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Event-related fMRI Will Penny (this talk was made by Rik Henson)

This overview by Will Penny discusses the benefits and challenges of event-related fMRI, including the BOLD impulse response, timing considerations, temporal basis functions, design optimization, and nonlinear modeling. Explore examples and potential disadvantages in fMRI research.

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Event-related fMRI Will Penny (this talk was made by Rik Henson)

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  1. Event-related fMRI Will Penny (this talk was made by Rik Henson)

  2. Overview 1. Advantages of efMRI 2. BOLD impulse response 3. Timing Issues 4.Temporal Basis Functions 5. Design Optimisation 6. Nonlinear Models 7. Examples

  3. Advantages ofEvent-related fMRI 1. Post hoc / subjective classification of trials e.g, according to subsequent memory (Wagner et al 1998) 2. Some events can only be indicated by subject (in time) e.g, spontaneous perceptual changes (Kleinschmidt et al 1998) 3. Some trials cannot be blocked e.g, “oddball” designs (Clark et al., 2000)

  4. Potential Disadvantages 1. Less efficient for detecting effects than are blocked designs (see later…) 2. Some psychological processes may be better blocked (eg task-switching, attentional instructions)

  5. Peak Brief Stimulus Undershoot Initial Undershoot BOLD Impulse Response • Function of blood oxygenation, flow, volume (Buxton et al, 1998) • Peak (max. oxygenation) 4-6s poststimulus; baseline after 20-30s • Initial undershoot can be observed (Malonek & Grinvald, 1996) • Similar across V1, A1, S1…

  6. Overview 1. Advantages of efMRI 2. BOLD impulse response 3. Timing Issues 4.Temporal Basis Functions 5. Design Optimisation 6. Nonlinear Models 7. Examples

  7. h(t)= ßi fi (t) u(t) T 2T 3T ... convolution General Linear (Convolution) Model GLM for a single voxel: y(t) = u(t)  h(t) + (t) u(t) = neural causes (stimulus train) u(t) =   (t - nT) h(t) = hemodynamic (BOLD) response h(t) =  ßi fi (t) fi(t) = temporal basis functions y(t) =  ßi fi (t - nT) + (t) y = X ß + ε sampled each scan Design Matrix

  8. T=16, TR=2s T0=16 o T0=9 o Scan 1 0 A word about down-sampling x2 x3

  9. Timing Issues : Practical • …but “Slice-timing Problem” (Henson et al, 1999) Slices acquired at different times, yet model is the same for all slices

  10. Timing Issues : Practical Bottom Slice Top Slice • …but “Slice-timing Problem” (Henson et al, 1999) Slices acquired at different times, yet model is the same for all slices => different results (using canonical HRF) for different reference slices TR=3s SPM{t} SPM{t}

  11. Timing Issues : Practical Bottom Slice Top Slice • …but “Slice-timing Problem” (Henson et al, 1999) Slices acquired at different times, yet model is the same for all slices => different results (using canonical HRF) for different reference slices • Solutions: 1. Temporal interpolation of data … but less good for longer TRs TR=3s SPM{t} SPM{t} Interpolated SPM{t}

  12. Timing Issues : Practical TR=4s Scans • Typical TR for 48 slice EPI at 3mm spacing is ~ 4s • Sampling at [0,4,8,12…] post- stimulus may miss peak signal Stimulus (synchronous) SOA=8s Sampling rate=4s

  13. Timing Issues : Practical TR=4s Scans • Typical TR for 48 slice EPI at 3mm spacing is ~ 4s • Sampling at [0,4,8,12…] post- stimulus may miss peak signal • Higher effective sampling by: 1. Asynchrony eg SOA=1.5TR Stimulus (asynchronous) SOA=6s Sampling rate=2s

  14. Timing Issues : Practical TR=4s Scans • Typical TR for 48 slice EPI at 3mm spacing is ~ 4s • Sampling at [0,4,8,12…] post- stimulus may miss peak signal • Higher effective sampling by: 1. Asynchrony eg SOA=1.5TR2. Random Jitter eg SOA=(2±0.5)TR Stimulus (random jitter) Sampling rate=2s

  15. Timing Issues : Practical TR=4s Scans • Typical TR for 48 slice EPI at 3mm spacing is ~ 4s • Sampling at [0,4,8,12…] post- stimulus may miss peak signal • Higher effective sampling by: 1. Asynchrony eg SOA=1.5TR2. Random Jitter eg SOA=(2±0.5)TR • Better response characterisation (Miezin et al, 2000) Stimulus (random jitter) Sampling rate=2s

  16. Overview 1. Advantages of efMRI 2. BOLD impulse response 3. Timing Issues 4.Temporal Basis Functions 5. Design Optimisation 6. Nonlinear Models 7. Examples

  17. Peak Brief Stimulus Undershoot Initial Undershoot BOLD Impulse Response • Similar across V1, A1, S1… • … but differences across:other regions (Schacter et al 1997) individuals (Aguirre et al, 1998)

  18. Temporal Basis Functions • Fourier Set Windowed sines & cosines Any shape (up to frequency limit) Inference via F-test • Gamma Functions Bounded, asymmetrical (like BOLD) Set of different lags Inference via F-test • “Informed” Basis Set Best guess of canonical BOLD response Variability captured by Taylor expansion “Magnitude” inferences via t-test…?

  19. Temporal Basis Functions

  20. Temporal Basis Functions “Informed” Basis Set (Friston et al. 1998) • Canonical HRF (2 gamma functions) plus Multivariate Taylor expansion in: time (Temporal Derivative) width (Dispersion Derivative) Canonical Temporal Dispersion

  21. Temporal Basis Sets: Which One? In this example (rapid motor response to faces, Henson et al, 2001)… Canonical + Temporal + Dispersion + FIR …canonical + temporal + dispersion derivatives appear sufficient …may not be for more complex trials (eg stimulus-delay-response) …but then such trials better modelled with separate neural components (ie activity no longer delta function) + constrained HRF (Zarahn, 1999)

  22. Auditory words every 20s Gamma functions ƒi() of peristimulus time  (Orthogonalised) SPM{F} Sampled every TR = 1.7s Design matrix, X [x(t)ƒ1() | x(t)ƒ2() |...] … 0 time {secs} 30 General Linear Model (in SPM)

  23. Timing Issues : Practical Bottom Slice Top Slice • …but “Slice-timing Problem” (Henson et al, 1999) Slices acquired at different times, yet model is the same for all slices => different results (using canonical HRF) for different reference slices • Solutions: 1. Temporal interpolation of data … but less good for longer TRs 2. More general basis set (e.g., with temporal derivatives) … but inferences via F-test TR=3s SPM{t} SPM{t} Interpolated SPM{t} Derivative SPM{F}

  24. Overview 1. Advantages of efMRI 2. BOLD impulse response 3. Timing Issues 4.Temporal Basis Functions 5. Design Optimisation 6. Nonlinear Models 7. Examples

  25. Fixed SOA = 16s Stimulus (“Neural”) HRF Predicted Data  = Not particularly efficient…

  26. = Fixed SOA = 4s Stimulus (“Neural”) HRF Predicted Data Very Inefficient…

  27. = Randomised, SOAmin= 4s Stimulus (“Neural”) HRF Predicted Data More Efficient…

  28. = Blocked, SOAmin= 4s Stimulus (“Neural”) HRF Predicted Data Even more Efficient…

  29. = = Blocked, epoch = 20s Stimulus (“Neural”) HRF Predicted Data  Blocked-epoch (with small SOA) and Time-Freq equivalences

  30. =  = Sinusoidal modulation, f = 1/33s Stimulus (“Neural”) HRF Predicted Data The most efficient design of all!

  31. =  = Randomised, SOAmin=4s, highpass filter = 1/120s Stimulus (“Neural”) HRF Predicted Data (Randomised design spreads power over frequencies)

  32. Differential Effect (A-B) Common Effect (A+B) 4s smoothing; 1/60s highpass filtering Efficiency - Multiple Event-types • Design parametrised by: SOAmin Minimum SOA pi(h) Probability of event-type i given history h of last m events • With n event-types pi(h) is a nm nTransition Matrix • Example: Randomised AB A B A 0.5 0.5 B 0.5 0.5 => ABBBABAABABAAA...

  33. Null Events (A-B) Null Events (A+B) 4s smoothing; 1/60s highpass filtering Efficiency - Multiple Event-types • Example: Null events A B A 0.33 0.33 B 0.33 0.33 => AB-BAA--B---ABB... • Efficient for differential and main effects at short SOA • Equivalent to stochastic SOA (Null Event like third unmodelled event-type) • Selective averaging of data (Dale & Buckner 1997)

  34. Optimal design for one contrast may not be optimal for another Blocked designs generally most efficient with short SOAs (but earlier restrictions and problems of interpretation…) With randomised designs, optimal SOA for differential effect (A-B) is minimal SOA (assuming no saturation), whereas optimal SOA for main effect (A+B) is 16-20s Inclusion of null events improves efficiency for main effect at short SOAs (at cost of efficiency for differential effects) Efficiency - Conclusions

  35. Overview 1. Advantages of efMRI 2. BOLD impulse response 3. Timing Issues 4.Temporal Basis Functions 5. Design Optimisation 6. Nonlinear Models 7. Examples

  36. [u(t)] input u(t) response y(t) Stimulus function kernels (h) estimate Nonlinear Model Volterra series - a general nonlinear input-output model y(t) = 1[u(t)] + 2[u(t)] + .... + n[u(t)] + .... n[u(t)] = ....  hn(t1,..., tn)u(t - t1) .... u(t - tn)dt1 .... dtn

  37. Nonlinear Model Friston et al (1997) kernel coefficients - h SPM{F} p < 0.001 SPM{F} testing H0: kernel coefficients, h = 0

  38. Nonlinear Model Friston et al (1997) kernel coefficients - h SPM{F} p < 0.001 SPM{F} testing H0: kernel coefficients, h = 0 Significant nonlinearities at SOAs 0-10s: (e.g., underadditivity from 0-5s)

  39. Nonlinear Effects Underadditivity at short SOAs Linear Prediction Volterra Prediction

  40. Nonlinear Effects Underadditivity at short SOAs Linear Prediction Volterra Prediction

  41. Nonlinear Effects Underadditivity at short SOAs Linear Prediction Implications for Efficiency Volterra Prediction

  42. Overview 1. Advantages of efMRI 2. BOLD impulse response 3. Timing Issues 4.Temporal Basis Functions 5. Design Optimisation 6. Nonlinear Models 7. Examples

  43. Example 1: Intermixed Trials (Henson et al 2000) • Short SOA, fully randomised, with 1/3 null events • Faces presented for 0.5s against chequerboard baseline, SOA=(2 ± 0.5)s, TR=1.4s • Factorial event-types: 1. Famous/Nonfamous (F/N) 2. 1st/2nd Presentation (1/2)

  44. Lag=3 . . . Famous Nonfamous (Target)

  45. Example 1: Intermixed Trials (Henson et al 2000) • Short SOA, fully randomised, with 1/3 null events • Faces presented for 0.5s against chequerboard baseline, SOA=(2 ± 0.5)s, TR=1.4s • Factorial event-types: 1. Famous/Nonfamous (F/N) 2. 1st/2nd Presentation (1/2) • Interaction (F1-F2)-(N1-N2) masked by main effect (F+N) • Right fusiform interaction of repetition priming and familiarity

  46. Example 4: Oddball Paradigm (Strange et al, 2000) • 16 same-category words every 3 secs, plus … • … 1 perceptual, 1 semantic, and 1 emotional oddball

  47. Perceptual Oddball Semantic Oddball CORN Emotional Oddball PLUG RAPE ~3s WHEAT BARLEY OATS RYE HOPS …

  48. Right Prefrontal Cortex Controls Parameter Estimates Oddballs Example 4: Oddball Paradigm (Strange et al, 2000) • 16 same-category words every 3 secs, plus … • … 1 perceptual, 1 semantic, and 1 emotional oddball • 3 nonoddballs randomly matched as controls

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