TReNDS - XA Sicatb.sourceforge.net/gift/Lecture2_04.pdf · 2005. 4. 15. · KNNK λλ θ λλ − + + ... source #2 map (whereas all of the nine “subjects” had a similar, source

1

GIFT CourseGIFT CourseLecture 2: Group ICALecture 2: Group ICA

X A S= ×

Vince D. Calhoun, Ph.D.Vince D. Calhoun, Ph.D.Director, Medical Image Analysis LaboratoryDirector, Medical Image Analysis Laboratory

Olin Neuropsychiatry Research Center,Olin Neuropsychiatry Research Center,Institute of LivingInstitute of Living

Assistant Clinical Professor, PsychiatryAssistant Clinical Professor, PsychiatryYale University School of MedicineYale University School of Medicine

SoliSoli DeoDeo Gloria Gloria 2

IntroductionIntroduction•• Using ICA to analyze fMRI data of multiple Using ICA to analyze fMRI data of multiple

subjects raises several questions:subjects raises several questions:•• How many components should be calculated?How many components should be calculated?•• How are these components to be combined across How are these components to be combined across

subjects?subjects?•• How should the final results be thresholded and/or How should the final results be thresholded and/or

presented? presented?

•• Several approaches presented:Several approaches presented:•• Calhoun 2001 Calhoun 2001 –– stack images and backstack images and back--reconstructreconstruct•• Svensen 2002 Svensen 2002 –– stack time coursesstack time courses•• Schmidthorst 2004 Schmidthorst 2004 –– compared three approachescompared three approaches

2


ApproachesApproaches•• Separate ICA analysis for each subjectSeparate ICA analysis for each subject

•• Must select which components to compare between the Must select which components to compare between the individualsindividuals

•• Sensitive to incorrect or Sensitive to incorrect or ‘‘differentdifferent’’ source separations source separations due to noise or other factors (some components may be due to noise or other factors (some components may be split differently in different subjects)split differently in different subjects)

•• Group ICA (stacking images)Group ICA (stacking images)•• Will do best for subjects which share common sources Will do best for subjects which share common sources

(assumes spatial stationarity)(assumes spatial stationarity)•• Components can easily be comparedComponents can easily be compared•• Time courses can also be comparedTime courses can also be compared


Approach 1: MVPTApproach 1: MVPT--RR

……15 15 ““eventsevents””

Press buttons (1Press buttons (1--4) to 4) to indicate choiceindicate choice

11 22 33 44

Time (seconds)Time (seconds)

00 15.4 15.4 31.531.5 47.047.0 300 300

3


MethodsMethods• Scan Parameters

• Single-shot EPI• FOV = 24cm, 64x64• TR=1s, TE=40ms• 18 slices• Slice thickness = 5mm• Gap = .5mm• 300 volumes acquired

• Preprocessing• Timing correction• Motion correction• Normalization• Smoothing

• ICA• An ICA estimation was performed on each of the ten subjects• Data were first reduced from 300 to 25 using principal

component analysis (PCA)• Maps from each subject were inspected for similarity and

similar maps were averaged across subjects (e.g. all visual areas were averaged together)

• Group averaged maps were then thresholded at Z

4


ICA ResultsICA ResultsN=10N=10Z>3.1Z>3.1

ICA revealed a large network of ICA revealed a large network of similar areas including: similar areas including: ••frontal eye fields (blue) frontal eye fields (blue) ••supplementary motor areas (green supplementary motor areas (green w/ outline)w/ outline)••primary visual (red)primary visual (red)••visual association (red)visual association (red)••thalamic (red)thalamic (red)••basal ganglia (green w/ outline)basal ganglia (green w/ outline)••a large cerebellar activation (red)a large cerebellar activation (red)••bilateral inferior parietal bilateral inferior parietal deactivationsdeactivations (not shown)(not shown)

ICA also revealed areas not identified ICA also revealed areas not identified by SPM including:by SPM including:••primary motor (green)primary motor (green)••frontal regions anterior to the frontal regions anterior to the frontal eye fields (blue)frontal eye fields (blue)••superior parietal regions (blue)superior parietal regions (blue)


ICA: Single SubjectICA: Single SubjectThe ICA maps from The ICA maps from one subject for the one subject for the visual and basal visual and basal

ganglia components ganglia components are depicted along are depicted along

with their time with their time courses courses (basal (basal

gangliaganglia in green and in green and visualvisual in pink)in pink)

Note that the visual Note that the visual time coursetime course

preceedspreceeds the motor the motor time coursetime course

5


EventEvent--Averaged Time CoursesAveraged Time Courses••Time courses from selected Time courses from selected voxels in the raw data (a) and voxels in the raw data (a) and time courses produced by the time courses produced by the ICA method (b).ICA method (b).••In all cases the time courses In all cases the time courses are eventare event--averaged (according averaged (according to when the figure was to when the figure was presented) within each presented) within each participant and then averaged participant and then averaged across all ten participants.across all ten participants.••Voxels from the raw data Voxels from the raw data were selected by choosing a were selected by choosing a local maximum in the local maximum in the activation map and averaging activation map and averaging the two surrounding voxels in the two surrounding voxels in each direction.each direction.••Dashed lines indicate the Dashed lines indicate the standard error of the mean.standard error of the mean.


Approach 2: Group ICAApproach 2: Group ICA

6


Order SelectionOrder Selection( ) ( ) ( ) ( )1ˆ2 2 1 12NAIC N M K N NK Nθ

⎛ ⎞= − − + + + −⎜⎝ ⎠

L

( ) ( ) ( ) ( )1 1ˆ 1 1 ln2 2NMDL N M K N NK N Mθ⎛ ⎞= − − + + + −⎜ ⎟⎝ ⎠

L

( ) ( )( )

1

1

1

...ˆ ln 1 ...

K NN K

N

N KK N

λ λθ

λ λ

−+

+

⎛ ⎞⎜ ⎟

= ⎜ ⎟⎜ ⎟+ +

−⎝ ⎠

L

M=number of voxelsM=number of voxelsK=number of time pointsK=number of time pointsN=number of sourcesN=number of sourcesλλ=eigenvalues from PCA=eigenvalues from PCA


BackreconstructionBackreconstruction and Hypothesis Testing and Hypothesis Testing

•• Single subject maps can be calculated by backSingle subject maps can be calculated by back--reconstructing from the ICA analysis of all the reconstructing from the ICA analysis of all the subjectssubjects

•• These maps can then be tested for a significant These maps can then be tested for a significant amplitude by using a voxelamplitude by using a voxel--byby--voxel voxel tt--test on the test on the single subject mapssingle subject maps

†1 1 1

†

ˆ ˆ

M M M

⎡ ⎤⎡ ⎤⎢ ⎥⎢ ⎥ = ⎢ ⎥⎢ ⎥⎢ ⎥⎢ ⎥⎣ ⎦ ⎣ ⎦

G F YAS

G F Y

full decompositionfull decomposition

( )†1 †ˆ ˆi i i i−=S G A F Ysinglesingle--subject mapsubject map

ˆi iFG A

singlesingle--subjectsubjecttime coursetime course

1ˆ i τ≥shypothesishypothesis

test for component 1test for component 1(first row of (first row of ŜŜii))

7


SimulationSimulation

Nine simulated source maps and time Nine simulated source maps and time courses were generated, followed by courses were generated, followed by an ICA estimation. The red lines an ICA estimation. The red lines indicate the indicate the tt

8


The Stationarity AssumptionThe Stationarity Assumption

••The ICA estimation requires the The ICA estimation requires the data to be stationary across subjectsdata to be stationary across subjects••Some signals in the data (e.g. Some signals in the data (e.g. physiologic noise) will most likely physiologic noise) will most likely *not* be stationary*not* be stationary••However it is reasonable to However it is reasonable to assume the signal of interest (fMRI assume the signal of interest (fMRI activation) will be stationaryactivation) will be stationary••A simulation was performed to A simulation was performed to examine how nonexamine how non--stationary stationary sources would affect the resultssources would affect the results••One stationary signal (fMRI One stationary signal (fMRI activation) and one nonactivation) and one non--stationary stationary signal were simulated for a fivesignal were simulated for a five--subject analysissubject analysis••The ICA results reveal that the The ICA results reveal that the fMRI activation is preservedfMRI activation is preserved

ICA resultsICA results

Stationary source S common to Stationary source S common to all five all five ““subjectssubjects””

source #2source #2source #1source #1

Sources S1Sources S1--S5 S5 differing across the differing across the

five five ““subjectssubjects””

S1S1 S2S2

S3S3 S4S4 S5S5

SS


MethodsMethods• Scan Parameters

• 9 slice Single-shot EPI• FOV = 24cm, 64x64• TR=1s, TE=40ms• Thickness = 5/.5 mm• 360 volumes acquired

• Preprocessing• Timing correction• Motion correction• Normalization• Smoothing

• ICA• An ICA estimation was performed on each of the nine subjects• Data were first reduced from 360 to 25 using PCA, the data were

concatenated and reduced a second time from 225 to 20 using PCA• An ICA estimation was performed after which single subject maps and

time courses were calculated• Group averaged maps were thresholded at t

9


Are the data separable? (fMRI experiment)Are the data separable? (fMRI experiment)

••The same slice from nine subjects when the right (red) and left The same slice from nine subjects when the right (red) and left (blue) visual fields (blue) visual fields were stimulated, (a) analyzed via linear modeling (LM), (b) backwere stimulated, (a) analyzed via linear modeling (LM), (b) back--reconstructed from a reconstructed from a group ICA analysis, or (c) calculated from an ICA analysis perfogroup ICA analysis, or (c) calculated from an ICA analysis performed on each subject rmed on each subject separately. A transiently taskseparately. A transiently task--related component is depicted in green.related component is depicted in green.••The results between the two ICA methods appear quite similar andThe results between the two ICA methods appear quite similar and match well with match well with the LM results as well (note that there may be small differencesthe LM results as well (note that there may be small differences due to different initial due to different initial conditions for the ICA estimation) conditions for the ICA estimation)


Comparison with RFX GLM ApproachComparison with RFX GLM Approach

RR LL

V.D. Calhoun, T. Adali, G.D. Pearlson, and J.J. Pekar, "A Method for Making Group Inferences From Functional MRI Data Using Independent Component Analysis," Hum. Brain Map., vol. 14, pp. 140-151, 2001.

10


Group Inferences using ICAGroup Inferences using ICA•• Group ICA can be broken up into 6 stages.Group ICA can be broken up into 6 stages.

•• PreprocessingPreprocessing•• Same Preprocessing that you normally do in SPM. Realignment, Same Preprocessing that you normally do in SPM. Realignment,

motion correction, comotion correction, co--registration, etc.registration, etc.•• Data ReductionData Reduction

•• Implemented using PCA.Implemented using PCA.•• ICAICA

•• Implemented using any ICA algorithm( Infomax, Optimal ICA, Implemented using any ICA algorithm( Infomax, Optimal ICA, FastICA).FastICA).

•• Back ReconstructionBack Reconstruction•• Individual Subject Components are back reconstructed using the Individual Subject Components are back reconstructed using the

results from PCA.results from PCA.•• Component calibration including 1)Component calibration including 1) scaling scaling and 2) and 2) sign changesign change

•• Using the functional data the components, time courses and spatiUsing the functional data the components, time courses and spatial al maps, are converted from arbitrary units to percent signal changmaps, are converted from arbitrary units to percent signal change.e.

•• Group StatisticsGroup Statistics•• Using the subjectUsing the subject’’s back reconstructed components statistics are s back reconstructed components statistics are

calculated.calculated.


Group Inferences using ICA contGroup Inferences using ICA cont……

•• Data ReductionData Reduction –– Starting with 4 subjectsStarting with 4 subjects

Subject 1Functional Data

PCA#1 CAT#2




PCA 1(reduced data)

PCA 2(reduced data)

PCA 3(reduced data)

PCA 4(reduced data)

PCA 1PCA 2

PCA 3PCA 4

PCA#2

PCA 2-1(reduced data)

PCA 3-1(reduced data)

CAT#3

PCA 2-1PCA 2-2

PCA 3(reduced data)

PCA#3

Parameters for examples- 3 Data Reduction Steps- 5 IC extracted- 4 Subjects- 1Session

11


Group Inferences using ICA cont..Group Inferences using ICA cont..

•• ICAICA -- Extracting 5 components from reduced dataExtracting 5 components from reduced data

PCA 3(reduced data)

ICA

Group Components

Component 1: Spatial Map and Time course






Group Inferences using ICA cont..Group Inferences using ICA cont..•• Back ReconstructionBack Reconstruction –– Group components reconstructed to subject components. Back Group components reconstructed to subject components. Back

Reconstruction uses information from the data reduction stage.Reconstruction uses information from the data reduction stage.

Group Components

BR#1 UNCAT#1 BR#2 UNCAT#1Subject 1’sComponents

Subject 2’sComponents



BR#3

12


Group Inferences using ICA cont..Group Inferences using ICA cont..

•• Calibrating ComponentsCalibrating Components 1 Subject and 5 Components Calibrated to percent 1 Subject and 5 Components Calibrated to percent signal changesignal change

Subject 1 Components( Units Arbitrary)






Subject 1Functional Dataand

Subject 1 Components( Units in Percent Signal Change)






Convert


Group Inferences Using ICA cont..Group Inferences Using ICA cont..

•• Group StatsGroup Stats -- Component 1 for all 4 subjects is used to Component 1 for all 4 subjects is used to computecompute statistical spatial mapsstatistical spatial maps

Subject 1 Component 1




Mean Component 1

STDComponent 1

T StatisticComponent 1

Statistics

13


Group Inferences Using ICA contGroup Inferences Using ICA cont……

•• All components from Group ICA (4 subject, 5 components)All components from Group ICA (4 subject, 5 components)

Subject 1Component 1

Component 2

Component 3

Component 4

Component 5


Component 2

Component 3

Component 4

Component 5


Component 2

Component 3

Component 4

Component 5


Component 2

Component 3

Component 4

Component 5

Back Reconstructed Components

MeanComponent 1

Component 2

Component 3

Component 4

Component 5

T StatisticComponent 1

Component 2

Component 3

Component 4

Component 5

STDComponent 1

Component 2

Component 3

Component 4

Component 5

Group Statistics Components

Independent Components


ApplicationApplication•• Simulated DrivingSimulated Driving

14


Applications: Simulated Driving (Naturalistic Behavior)Applications: Simulated Driving (Naturalistic Behavior)

Higher Order Visual/Motor: Higher Order Visual/Motor: Increases during driving; less Increases during driving; less during watching.during watching.

Low Order Visual: Low Order Visual: Increases during driving; Increases during driving; less during watching.less during watching.Motor control: Motor control: Increases Increases only during driving.only during driving.Vigilance: Vigilance: Decreases only Decreases only during driving; amount during driving; amount proportional to speed.proportional to speed.

Error Monitoring & Error Monitoring & Inhibition: Inhibition: Decreases only Decreases only during driving; rate during driving; rate proportional to speed.proportional to speed.Visual Monitoring: Visual Monitoring: Increases during epoch Increases during epoch transitions.transitions.

N=12N=12

* Drive Watch


Orbitofrontal/Anterior CingulateOrbitofrontal/Anterior Cingulate•• InvolvementInvolvement

•• Involved in disinhibition Involved in disinhibition ““taking off the braketaking off the brake”” and and error detection (error detection (BlumerBlumer, , Rauch, Rauch, NobreNobre))

•• Anterior cingulate divided Anterior cingulate divided into rostral into rostral ‘‘affectaffect’’ region region and caudal and caudal ‘‘cognitioncognition’’region (region (DevinskyDevinsky))

•• DrivingDriving•• Speed related decrease is Speed related decrease is

consistent with disinhibitionconsistent with disinhibition•• EEG study using NFS EEG study using NFS

found greater alpha power found greater alpha power during drivingduring driving

15


FrontoparietalFrontoparietal•• InvolvementInvolvement

•• Visual awareness, anterior and posterior Visual awareness, anterior and posterior attentional system (Rees, Posner, attentional system (Rees, Posner, Schneider)Schneider)

•• Anterior cingulate divided into rostral Anterior cingulate divided into rostral ‘‘affectaffect’’ region and caudal region and caudal ‘‘cognitioncognition’’region (region (DevinskyDevinsky))

•• DrivingDriving•• Specifically decreasedSpecifically decreased•• Speed related decrease is consistent Speed related decrease is consistent

with change in awarenesswith change in awareness


MotorMotor•• InvolvementInvolvement

•• Motor preparation (Motor preparation (ThachThach))•• Visuomotor integrationVisuomotor integration•• MovementMovement

•• DrivingDriving•• Switched on during drivingSwitched on during driving

VisualVisual•• InvolvementInvolvement

•• Visual InputVisual Input•• Visual ProcessingVisual Processing•• (W) Visual motion(W) Visual motion•• (W) Orientation (Allen) or Memory processing (W) Orientation (Allen) or Memory processing

((MenonMenon))

•• DrivingDriving•• Increased during drivingIncreased during driving•• Increased less during watchingIncreased less during watching•• Consistent with attentional modulation (Gandhi)Consistent with attentional modulation (Gandhi)

Transient VisualTransient Visual•• InvolvementInvolvement

•• Visual InputVisual Input•• Visual ProcessingVisual Processing•• Transient changes (Transient changes (KonishiKonishi))

•• DrivingDriving•• Transiently increased between epochsTransiently increased between epochs•• Possibly due to Possibly due to ““flashflash””

16


Interpretation of ResultsInterpretation of Results


Group ICA of fMRI ToolboxGroup ICA of fMRI Toolbox

Left HemisphereVisual Stimuli OnsetLeft HemisphereVisual Stimuli Onset

VoxelVoxel

BOLD Signal

Documents

TReNDS - XA Sicatb.sourceforge.net/gift/Lecture2_04.pdf · 2005. 4. 15. · KNNK λλ θ λλ − + + ... source #2 map (whereas all of the nine “subjects” had a similar, source