Temporal Processing

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. Time 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 Time

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. Predicted HRF Time

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. Neural Signal HRF Convolved Response =

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 pagewww.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) • 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

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). • Low amplitude, slow frequency • High amplitude, high frequency • 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? • 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).

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. • HRF • -TD 0 5 10 15 Time (sec)

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.