Temporal%20Processing

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Temporal Processing

• Chris Rorden
• Temporal Processing can reduce error in our model
• Slice Time Correction
• Temporal Autocorrelation
• High and low pass temporal filtering
• Temporal Derivatives

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The slice timing problem

• Each 2D slice like a photograph.
• Each 2D slice within a 3D volume taken at
  different time.
• Hemodynamic response changes with time.
• Therefore, we need to adjust for slice timing
  differences.

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Slice timing correction

• Each 2D EPI fMRI slice collected almost at once
• Over time, we collect a full 3D volume (once per
  2-4 seconds, compare to 7 minutes for T1)

Time
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Why slice time correct?

• Consider 3D volumes collected as ascending axial
  slices
• For each volume, we see inferior slices before
  superior slices

Statistics assume all slices are seen
simultaneously
Time
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Why slice time correct?

• Statistics assume all slices are seen
  simultaneously
• In reality slices collected at different times.
• Model of hemodynamic response will only be
  accurate for middle slice some slices seen too
  early, others to late.

HRF
Time
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Why slice time correct?

• Statistics assume all slices are seen
  simultaneously
• In reality slices collected at different times.
• Model of hemodynamic response will only be
  accurate for middle slice some slices seen too
  early, others to late.

Predicted HRF
Time
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Slice timing correction

• Timing of early slices weighted with later image
  of same slice
• Timing of late slices is balanced with previous
  image of same slice
• Result each volume represents single point in
  time
• Typically, volume corrected to mean volume image
  time (estimate time of middle slice in volume)

Time
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Should we slice time correct?

• If we acquire images quickly (TR lt 2sec)
• Very little time difference between slices
• Therefore, STC will have little influence
• If we acquire images slowly
• We only rarely see a particular slice
• Therefore, STC interpolation will not be very
  accurate.
• General guideline not required for block
  designs, sometimes helpful for event related
  designs.

With long TRs, STC can be inaccurate e.g. miss
HRF peak
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Temporal Properties of fMRI Signal

• Effects of interest are convolved with
  hemodynamic response function (HRF), to capture
  sluggish nature of response
• Scans are not independent observations - they are
  temporally autocorrelated
• Therefore, each sample is not independent, and
  degrees of freedom is not simply the number of
  scans minus one.

Convolved Response
Neural Signal
HRF

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Autocorrelated Data

• Solutions for temporal autocorrelation
• FSL Uses pre-whitening is sensitive, but can
  be biased if K misestimated
• SPM99 Temporally smooth the data with a known
  autocorrelation that swamps any intrinsic
  autocorrelation. Robust, but less sensitive
• SPM2 restrict K to highpass filter, and estimate
  residual autocorrelation
• For more details, see Rik Hensons
  page www.mrc-cbu.cam.ac.uk/Imaging/Common/rikSPM-
  GLM.ppt

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Autocorrelated Data

• FSL uses the autocorrelation function (ACF) to
  whiten model (Woolrich et al., NI, 2001,
  1370-1386)
• Fit a GLM (assuming no autocorrelation) and
  estimate autocorrelation of residuals
• Spatially and spectrally smooth autocorrelation
  estimate
• Estimates whitening matrix, then whiten and
  estimate model

Raw ACF
Tukey Taper
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Signal Intensity Drift

• Succesive images change brightness.
• If uncorrected, this drift will reduce
  statistical power (e.g. blue line in upper image
  has both task related signal and error from
  signal drift).
• Simple correction is global scaling (FSL
  intensity normalization, SPM8 global
  intensity normalisation)
• Make each 3D image have same mean intensity.
• Problem
• If a large portion of the brain shows task
  related activity, global scaling will reduce
  related activity and add task-related noise to
  unrelated brain areas
• Example lower panel, where 30 of brain has
  related activity. Will selectively decrease
  signal (that is consistent across related voxels)
  and not reduce noise (which is not).
• Never use this correction for fMRI!
• Next slides temporal filters can preserve BOLD
  signal while eliminating lower-frequency drift.

Data with drift images get brighter
Corrected with global scaling
see NeuroImage 13, 11931206 (2001)
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Fourier Transforms and Spectral Power

• fMRI signal includes many periodic frequencies.
• The can be detected with a fourier transform,
  typically illustrated as spectral power.
• Plots show signal (blue) and spectral power
  (red).
• Low amplitude, slow frequency
• High amplitude, high frequency
• Mixture of 1 and 2 note fourier analysis
  identifies component frequencies.

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Spectral power of fMRI signal

• Our raw fMRI data includes
• Task related frequencies our signal
• Block design fundamental period is twice the
  duration of block, plus higher frequency
  harmonics.
• Below 15s blocks show peaks at 30 and 15s
  duration
• Event related designs
• HRF has a frequency with a fundamental period
  20s, harmonics will include higher frequencies.
• Unrelated frequencies
• Low frequency scanner drift
• Aliased physiological artifacts
• cardiac, respiration

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High Pass Filter

• We should apply a high pass filter.
• Eliminate very slow signal changes.
• Attenuate Scanner drift and other noise.
• A high-pass filter selectively removes low
  frequencies

High Pass Filter
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High Pass Filter Choosing a threshold

• What value should we use for high-pass filter?
• Block designs
• Our fundamental frequency will be duration of
  blocks.
• For 12s-long blocks, frequency is 24s (period for
  on-off cycle). We would therefore apply a 48-s
  high pass filter.
• Event related designs 100s filter is typical.

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Temporal Filtering

• Nyquist theorem One can only detect frequencies
  with a period slower than twice the sampling
  rate.
• For fMRI, the TR is our sampling rate (3sec for
  whole brain).

Example Sample exactly once per cycle, and
signal appears constant
Example Sample 1.5 times per cycle, and you will
infer a lower frequency (aliasing)
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High Pass Filter

• Aliasing High frequency information can appear
  to be lower frequency
• E.G. For fMRI, high frequency noise can include
  cardiac (1 Hz) respiration (0.25 Hz)
• Aliasing is why wheels can appear to spin
  backwards on TV.

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Low Pass Filter

• We could also eliminate high frequency noise.
• Event related designs have high frequency
  information, so low pass filters will reduce
  signal.
• In theory, block designs can benefit.
• In practice, low pass filters rarely used
• Most of the MRI noise is in the low frequencies
• Most high frequency noise (heart, breathing) too
  high for our sampling rate.

Low Pass Filter
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Physiological Noise

• Respiration causes head motion
• Some brain regions show cardiac-related
  pulsation.
• What to do about physiological noise?
• Ignore
• Monitor pulse/respiration during scanning, then
  retrospectively correct images.
• Acquire scans faster than the nyquist
  frequency(TR lt0.5sec), e.g. Anand et al. 2005
• The whole brain's fMRI signal fluctuates with
  physiological (respiratory) cycle. Therefore, one
  approach is to model this effect as a regressor
  in your analysis (Birn, 2006 though global
  scaling problem).

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Retrospective Correction

• Monitor pulse/respiration during scanning,
  correct images later.
• Here is data from Deckers et al. (2006) before
  and after correction.
• This correction implemented in my NPM software.

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Physio Recording with the Trio
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HRF used by statistics

• SPM models HRF using double gamma function
  intensity increase followed by undershoot.
• By default, FSL uses a single gamma function
  intensity increase.

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HRF variability

• Different people show different HRF timecourses
• E.G. 5 people scanned by Aguirre et al. 1998
• Different Brain Areas show different HRFs

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Variability in HRF

• The temporal properties of the HRF vary between
  people.
• Our statistics uses a generic estimate for the
  HRF.
• If our subjects HRF differs from this canonical
  model, we will lose statistical power.
• The common solution is to model both the
  canonical HRF and its temporal derivative.

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Temporal Derivative

• Temporal Derivative is the rate of change in the
  convolved HRF.
• TD is to HRF as acceleration is to speed.
• By adding TD to statistical model, we allow some
  variability in individual HRF to be removed from
  model.

• HRF
• -TD

0 5 10
15
Time (sec)
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How does the TD work?

• Consider individual with slightly slow HRF (green
  line).
• The canonical (red) HRF is not a great match, so
  the models fit will not be strong.
• The TD (blue) predicts most of the discrepancy
  between the canonical and observed HRF.
• Adding the TD as a regressor will remove the TDs
  effect from the observed data. The result
  (subtract blue from green) will allow a better
  fit of the canonical HRF.

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Temporal Derivative

• TD is usually a nuisance variable in our analysis
• Reduces noise by explaining some variability.
• In theory, you could analyze TD and use HRF as
  covariate
• Analyze HRF magnitude inference
• Analyze TD latency inference
• Analyze Dispersion Duration inference
• Note the TD can be detrimental to block designs.
• With long events, strong correlation with HRF.

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Alternatives to TD

• Another approach is to directly tune the HRF.
• By default, FSL uses a single gamma function for
  convolution
• Alternatively, you can design more accurate
  convolutions (e.g. FSLs FLOBs, right). Note that
  some of these options can make all your
  statistics two-tailed.