# 1 Temporal Processing Chris Rorden Temporal Processing can reduce error in our model –Slice Time Correction –Temporal Autocorrelation –High and low pass.

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1 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

2 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.

3 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

4 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

5 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

6 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. Time Predicted HRF

7 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

8 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

9 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 SignalHRF

10 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

11 Autocorrelated Data FSL uses the autocorrelation function (ACF) to whiten model (Woolrich et al., NI, 2001, 1370- 1386) 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 Raw ACF Tukey Taper

12 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.

13 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

14 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

15 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.

16 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)

17 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.

18 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

19 Physiological Noise Respiration causes head motion Some brain regions show cardiac-related pulsation. What to do about physiological noise? 1.Ignore 2.Monitor pulse/respiration during scanning, then retrospectively correct images. 3.Acquire scans faster than the nyquist frequency(TR <0.5sec), e.g. Anand et al. 2005 4.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).

20 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.

21 Physio Recording with the Trio

22 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.

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

24 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.

25 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. Time (sec) 0 5 10 15 -HRF -TD

26 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.

27 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.

28 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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