experimental design of fmri studies · 2019. 8. 18. · overview experimental designs 11/42....
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Methods & Models for fMRI Analysis 2017
Experimental design of fMRI studies
Sara Tomiello
With many thanks for slides & images to:
Sandra Iglesias,Klaas Enno Stephan,FIL Methods group, Christian Ruff
Overview of SPM
Realignment Smoothing
Normalisation
General linear model
Statistical parametric map (SPM)Image time-series
Parameter estimates
Design matrix
Template
Kernel
Gaussian field theory
p <0.05
Statisticalinference
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Research question:Which neuronal structures support face recognition?
Hypothesis:The fusiform gyrus is
implicated in face recognition
Experimental design
General linear model
Statistical parametric map (SPM)
Parameter estimates
Design matrix
Gaussian field theory
p <0.05
Statisticalinference
Overview of SPM2/42
General linear model
Statistical parametric map (SPM)
Parameter estimates
Design matrix
Gaussian field theory
p <0.05
Statisticalinference
Overview of SPM
Research question:Which neuronal structures support face recognition?
Hypothesis:The fusiform gyrus is
implicated in face recognition
Experimental design
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• Categorical designsSubtraction - Pure insertion, evoked / differential responsesConjunction - Testing multiple hypotheses
• Parametric designsLinear - Adaptation, cognitive dimensionsNonlinear - Polynomial expansions, neurometric functions
• Factorial designsCategorical - Interactions and pure insertionParametric - Linear and nonlinear interactions
- Psychophysiological interactions
Overview Experimental Designs4/42
– =
Categorical DesignsSubtraction
• Aim: Find neuronal structures underlying a single process P
• Procedure: Under the critical assumption of „pure insertion“
[task with P ] – [control task without P ] = P
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• Aim: Find neuronal structures underlying a single process P
• Procedure: Under the critical assumption of „pure insertion“
[task with P ] – [control task without P ] = P
Categorical DesignsSubtraction
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F.C. Donders 1868
Categorical DesignsSubtraction, Example
Cognitive subtraction originated with reaction time experiments (F. C. Donders).
Measure the time for a process to occur by comparing two reaction times, one which has the same components as the other + the process of interest.
Example:
T1: Hit a button when you see a lightT2: Hit a button when the light is green but not redT3: Hit the left button when the light is green and the right button
when the light is red
T2 – T1 = time to make discrimination between light color
T3 – T2 = time to make a decision
Assumption of pure insertion:You can insert a component process into a task without disrupting the other components. 7/42
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-
„Queen!“ „Aunt Jenny?“
• „Related“ stimuli
-
• „Distant“ stimuli
Name Person! Name Gender!
-
• Same stimuli, different task
Which neuronal structures support face recognition ?
Categorical DesignsSubtraction: Baseline problem
è Several components differ!
è P implicit in control condition?
è Interaction of task and stimuli
(i.e. do task differences depend on stimuli chosen)?
-
-
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Experimental design
Face viewing: FObject viewing: O
F - O = Face recognitionO - F = Object recognition
…under assumption of pure insertion
Categorical DesignsSubtraction, Example
Kanwisher et al., 1997, J. Neurosci.
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Categorical DesignsSubtraction, Example SPM
Task 1Task 2
Session
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• Categorical designsSubtraction - Pure insertion, evoked / differential responsesConjunction - Testing multiple hypotheses
• Parametric designsLinear - Adaptation, cognitive dimensionsNonlinear - Polynomial expansions, neurometric functions
• Factorial designsCategorical - Interactions and pure insertionParametric - Linear and nonlinear interactions
- Psychophysiological interactions
Overview Experimental Designs11/42
Categorical DesignsConjunction
• One way to minimize the baseline/pure insertion problem is to isolate the same process by two or more separate comparisons, and inspect the resulting simple effects for commonalities
• A test for such activation common to several independent contrasts is called “conjunction”
• Conjunctions can be conducted across a whole variety of different contexts:• tasks• stimuli• senses (vision, audition)• etc.
• Note: the contrasts entering a conjunction must be orthogonal (this is ensured automatically by SPM)
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Task (1/2)
Viewing Naming
Stim
uli (A
/B)
Obje
cts
C
olo
urs
Visual Processing: V Object Recognition: RPhonological Retrieval: P
A1 A2
B1 B2
Categorical DesignsConjunction, Example
Which neural structures support object recognition, independent of task (naming vs. viewing)?
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Common object recognition response (R)
(Object - Colour viewing) [B1 - A1] &
(Object - Colour naming) [B2 – A2]
[ V,R - V ] & [ P,V,R - P,V ] = R & R = R
A1 B1 A2 B2
A1
Visual Processing V
B1
Visual Processing V Object Recognition R
B2
Visual Processing V Phonological Retrieval PObject Recognition R
A2
Visual Processing V Phonological Retrieval P
Stim
uli (A
/B)
Obje
cts
C
olo
urs
Task (1/2)
Viewing Naming
Categorical DesignsConjunction, Example
Which neural structures support object recognition, independent of task (naming vs. viewing)?
Price et al. 1997, NeuroImage
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Categorical DesignsConjunction, Example SPM
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A1-A2
B1-B2 p(A1-A2) < a
+p(B1-B2) < a
+
Categorical DesignsTypes of Conjunctions
• Test of global null hypothesis: Significant set of consistent effectè“Which voxels show effects of similar direction
(but not necessarily individual significance) across contrasts?”
èH1: k > 0èH0: No contrast is significant: k = 0èDoes not correspond to a logical AND !
• Test of conjunction null hypothesis: Set of consistently significant effectsè“Which voxels show, for each specified contrast,
significant effects?”èH1: k = nèH0: Not all contrasts are significant: k < nèCorresponds to a logical AND
Friston et al., 2005, NeuroImageNichols et al., 2005, NeuroImage
k = effectsn = contrasts
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Categorical DesignsConjuction, Global Null Hypothesis
• Based on the "minimum t statistic":
• imagine a voxel where contrast A gives t=1 and contrast B gives t=1.4
• neither t-value is significant alone, but the fact that both values are larger than zero suggests that there may be a real effect
• Test: compare the observed minimum t value to the null distribution of minimal t-values fora given set of contrasts
• assuming independence between the tests, one can find uncorrected and corrected thresholds for a minimum of two or more t-values (Worsley & Friston, Stat. Probab. Lett., 2000, 47 (2), 135–140)
• this means the contrasts have to be orthogonal!
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grey area:bivariate t-distriutionunder global null hypothesis
è H1: k > 0è H0: No contrast is significant: k = 0
Categorical DesignsF-test vs. Conjunction based on global null
Friston et al., 2005, NeuroImage
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• Categorical designsSubtraction - Pure insertion, evoked / differential responsesConjunction - Testing multiple hypotheses
• Parametric designsLinear - Adaptation, cognitive dimensionsNonlinear - Polynomial expansions, neurometric functions
• Factorial designsCategorical - Interactions and pure insertionParametric - Linear and nonlinear interactions
- Psychophysiological interactions
Overview Experimental Designs19/42
Parametric Designs
• Parametric designs approach the baseline problem by:
• varying the stimulus-parameter of interest on a continuum, in multiple (n>2) steps...
• ... and relating measured BOLD signal to this parameter
• Possible tests for such relations are manifold:• Linear• Nonlinear: Quadratic/cubic/etc. (polynomial expansion)• Model-based (e.g. predictions from learning models)
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Büchel et al., 1998, NeuroImage
Parametric DesignsParametric modulation of regressors by time
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Polynomial expansion&
orthogonalisation
Parametric DesignsParametric modulation of regressors
Büchel et al., 1998, NeuroImage
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Stimulusawareness
Stimulusintensity
Painintensity
Pain threshold: 410 mJ
P1 P2 P3 P4
P0-P4: Variation of intensity of a laser stimulus applied to the right hand (0, 300, 400, 500, and 600 mJ)
P0 P0 P1 P2 P3 P4
Parametric DesignsInvestigating neurometric functions
P0 P1 P2 P3 P4 P0 P1 P2 P3 P4
Büchel et al., 1998, NeuroImage
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Ú Stimulus awarenesscingulate sulcus aACC
Ú Pain intensityventral pACC
Ú Stimulus intensitydorsal pACC
Parametric DesignsInvestigating neurometric functions
Büchel et al., 1998, NeuroImage
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Parametric DesignsModel-based regressors
• General idea:generate predictions from a computational model, e.g. of learning or decision-making
• Commonly used models:• Rescorla-Wagner learning model• Temporal difference (TD) learning model• Bayesian models
• Predictions used to define regressors
• Inclusion of these regressors in a GLM and testing for significant correlations with voxel-wise BOLD responses
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Parametric DesignsModel-based fMRI analysis, Example
Gläscher & O‘Doherty, 2010, WIREs Cogn. Sci.
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Parametric DesignsModel-based fMRI analysis, Example
Gläscher & O‘Doherty, 2010, WIREs Cogn. Sci.
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Hierarchical prediction errors about sensory outcome and its probability
0 50 100 150 200 250 3000
0.5
1
prediction800/1000/1200 ms
target150/300 ms
cue300 ms
orITI
2000 ± 500 ms
time
p(F
|HT)
trials
Parametric DesignsModel-based fMRI analysis, Example
Iglesias et al., 2013, Neuron
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!"($%")
', )
*
!+($%")
!,($%")
!+($)
!,($)
!"($)
p(x3(k)) ~ N(x3
(k-1),ϑ)
p(x2(k)) ~ N(x2
(k-1), exp(κx3+ω))
p(x1=1) = s(x2)
∆./ ∝ 23/%"2/
45/%"
6, = 8,$ 9"$
6+ ∝ 8+($)9,($)
Parametric DesignsModel-based fMRI analysis, Example
The Hierarchical Gaussian Filter (HGF)
Mathys et al., 2011, Front Hum Neurosci.
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6, in midbrain (N=45)
p<0.05, whole brain FWE correctedp<0.05, SVC FWE corrected
6, = 8,$ 9"$
6+ in basal forebrain (N=45)
p<0.05, SVC FWE correctedp<0.001, uncorrected
6+ ∝ 8+($)9,($)
Hierarchical prediction errors about sensory outcome and its probability
Parametric DesignsModel-based fMRI analysis, Example
Iglesias et al., 2013, Neuron
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• Categorical designsSubtraction - Pure insertion, evoked / differential responsesConjunction - Testing multiple hypotheses
• Parametric designsLinear - Adaptation, cognitive dimensionsNonlinear - Polynomial expansions, neurometric functions
• Factorial designsCategorical - Interactions and pure insertionParametric - Linear and nonlinear interactions
- Psychophysiological interactions
Overview Experimental Designs31/42
Factorial DesignsMain effects and Interactions
interaction effect(Stimuli x Task)
Viewing Naming
Objects
Is the inferotemporal region implicated inphonological retrieval during object naming?
Colours
• Main effect of task: (A1 + B1) – (A2 + B2)
• Main effect of stimuli: (A1 + A2) – (B1 + B2)
• Interaction of task and stimuli: Can show a failure of pure insertion
(A1 – B1) – (A2 – B2)
Task (1/2)
Viewing Naming
Stim
uli (A
/B)
Obje
cts
C
olo
urs
A1 A2
B1 B2
ObjectsColours
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A1B1A2B2
Main effect of task: (A1 + B1) – (A2 + B2)
Task (1/2)
Viewing Naming
Stim
uli (A
/B)
Obje
cts
C
olo
urs
A1 A2
B1 B2
Factorial DesignsMain effect, Example SPM
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A1B1A2B2
Main effect of stimuli: (A1 + A2) – (B1 + B2)
Task (1/2)
Viewing Naming
Stim
uli (A
/B)
Obje
cts
C
olo
urs
A1 A2
B1 B2
Factorial DesignsMain effect, Example SPM
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A1B1A2B2
Interaction of task and stimuli: (A1 – B1) – (A2 – B2)
Task (1/2)
Viewing Naming
Stim
uli (A
/B)
Obje
cts
C
olo
urs
A1 A2
B1 B2
Factorial DesignsInteraction, Example SPM
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Tricomi et al., 2010, Nature
Factorial DesignsExample
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We can replace one main effect in the GLM by the time series of an area that shows this main effect.
E.g. let's replace the main effect of stimulus type by the time series of area V1.
TaskfactorTaskA TaskB
Stim1
Stim2
Stim
ulusfactor TA/S1 TB/S1
TA/S2 TB/S2
eβVTT
βVTT y
BA
BA
+-+
+-=
3
2
1
1 )(1
)( b
eβSSTT
βSSTT y
BA
BA
+--+
-+-=
321
221
1
)( )()(
)( b
GLMofa2x2factorialdesign:
main effectof task
main effectof stim. type
interaction
main effectof task
V1 time series »main effect of stim. type
PPI
Factorial DesignsPsycho-Physiological Interactions (PPIs)
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R1
R5
cognitive process
Factorial DesignsPsycho-Physiological Interactions (PPIs)
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Radially moving dots
Conditions:- Stationary- Motion and attention
(“detect changes”)- Motion without attention
V1 V5
attention
Factorial DesignsPPI, Example
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V1
V1x
attention
=
V5
V5
attention
Friston et al. 1997, NeuroImage
Büchel & Friston, 1997, Cereb. Cortex
Factorial DesignsPPI, Example
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Two possibleinterpretations of the
PPI term
V1
Modulation of V1 ® V5 by attention Modulation of attention ® V5 by V1
V1 V5 V1 V5
attention
V1
attention
eβVTT
βVTT y
BA
BA
+-+
+-=
3
2
1
1 )(1
)( b
Factorial DesignsPPI, Example
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Questions?
• Categorical designsSubtraction - Pure insertion, evoked / differential responsesConjunction - Testing multiple hypotheses
• Parametric designsLinear - Adaptation, cognitive dimensionsNonlinear - Polynomial expansions, neurometric functions
• Factorial designsCategorical - Interactions and pure insertionParametric - Linear and nonlinear interactions
- Psychophysiological interactions