Design by hedongchenchen

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									Experimental Design and Efficiency in fMRI


     Heidi Bonnici and Sinéad Mullally

          Methods for Dummies
            13th January 2010
Overview

• Experimental Design
  – Types of Experimental Design
  – Timing parameters – Blocked and Event-Related Design


• Design Efficiency
  – Response vs Baseline (signal-processing)
  – Response 1 - Response 2 (statistics)
Overview

• Experimental Design
  – Types of Experimental Design
  – Timing parameters – Blocked and Event-Related Design


• Design Efficiency
  – Response vs Baseline (signal-processing)
  – Response 1 - Response 2 (statistics)
           Main Take Home Point
           of Experimental Design


Make sure you’ve chosen your analysis method and
    contrasts before you start your experiment
  Why is it so important to correctly design
              your experiment?

• Main design goal: To test specific hypotheses

• We want to manipulate the subject’s experience and
  behaviour in some way that is likely to produce a
  functionally specific neurovascular response.

• What can we manipulate?
   – Stimulus type and properties
   – Stimulus timing
   – Subject instructions
Overview

• Experimental Design
  – Types of Experimental Design
  – Timing parameters – Blocked and Event-Related Design


• Design Efficiency
  – Response vs Baseline (signal-processing)
  – Response 1 - Response 2 (statistics)
          Types of Experimental Design

1. Categorical – comparing the activity from one task to
   another task

2. Factorial - combining two or more factors within a task
   and looking at the effect of one factor on the response to
   other factor

•   Parametric – exploring systematic changes in the brain
    responses according to some performance attributes of
    task
             Categorical Design: Subtraction
Assumption of pure insertion: One task does not affect the effect of another task.


              Comparing the activity of one task to another task
    considering the fact that the neural structures supporting cognitive and
          behavioural processes combine in a simple additive manner

                           Can only test for one effect

Example:
Task: decide for each noun whether it refers to an animate or inanimate
object.

                                goat      bucket
         Categorical Design: Conjunction
         Tests multiple effects        A-B


  Does not depend on pure insertion
        – conjunction discounts
           interaction terms

two or more distinct task pairs each
                                       (AI-BI) & (AII-BII)
     share a common processing
              difference

    common areas of activation for
           each task pair

        Task pairs independent
                           Factorial design
Combining two or more factors within a task and looking at the effect of one
                        factor upon the other/s.


                                                  MOTION      NO MOTION
Load task         Rees, Frith &
                  Lavie (1997)

                                           LOW         A         B
                                    LOAD
                                           HIGH
                                                       C          D
            •   A – Low attentional load, motion
            •   B – Low attentional load, no motion
            •   C – High attentional load, motion
            •   D – High attentional load, no motion
                                     MOTION   NO MOTION
Terminology
                               LOW     A       B
                        LOAD
• Simple main effects      HIGH
                                       C        D
• Main effects

• Interaction terms
                                               MOTION    NO MOTION
SIMPLE MAIN EFFECTS
 • A – B: Simple main effect of         LOW       A        B
   motion (vs. no motion) in the      LOAD
   context of low load                  HIGH

 • B – D: Simple main effect of
                                                  C         D
   low load (vs. high load) in the
   context of no motion

 • D – C: ?
                                             The inverse simple
 • Simple main effect of no      OR
                                             main effect of motion
   motion (vs. motion) in the                (vs. no motion) in the
   context of high load                      Context of high load
                                             MOTION   NO MOTION
MAIN EFFECTS
• (A + B) – (C + D):                   LOW     A       B
• the main effect of low load (vs.    LOAD
  high load) irrelevant of motion     HIGH
• Main effect of load                         C        D
• (A + C) – (B + D): ?
• The main effect of motion (vs. no
  motion) irrelevant of load
•  Main effect of motion
                                                 MOTION   NO MOTION
INTERACTION TERMS
• (A - B) – (C - D):                       LOW     A       B
• the interaction effect of motion (vs.   LOAD
  no motion) greater under low (vs.       HIGH
  high) load                                       C        D
• (B - A) – (D - C): ?
• the interaction effect of no motion
  (vs. motion) greater under low (vs.
  high) load
Factorial design in SPM                        MOTION       NO MOTION

• How do we enter these effects in
  SPM?
                                      LOW        A           B
                                     LOAD
                                     HIGH
                                                 C            D
• Simple main effect of motion in
  the context of low load:
                                           A      B     C       D
• A vs. B or (A – B)


                                      [1         -1     0        0]
Factorial design in SPM
• Main effect of low load:
• (A + B) – (C + D)
                                        A    B        C      D



                                       [1    1        -1    -1]



• Interaction term of motion greater
  under low load:
• (A – B) – (C – D)                     A    B        C      D


                                        [1       -1    -1    1]
                           Parametric Design
         exploring systematic changes in the brain responses according to some
                               performance attributes of task

 • Linear                                    • Nonlinear
      Cognitive components and                    Polynomial expansion
        dimensions




Assumption: as the task becomes more difficult blood flow to the regions specialised for
task analysis will increase
 Overview

• Experimental Design
  – Types of Experimental Design
  – Timing parameters – Blocked and Event-Related Design


• Design Efficiency
  – Response vs Baseline (signal-processing)
  – Response 1 - Response 2 (statistics)
         Timing Parameters – Blocked Design

• It involves presenting two conditions – an activation (A)
  condition and a baseline (B) condition. Each condition is
  presented for an identical epoch of time.



Task A    Task B   Task A   Task B   Task A   Task B   Task A   Task B




Task A    REST     Task B   REST     Task A   REST     Task B   REST
What baseline should you choose?

• Task A vs. Task B
   – Example: Squeezing Right Hand vs. Left Hand
   – Allows you to distinguish differential activation between
     conditions
   – Does not allow identification of activity common to both tasks
       • Can control for uninteresting activity


• Task A vs. No-task
   – Example: Squeezing Right Hand vs. Rest
   – Shows you activity associated with task
   – May introduce unwanted results
Choosing Length of Blocks

• Longer blocks allow for stability of extended patterns of
  brain activation.


• Shorter blocks allow for more transitions between tasks.

   – Task-related variability increases with increasing
     numbers of transitions
Pros and Cons of Blocked Design
Pros:
• Avoid rapid task-switching (e.g. patients)
• Fast and easy to run;
• Good signal to noise ratio


Cons:
• Expectation
• Habituation
• Signal drift
• Poor choice of baseline may preclude meaningful conclusions
• Many tasks cannot be conducted repeatedly
 Timing Parameters – Event-Related Design

• It allows different trials or stimuli to be presented
  in arbitrary sequences.
• Jittering events can reduce possibility of
  correlated regressors – increased efficiency




                           time
Pros and Cons of Event-Related Design

Pros:

•   Real world testing

•   Eliminate predictability of block designs (e.g. expectation);

•   Can look at novelty and priming;

•   Can look at temporal dynamics of response.



Cons:
•   Low statistical power (small signal change)
•   More complex design and analysis (esp. timing and baseline issues).
Overview

• Experimental Design
  – Types of Experimental Design
  – Timing parameters – Blocked and Event-Related Design

• Design Efficiency
  – What is efficiency
  – Signal Processing perspective
  – General Advice
Efficiency is…

•   … a numerical value which reflects the ability of
    your design to detect the effect of interest.
Efficiency is…

•   … a numerical value which reflects the ability of
    your design to detect the effect of interest.



•   General Linear Model:
           Y     =        X          .       β        +    ε
          Data       Design Matrix       Parameters       error



•   Efficiency (e) is the ability to estimate β, given the design matrix X
Y=Xβ+ε


Efficiency is…
                           The inverse of the variance within the estimated β,
                                        for this specific contrast

•   e (c, X) = inverse (σ2 cT Inverse(XTX) c)

•   e (c, X) is specific for a given contrast (c), given
    the question that you are trying to answer (with your design X).

•   So, to optimise experimental design:
–   minimise the variance in the contrast i.e. minimise [cT (XTX)] by maximising [cT Inverse(XTX)]
–   we assume that noise variance (σ 2) is unaffected by changes in X.
–   All we can alter in this equation is X.


•   Therefore we minimise the variance (a priori) to maximise efficiency:
–   by the spacing and sequencing of epochs/events in our design matrix
–   ensuring that your regressors are not correlated (for more details see Rik Henson’s website)
Background: terminology

•   Trial - replications of a condition

•   A trial consists of one or more components, that may be:

     – “events” or “impulses” - brief bursts of neural activity

     – “epochs” - periods of sustained neural activity

•   SOA (Stimulus Onset Asynchrony) - time between the onsets of components. Also
    referred to as the ITI (inter-trial interval).

•   ISI (Inter-Stimulus Interval) - time between offset of one component and onset of next

•   SOA = ISI + Stimulus Duration

•   For events: SOA = ISI (as events are assumed to have zero duration)
Signal Processing

•   Signal processing is the analysis, interpretation, and manipulation of signals.



•   Given that we can treat fMRI volumes as time series (for each voxel) it is useful to adopt a
    signal-processing perspective.



•   Using a “linear convolution” model, the predicted fMRI series is obtained by convolving a
    neural function (e.g. stimulus function) was an assumed IR.
The BOLD Impulse Response (IR)
•   A BOLD response to an impulse (brief burst) of activity typically has the
    following characteristics:
     –   A peak occurring at 4-6s
     –   Followed by an undershoot from approximately 10-30s
                      Fixed SOA = 16s
Stimulus (“Neural”)                HRF                  Predicted Data




                                                   =




                      Not particularly efficient…
                      Fixed SOA = 4s
Stimulus (“Neural”)            HRF                Predicted Data




                                             =




                          Very Inefficient…
             Randomised, SOAmin= 4s
Stimulus (“Neural”)              HRF                 Predicted Data




                                             =




 More Efficient, despite using only half as many stimuli as previous…
                 Blocked, SOAmin= 4s
Stimulus (“Neural”)               HRF                Predicted Data




                                              =




                  but this design is even more Efficient…
Background: terminology

•   The fourier transformation decomposes a function into the sum of a (potentially infinite)
    number of sine wave frequency components.




•   A frequency domain graph shows how much of the signal lies within each given frequency
    band over a range of frequencies
     –   Here the sine wave that best matches the basic on-off alternation has a dominant frequency corresponding to its
         ‘fundamental’ frequency: F0 = 1/(20s+20s) = 0.025 Hz

     –   Plus ‘harmonics’ – capture the sharper edges of the square-wave function relative to the fundamental sinusoid
  1 1                               11                            1       1                                    1

0.50.5                             0.5
                                  0.5                            0.5 0.5                                     0.5

  0 0                               00                            0       0                                    0

   -0.5
-0.5                               -0.5
                                  -0.5                       -0.5-0.5                                        -0.5

 -1 -1                               -1
                                    -1                            -1 -1                                       -1
   0 0      100
          100       200
                  200     300
                            300        00    100
                                            100    200
                                                    200    300
                                                          300       0 0           100100   200200   300300          0   100   200   300


  100
100                                100
                                  100                        100100                                          100

 80 80                              80
                                   80                            80 80                                        80

 60 60                              60
                                   60                            60 60                                        60

 40 40                              40
                                   40                            40 40                                        40

 20 20                              20
                                   20                            20 20                                        20

  0 0                               00                            0       0                                    0
   0 0    50 50     100
                  100     150
                            150      00      50
                                            50      100
                                                   100    150
                                                           150        0       0   50 50    100100   150150          0   50    100   150
                       Blocked, epoch = 20s
 Stimulus (“Neural”)                              HRF                             Predicted Data




                                                                    =



                                                                     =

• A convolution in time is equivalent to a multiplication in frequency space
• In this way the transformed IR acts as a filter: passes low frequencies but attenuates higher frequencies.
                Blocked, epoch = 20s
Stimulus (“Neural”)                HRF                    Predicted Data




                                                =



                                                =


  Efficient design as most of the signal is ‘passed’ by the IR filter
So what is the most efficiency
design of all…
      Sinusoidal modulation, f = 1/33s
Stimulus (“Neural”)             HRF                   Predicted Data




                                           =


                  The most efficient design of all!
Highpass Filtering

•   fMRI noise tends to have two components:
     –   Low frequency ‘1/f’ noise e.g. physical (scanner drifts);

         physiological [cardiac (~1 Hz), respiratory (~0.25 Hz)]

     –   Background white noise




•   Highpass filters aims to maximise the loss of noise but minimise the loss of signal.



•   We apply the highpass filter to the lowpass filter inherent in the IR to creast a single ‘band-
    pass’ filter (or ‘effective HRF’).
   Blocked (80s), SOAmin=4s, highpass filter = 1/120s

Stimulus (“Neural”)                HRF                      Predicted Data




                                                 =

     “Effective HRF” (after highpass filtering) (Josephs & Henson, 1999)




                                                  =

                       Don’t have long (>60s) blocks!
    Randomised, SOAmin=4s, highpass filter = 1/120s
Stimulus (“Neural”)             HRF                     Predicted Data




                                              =




                                              =

          (Randomised design spreads power over frequencies)
General Advice (Rik Henson)

1.   Scan for as long as possible (as increasing the number of volumes increasing
     the degrees of freedom).

2.   For group studies increasing the number of participants adds more statistical
     power that increasing the number of DF.

3.   Do not contrast conditions that are far apart in time (because of low-frequency
     noise in the data).

4.   Randomize the order, or randomize the SOA, of conditions that are close in
     time.




        http://www.mrc-cbu.cam.ac.uk/Imaging/Common/fMRI-efficiency.shtml
Conclusions:
1.   Blocked designs generally most efficient (with short SOAs, given optimal block
     length is not exceeded)
2.   However, psychological efficiency often dictates intermixed designs, and often
     also sets limits on SOAs
3.   With randomised designs, optimal SOA for differential effect (A-B) is minimal
     SOA (>2 seconds, and assuming no saturation), whereas optimal SOA for main
     effect (A+B) is 16-20s
4.   Inclusion of null events improves efficiency for main effect at short SOAs (at
     cost of efficiency for differential effects)
5.   If order constrained, intermediate SOAs (5-20s) can be optimal
6.   If SOA constrained, pseudorandomised designs can be optimal (but may
     introduce context-sensitivity)
7.   Remember an optimal design for one contrast may not be optimal for another




        http://www.mrc-cbu.cam.ac.uk/Imaging/Common/fMRI-efficiency.shtml
Useful links and thanks



• Antoinette Nicolle
• http://imaging.mrc-
  cbu.cam.ac.uk/imaging/DesignEfficiency
• Nick and Edoardo’s slides from MfD 2008

								
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