also called nuisance regressors
• Imagine an experiment about visual processing of
  faces versus other classes of object
• Why add EVs to the design matrix based on the
  time course of
• head motion parameters
• image intensity spikes
• physiological variables
• galvanic skin response, heart rate, pupil
  diameter
• Answer to reduce the size of the residual error
  term
• t will be bigger when PE is bigger, but t will
  also be bigger when error is smaller
• You can model residual variation that is
  systematic in some way, but some of the residual
  variation is truly random in nature, e.g. thermal
  noise from the scanner, and cannot be modelled out

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t contrasts

• Contrast is short for Contrast of Parameter
  Estimates (COPE)
• it means a linear sum of PEs. The simplest
  examples are implicit contrasts of individual
  PEs with baseline. Using the example from the
  interactive spreadsheet
• visual PE 1 auditory PE 0
• visual PE 0 auditory PE 1
• To locate voxels where the visual PE is larger
  than the auditory PE
• visual PE 1 auditory PE -1
• To locate voxels where the auditory PE is larger
  than the visual PE
• visual PE -1 auditory PE 1

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t contrasts

• The value of the contrast in each voxel is
  divided by an estimate of the residual variation
  in the voxel time course (standard error)
• produces a t statistic of the contrast
• residual variation is based on the raw time
  course values minus the predicted values from the
  fitted model
• Activation maps (red and yellow blobs
  superimposed on anatomical images) are produced
  by mapping the t value at each voxel to a colour
• crudely, thresholding is just setting a value of
  t below which no colour is assigned.

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What will the 1 1 contrast give you?
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F contrasts

• These can be used to find voxels that are active
  in any one or more of a set of t contrasts
• Visual Auditory Tactile
• 1 -1 0
• 1 0 -1
• F contrasts are bidirectional (1 -1 also implies
  -1 1)
• rarely a good thing in practice..
• If the response to an event was modelled with the
  standard HRF regressor plus time derivative then
  you can use an F contrast to view both components
  of model of the response to the event on a single
  activation map
• If you are relying on the time derivative to deal
  with slice timing correction then you are
  strongly advised to do this

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Thresholding / multiple comparisons problem
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Temporal autocorrelation

• The image intensity value in a voxel at time X is
  partially predictable from the same voxel at
  times X-1, X-2, X-3 etc (even in baseline scans
  with no experiment)
• why is this a problem?
• it makes it hard to know the number of
  statistically independent observations in a voxel
  time course
• life would be simple if the number of
  observations was equal to the number of
  functional volumes
• temporal autocorrelation results in a true N is
  lower than this
• Why do we need to know the number of independent
  observations?
• because calculating a t statistic requires
  dividing by the standard error, and the standard
  error is SD / square root (N-1)
• Degrees of freedom are needed to convert t stats
  to p values
• If you use the number of time points in the voxel
  time course as N then p values will be too small
  (false positive)

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Measuring autocorrelation
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Measuring autocorrelation
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Measuring autocorrelation
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Measuring autocorrelation (SPSS style)
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Plot the correlation against the degree of shift
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Temporal autocorrelation

• Generally, the value of a voxel at time t is
  partially predictable from nearby time points
  about 3-6 seconds in the past
• So, if you use a very long TR, e.g. 6, then you
  mostly avoid the problem as the original time
  points will have sufficient independence from
  each other
• Voxel values are also predictable from more
  distant time points due to low frequency noise
  with periodic structure
• but the high pass filter should deal with this
  problem

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Autocorrelation FILM prewhitening

• First, fit the model (regressors of interest and
  no interest) to the voxel time course using the
  GLM
• (ignoring the autocorrelation for the moment)
• Estimate the temporal autocorrelation structure
  in the residuals
• note if model is good residuals noise?
• The estimated structure can be inverted and used
  as a temporal filter to undo the autocorrelation
  structure in the original data
• the time points are now independent and so N
  the number of time points (volumes)
• the filter is also applied to the design matrix
• Refit the GLM
• Run t and F tests with valid standard error and
  degrees of freedom
• Prewhitening is selected on the stats tab in FEAT
• it is computationally intensive, but with a
  modern PC it is manageable and there are almost
  no circumstances where you would turn this option
  off

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Spatial smoothing

• FMRI noise varies across space as well as time
• smoothing is a way of reducing spatial noise and
  thereby increasing the ratio of signal to noise
  (SNR) in the data
• Unlike FMRI temporal noise, FMRI spatial noise is
  more like white noise, making it easier to deal
  with
• it is essentially random, essentially independent
  from voxel to voxel, and has as mean of about
  zero
• therefore if you average image intensity across
  several voxels, noise tends to average towards
  zero, whereas signal that is common to the voxels
  you are averaging across will remain unchanged,
  dramatically improving the signal to noise ratio
  (SNR)
• A secondary benefit of smoothing is to reduce
  anatomical variation between participants that
  remains after registration to the template image
• this is because smoothing blurs the images

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Spatial smoothing FWHM

• FSL asks you to specify a Gaussian smoothing
  kernel defined by its Full Width at Half Maximum
  (FWHM) in mm
• To find the FWHM of a Gaussian
• Find the point on the y axis where the function
  attains half its maximum value
• Then read off the corresponding x axis values

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Spatial smoothing FWHM

• The Gaussian is centred on a voxel, and the value
  of the voxel is averaged with that of adjacent
  voxels that fall under the Gaussian
• The averaging is weighted by the y axis value of
  the Gaussian at the appropriate distance

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No smoothing
4 mm
9 mm
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Effects of Smoothing on activations
Unsmoothed Data
Smoothed Data (kernel width 5 voxels)
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When should you smooth? When should you not?

• Smoothing is a good idea if
• You're not particularly concerned with
  voxel-by-voxel resolution.
• You're not particularly concerned with finding
  small (less than a handful of voxels) clusters
• You want (or need) to improve your
  signal-to-noise ratio
• You're averaging results over a group, in a brain
  region where functional anatomy and organization
  isn't precisely known
• You want to use p-values corrected for multiple
  comparisons with Gaussian field theory (as
  opposed to False Discovery Rate)
• this is the Voxel option in FSL and the FWE
  option in SPM
• Smoothing kernel should be small (or no
  smoothing) if
• You need voxel-by-voxel resolution
• You believe your activations of interest will
  only be a few voxels in size
• You're confident your task will generate large
  amounts of signal relative to noise
• You're working primarily with single-subject
  results
• You're mainly interested in getting
  region-of-interest data from very specific
  structures that you've drawn with high resolution
  on single subjects

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How do you determine the size of the kernel?

• Based on functional voxel size? Or brain
  structure size?
• A little of both, it seems.
• The matched filter theorem, from the signal
  processing field, tells us that if we're trying
  to recover a signal (like an activation) in noisy
  data (like FMRI), we can best do it by smoothing
  our data with a kernel that's about the same size
  as our activation.
• Trouble is, though, most of us don't know how big
  our activations are going to be before we run our
  experiment
• Even if you have a particular structure of
  interest (say, the hippocampus), you may not get
  activation over the whole region - only a part
• A lot of people set FWHM to functional voxel size
  2

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Old slides beyond this point
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Slice timing correction

• Each functional volume that forms part of the 4D
  time series is made up of slices
• Each slice is acquired at a different point in
  time relative to the start of the TR
• e.g., slice 1 at 100 msec, slice 2 at 200 msec,
  etc
• For each slice, its the same time point relative
  to the start of the TR in every volume
• So, the interval between successive acquisitions
  is constant for every voxel
• But the actual time of acquisition is different
  for every slice
• The model of the time course assumes that within
  each volume, every slice was acquired
  simultaneously at the mid point of the TR
• so, the model is likely to fit better for one
  slice than all the others (bad)
• To use slice timing correction, you will need to
  tell FSL the order your slices were acquired in
• interleaved is the most common, but ask your
  scanner technician!
• Adjustment is to the middle of the TR period

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Slice timing correction

• For each voxel, slice-timing correction examines
  the time course and shifts it by a small amount
• This requires interpolating between the time
  points you actually sampled to infer a more
  detailed version of the time course
• The more detailed time course can have small
  shifts applied to it that are slightly different
  for each voxel, depending on the actual order the
  slices were acquired in
• This allows you to make the assumption in your
  modelling that every voxel in each volume was
  acquired simultaneously

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Slice timing correction

• The problem this tries to solve is more severe if
  you have a longer TR (e.g. 4 seconds)
• two adjacent slices in an interleaved sequence
  could be sampled almost 2 seconds apart
• But temporal interpolation also becomes dodgy
  with longer TRs ?
• For block designs (stimuli that are long relative
  to the TR, e.g. TR 2 sec, stimulus lasts 16
  sec) slice timing errors are not a significant
  factor influencing the fitting of a model to the
  data
• For event related designs (brief stimuli
  separated by variable pauses), slice timing
  correction is important
• People argue about whether to do slice timing
  correction before or after motion correction
• FSL does motion correction first
• some people advise against any slice timing
  correction

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Temporal derivatives

• In the FEAT practical you will add temporal
  derivatives of the HRF convolved experimental
  time courses to the design matrix
• what is the purpose of this?

• Each experimental time course is convolved with a
  model of the HRF
• this is to build the delay and blurring of the
  blood flow response relative to the neural
  response into the model
• but the delay varies between brain areas and
  between people

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Temporal Derivatives

• The green line is the first temporal derivative
  of the blue line
• its rate of change
• the positive max of the derivative is earlier
  than the normal HRF peak
• the negative max of the derivative is later than
  the normal HRF peak
• If fitting the model results in a positive beta
  weight on a derivative this implies that the HRF
  peak is earlier in that voxel
• A negative beta weight for the derivative implies
  a later peak than typical

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Temporal derivatives

• The basic HRF shape (blue on the previous slide)
  has some physiological underpinning (in visual
  cortex)
• But the use of the derivative to model faster /
  slower responses is just a mathematical
  convenience
• The second temporal derivative (dispersion in
  time) can be used to model haemodynamic responses
  that are thinner or fatter in time than the
  basic shape
• The three functions together are sometimes called
  the informed basis set by SPM users
• the blue line is referred to as canonical, but
  in fact it is only canonical for primary visual
  cortex
• The informed basis set can only model slight
  departures from the canonical response shape
• If you are interested in the prefrontal cortex of
  the elderly youll need to use a more flexible
  basis set to model the temporal dynamics of the
  response
• or use a block design where timing issues are
  less severe

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Cluster size based thresholding

• Intuitively, if a voxel with a Z statistic of
  1.96 for a particular COPE is surrounded by other
  voxels with very low Z values this looks
  suspicious
• unless you are looking for a very small brain
  area
• Consider a voxel with a Z statistic of 1.96 is
  surrounded by many other voxels with similar Z
  values, forming a large blob
• Intuitively, for such a voxel the Z of 1.96 (p
  0.05) is an overestimate of the probability of
  the model fit to this voxel being a result of
  random, stimulus unrelated, fluctuation in the
  time course
• The p value we want to calculate is the
  probability of obtaining one or more clusters of
  this size or larger under a suitable null
  hypothesis
• one or more gives us control over the multiple
  comparisons problem by setting the family wise
  error rate
• p value will be low for big clusters
• p value will be high for small clusters

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Comparison of voxel (height based) thresholding
and cluster thresholding
?
space
Significant Voxels
No significant Voxels
? is the height threshold, e.g. 0.001 applied
voxelwise (will be Z about 3)
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Comparison of voxel (height based) thresholding
and cluster thresholding
?
space
Cluster significant
Cluster not significant
k?
k?
K? is the probability of the image containing 1
or more blobs with k or more voxels (and you can
control is at 0.05) The cluster size, in voxels,
that corresponds to a particular value of K?
depends upon the initial value of height
threshold ? used to define the number of clusters
in the image and their size It is usual to set
height ? quite low when using cluster level
thresholding, but this arbitrary choice will
influence the outcome
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Dependency of number of clusters on choice of
height threshold
The number and size of clusters also depends upon
the amount of smoothing that took place in
preprocessing
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• Nyquist frequency is important to know about
• Half the sampling rate (e.g. TR 2 sec is 0.5 Hz,
  so Nyquist is 0.25 hz, or 4 seconds)
• No signal higher frequency than Nyquist can be
  present in the data (important for experimental
  design)
• But such signal could appear as an aliasing
  artefact at a lower frequency

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Overview

• Todays practical session will cover processing
  of a single functional session from a single
  participant using FEAT
• FEAT is an umbrella program that brings together
  various other FSL programs into a customisable
  processing pipeline
• for example, it makes use of BET and FLIRT, which
  were programs covered in week 1
• Definitions of single session and multi
  session
• We will also make use of an interactive
  spreadsheet that demonstrates how the general
  linear model (GLM) can be used to locate active
  regions of the brain given your predictions about
  the time course of activation
• The lecture will provide theoretical background
  for each processing step
• There is no formal meeting in week 3 of the
  course, but the room will be open for you to
  complete worksheets from today and last week
• at least one experienced FSL user will be here to
  help

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Overview of single session FMRI

• The data is a 4D functional time series
• Many thousands of spatial locations (voxels)
• Each voxel has a time course defined by a single
  intensity value per TR ( per volume acquired)
• The task is to model the changes in image
  intensity over time separately for each voxel
• mass univariate approach
• begin with a set of regressors (design matrix /
  model)
• regressors usually reflect the time course of
  experimental conditions
• find the best linear combination of regressors to
  explain each voxel time course (basically,
  multiple regression)
• Before modelling the 4D time series a number of
  preprocessing steps are applied to the data
• remove unwanted sources of variation from the
  time series
• increase the signal to noise ratio

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Voxel-wise single session modelling

• After the data has been optimised by
  preprocessing you search for voxels where the
  time course of image intensity changes is
  correlated with the experimental time course
• activation
• This is achieved using the General Linear Model
  (GLM)
• similar to multiple regression
• The input to the GLM is the data, plus a set of
  explanatory variables called the Design Matrix
• sometimes EVs are included to model sources of
  variation that are of no interest to the
  experimenter
• this is to reduce the residual (error) variance
• The GLM is fitted independently for each voxel
  timecourse
• ignores the spatial structure in the brain

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Regressor 0 (stimulus on)
Regressor 1 (stimulus off)
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The voxel time courses are standardised so that
beta weights are comparable between voxels
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If there is structure in the residual time
courses something important has not been modelled
Experimental time course regressors no longer
square wave because convolved with HRF model
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Autocorrelation FILM prewhitening

• First, fit the GLM
• Estimate the temporal autocorrelation structure
  in the residuals
• The estimated structure can be inverted and used
  as a temporal filter to undo the autocorrelation
  structure in the data
• the filter is also applied to the design matrix
• Refit the GLM
• DOF n-1 will now correctly reflect what is really
  free to vary in the timecourse
• Prewhitening is selected on the stats tab in FEAT
• it is computationally intensive, but with a
  modern PC it is manageable and there are almost
  no circumstances where you would turn this option
  off

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Temporal filtering

• Filtering in time and/or space is a
  long-established method in any signal detection
  process to help "clean up" your signal
• The idea is if your signal and noise are present
  at separable frequencies in the data, you can
  attenuate the noise frequencies and thus increase
  your signal to noise ratio

I could illustrate this by drawing a low
frequency sinusoid called noise on the board, or
with matlab. Then draw a high frequency one
called signal underneath. Draw a third where they
are added together, and point out that the two
sinusoids could be seperated mathematically, even
if you did not know apriori their amplitudes and
frequencies. In a second example I make noise and
signal have similar frequency and show that when
added together they are inseperable. This is
key point of FMRI data analysis and guiding
principle in experimental design.