Transcript Temporal Aspects of Visual Extinction

Temporal Processing
 Chris Rorden
 Temporal Processing can reduce error in our model
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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
Time
Statistics assume all slices are seen simultaneously…
Time
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Why slice time correct?
HRF
 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.
Time
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Why slice time correct?
Predicted HRF
 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.
Time
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Slice timing correction
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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 < 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.
Neural Signal
HRF
Convolved Response
=
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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 Henson’s page
www.mrc-cbu.cam.ac.uk/Imaging/Common/rikSPM-GLM.ppt
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Autocorrelated Data
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FSL uses the autocorrelation
function (ACF) to whiten model
(Woolrich et al., NI, 2001, 13701386)
Raw ACF
Tukey Taper
1. Fit a GLM (assuming no
autocorrelation) and estimate
autocorrelation of residuals
2. Spatially and spectrally smooth
autocorrelation estimate
3. Estimates whitening matrix, then
whiten and estimate model
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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).
1. Low amplitude, slow frequency
2. High amplitude, high frequency
3. 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
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Respiration causes head motion
Some brain regions show cardiac-related pulsation.
What to do about physiological noise?
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Ignore
Monitor pulse/respiration during scanning, then retrospectively correct images.
Acquire scans faster than the nyquist frequency(TR <0.5sec), 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 subject’s 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
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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 model’s 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 TD’s 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.
FSL’s FLOBs, right). Note that
some of these options can make
all your statistics two-tailed.
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