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(Epoch and) Event-related fMRI

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  1. (Epoch and) Event-related fMRI Karl Friston Rik Henson Oliver Josephs Wellcome Department of Cognitive Neurology & Institute of Cognitive Neuroscience University College London UK

  2. A B A B… Boxcar function “fMRI Event-related conception” Delta functions Scans 1-10 Scans 21-30 Scans 11-20… Condition A Condition B => Design Matrix Convolved with HRF … … … … Epoch vsEvent-related fMRI “PET Blocked conception” (scans assigned to conditions) “fMRI Epoch conception” (scans treated as timeseries)

  3. Overview 1. Advantages of efMRI 2. BOLD impulse response 3. General Linear Model 4. Temporal Basis Functions 5. Timing Issues 6. Design Optimisation 7. Nonlinear Models 8. Example Applications

  4. Advantages ofEvent-related fMRI 1. Randomisedtrial order c.f. confounds of blocked designs (Johnson et al 1997)

  5. Data O = Old Words Model N = New Words O1 O2 O3 N1 N2 N3 Randomised N2 O3 O1 N1 O2 Blocked

  6. Advantages ofEvent-related fMRI 1. Randomised trial order c.f. confounds of blocked designs (Johnson et al 1997) 2. Post hoc / subjective classification of trials e.g, according to subsequent memory (Wagner et al 1998)

  7. R = Words Later Remembered F = Words Later Forgotten Event-Related ~4s R R R F F Data Model

  8. Advantages ofEvent-related fMRI 1. Randomised trial order c.f. confounds of blocked designs (Johnson et al 1997) 2. Post hoc / subjective classification of trials e.g, according to subsequent memory (Wagner et al 1998) 3. Some events can only be indicated by subject (in time) e.g, spontaneous perceptual changes (Kleinschmidt et al 1998)

  9. Advantages ofEvent-related fMRI 1. Randomised trial order c.f. confounds of blocked designs (Johnson et al 1997) 2. Post hoc / subjective classification of trials e.g, according to subsequent memory (Wagner et al 1998) 3. Some events can only be indicated by subject (in time) e.g, spontaneous perceptual changes (Kleinschmidt et al 1998) 4. Some trials cannot be blockede.g, “oddball” designs (Clark et al., 2000)

  10. “Oddball” … Time

  11. Advantages ofEvent-related fMRI 1. Randomised trial order c.f. confounds of blocked designs (Johnson et al 1997) 2. Post hoc / subjective classification of trials e.g, according to subsequent memory (Wagner et al 1998) 3. Some events can only be indicated by subject (in time) e.g, spontaneous perceptual changes (Kleinschmidt et al 1998) 4. Some trials cannot be blocked e.g, “oddball” designs (Clark et al., 2000) 5. More accurate models even for blocked designs?e.g, “state-item” interactions (Chawla et al, 1999)

  12. O1 O2 O3 N1 N2 N3 “Event” model O1 O2 O3 N1 N2 N3 Blocked Design Data Model “Epoch” model

  13. (Disadvantages of Randomised Designs) 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)

  14. Overview 1. Advantages of efMRI 2. BOLD impulse response 3. General Linear Model 4. Temporal Basis Functions 5. Timing Issues 6. Design Optimisation 7. Nonlinear Models 8. Example Applications

  15. 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… • … but differences across:other regions (Schacter et al 1997) individuals (Aguirre et al, 1998)

  16. Peak Brief Stimulus Undershoot Initial Undershoot BOLD Impulse Response • Early event-related fMRI studies used a long Stimulus Onset Asynchrony (SOA) to allow BOLD response to return to baseline • However, if the BOLD response is explicitly modelled, overlap between successive responses at short SOAs can be accommodated… • … particularly if responses are assumed to superpose linearly • Short SOAs are more sensitive…

  17. Overview 1. Advantages of efMRI 2. BOLD impulse response 3. General Linear Model 4. Temporal Basis Functions 5. Timing Issues 6. Design Optimisation 7. Nonlinear Models 8. Example Applications

  18. h(t)= ßi fi (t) x(t) T 2T 3T ... convolution General Linear (Convolution) Model GLM for a single voxel: Y(t) = x(t)  h(t) +  x(t) = stimulus train (delta functions) x(t) =   (t - nT) h(t) = hemodynamic (BOLD) response h(t) =  ßi fi(t) fi(t) = temporal basis functions Y(t) =  ßi fi (t - nT) +  sampled each scan Design Matrix

  19. 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)

  20. Overview 1. Advantages of efMRI 2. BOLD impulse response 3. General Linear Model 4. Temporal Basis Functions 5. Timing Issues 6. Design Optimisation 7. Nonlinear Models 8. Example Applications

  21. Temporal Basis Functions • Fourier Set Windowed sines & cosines Any shape (up to frequency limit) Inference via F-test

  22. Temporal Basis Functions • Finite Impulse Response Mini “timebins” (selective averaging) Any shape (up to bin-width) Inference via F-test

  23. 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

  24. 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…?

  25. Temporal Basis Functions

  26. Temporal Basis Functions “Informed” Basis Set (Friston et al. 1998) • Canonical HRF (2 gamma functions) Canonical

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

  28. 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

  29. 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) • “Magnitude” inferences via t-test on canonical parameters (providing canonical is a good fit…more later) Canonical Temporal Dispersion

  30. 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) • “Magnitude” inferences via t-test on canonical parameters (providing canonical is a good fit…more later) • “Latency” inferences via tests on ratio of derivative: canonical parameters (more later…) Canonical Temporal Dispersion

  31. (Other Approaches) • Long Stimulus Onset Asychrony (SOA) • Can ignore overlap between responses (Cohen et al 1997) • … but long SOAs are less sensitive • Fully counterbalanced designs • Assume response overlap cancels (Saykin et al 1999) • Include fixation trials to “selectively average” response even at short SOA (Dale & Buckner, 1997) • … but unbalanced when events defined by subject • Define HRF from pilot scan on each subject • May capture intersubject variability (Zarahn et al, 1997) • … but not interregional variability • Numerical fitting of highly parametrised response functions • Separate estimate of magnitude, latency, duration (Kruggel et al 1999) • … but computationally expensive for every voxel

  32. 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)

  33. Overview 1. Advantages of efMRI 2. BOLD impulse response 3. General Linear Model 4. Temporal Basis Functions 5. Timing Issues 6. Design Optimisation 7. Nonlinear Models 8. Example Applications

  34. Timing Issues : Practical TR=4s Scans • Typical TR for 48 slice EPI at 3mm spacing is ~ 4s

  35. 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

  36. 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

  37. 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

  38. 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

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

  40. 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}

  41. 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}

  42. 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}

  43. Timing Issues : Latency • Assume the real response, r(t), is a scaled (by ) version of the canonical, f(t), but delayed by a small amount dt: r(t) =  f(t+dt) ~  f(t) +  f ´(t) dt 1st-order Taylor • If the fitted response, R(t), is modelled by the canonical + temporal derivative: R(t) = ß1 f(t) + ß2 f ´(t) GLM fit • Then canonical and derivative parameter estimates, ß1and ß2,are such that : •  = ß1 dt = ß2 / ß1 (Henson et al, 2002) (Liao et al, 2002) • ie, Latency can be approximated by the ratio of derivative-to-canonical parameter estimates (within limits of first-order approximation, +/-1s)

  44. Basis Functions Canonical Canonical Derivative Delayed Responses (green/ yellow) Parameter Estimates Actual latency, dt, vs. ß2 / ß1 ß1 ß2 ß1 ß2 ß1 ß2 ß2 /ß1 Timing Issues : Latency Face repetition reduces latency as well as magnitude of fusiform response

  45. Neural BOLD Timing Issues : Latency A. Decreased B. Advanced C. Shortened(same integrated) D. Shortened(same maximum) A. Smaller Peak B. Earlier Onset C. Earlier Peak D. Smaller Peak and earlier Peak

  46. Overview 1. Advantages of efMRI 2. BOLD impulse response 3. General Linear Model 4. Temporal Basis Functions 5. Timing Issues 6. Design Optimisation 7. Nonlinear Models 8. Example Applications

  47. Design Efficiency • Maximise detectable signal (assume noise independent) • Minimise variability of parameter estimates (efficient estimation) • Efficiency of estimation  covariance of (contrast of) covariates (Friston et al. 1999) trace { cT (XTX)-1 c }-1 • = maximise bandpassed energy (Josephs & Henson, 1999)

  48. Design Efficiency • Maximise detectable signal (assume noise independent) • Minimise variability of parameter estimates (efficient estimation) • Efficiency of estimation  covariance of (contrast of) covariates (Friston et al. 1999) trace { cT (XTX)-1 c }-1 • = maximise bandpassed energy (Josephs & Henson, 1999) Events (A-B)

  49. Design Efficiency • Maximise detectable signal (assume noise independent) • Minimise variability of parameter estimates (efficient estimation) • Efficiency of estimation  covariance of (contrast of) covariates (Friston et al. 1999) trace { cT (XTX)-1 c }-1 • = maximise bandpassed energy (Josephs & Henson, 1999) Convolved with HRF