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Tutorial MICCAI'04

fMRI data analysis: state of the art and future challenges

Jean-Baptiste PolinePhilippe CiuciuAlexis Roche

CEA/SHFJ, Orsay (France)

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Goal of this tutorial and plan

I. Talk 1: will orientate you in the jungle of fMRI data analyses and associated questions in neurosciences

II. Talk 2: will teach you what you should know on the BOLD hemodynamic response and its models

III. Talk 3: will develop the specific challenges of group analyses

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A road map of fMRI data analysis : from acquisition to publication

I. Introduction: what are fMRI data ? What are they used for ? Some background on neuroimaging

II.The standard fMRI analysis and « classical » activation detection

III. Emerging themes in fMRI

IV. Conclusion

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Introduction: what are fMRI data ?

I. fMRI data are a tradeoff between

– spatial resolution (2/3D) from .3 mm to 5mm

– sequences of 2/3D images (50 ms to 5s). From 100 to 1000 per subject

II. They are acquired with Magnetic Resonance scanners (.5T – 9T) T2* images prone to artefacts

III. They are functional: reflect the brain activity (this will be developed)

time

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fMRI data: What are they used for ?

Localize brain regions involved in the realization of sensori, motor, or cognitive processes

time

Experimental Paradigm

64x64x32x1000 time

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Neo-phrenology ?

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A new multi-disciplinary field

MRIPhysic, Bio-physic

ElectronicsElectromagnetic

NeurobiologyNeurosciences (cellular)

Physiology

Cognitive Sciences Cognitive Neurosciences

NeuropsychologyNeurology, Psychiatry

Data analysisModeling

Applied Mathematics

Neuroimaging

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fMRI data: they can be used for

I. Reveal maps of the brain organization during cognitive processes ?

– Continuous maps … or

– Explore the brain segregation in modules ?

II. During “uncontrolled” brain states (rest, sleep, coma,)

III. Get the timing of the brain processes ? Causality ?

IV. Inform on the functional/effective connectivity ?

V. Provide biomarkers for the pathology using analyses across populations / diagnosis

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Methods used in fMRI analyses

I. Simple voxel wise statistics (t, F, Chi2, …)

II. Multivariate Methods (PCA, PLS, CVA, ICA, pICA, IB, etc)

III. Wavelets (1D, 2D, 3D ?)

IV. Clustering (supervised, unsupervised, LDA, SVM, …)

V. Bayesian Statistics; PEB; Non parametric statistics

VI. Markov fields; Spatial models

VII. Information theory

VIII. Optimisation/Estimation (EM, MCMC, …)

IX. Graph theory, dynamical systems, …

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The growth of neuroimaging in general and of fMRI in particular

Number of published papers

Papers that contain fMRI in their titleSource : pubmed

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Part II: Standard analyses

• The truth about fMRI data

• Modelling the experimental paradigm

i. Univariate

ii. Multivariate

• The Multiple comparison problem

Part II

Part I

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Part II: The truth about fMRI data

64x64 Pixels ~ 3 x 3 mm 128x128Pixels ~ 1.5 x 1.5mm

I. They are distorted

II. They are noisy

III. They don’t have signal everywhere in the brain

IV. They depend on many parameters: T2*, B0, TE, …

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Part II: The truth about fMRI data

1 brain volume (64x64x30) in 3 sec (TR =1)

V. They are big … and are getting bigger

T=1T=2

T=30

T=1T=2

T=30

TR =200

T=1T=16

T=30

T=2

This is ONE run; often 3-8 runs X 15 subjects 6D Data (~20 Go)

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Part II: The standard fMRI analysis and « classical » activation detection

I. A method used in 95% of the publications

II. Simple, fast, easy to understand for neuroscientists, found in most packages (SPM, FSL, AFNI, BrainVoyager, Rumba, etc …)

III. Developed in the framework of medical statistics (Analysis of Variance) and easily accepted by journals

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realignment &coregistration smoothing

normalisation

Corrected p-values

images

Adjusted dataDesignmatrix

Anatomical Reference

Spatial filter

Random Field Theory

Your question:a contrast

Statistical MapUncorrected p-values

General Linear Model

Linear fit

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Realignment : spatial & temporal

Original Distorted Rotated, distorted

and realigned

A B C D E

B - D

1st eigenimage : loads of variance on the border

T=1T=2

T=30T=1T=16

T=30

T=2

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Inter-subjects normalization

Subj 1 Subj 2 Subj 3

Subj 4 Subj 5 Subj 6

Template / canonical brain

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Time

Intensity

Tim

e

single voxeltime series

Voxel by voxel fMRI response analysis

modelspecification

parameterestimation

hypothesis

statistic

SPM

Passive word listeningversus rest; one

session

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Intensity

Tim

e

Regression model

= + + erro

r

Error: normal andindependently and

identically distributedor

more complex models

Question: Is there a change in the BOLD response between listening and rest?

Hypothesis test: β 1 = 0?(using t-statistic)

1β2β

1x 2x ε

),0(~ 2IN σε

Part II

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Design matrix

= +

2

1

ˆ

ˆ

β

β

y + ε= X β

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Modeling low frequency drift

Three different models

X:

The good: All sort of effect (measured or assumed) can be added The bad: We don’t know which one should be inThe ugly: Models are rarely checked, assumed constant across voxels,

assumed linearity

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temporal correlation

Confounds, noise … and signal

1. Scanner drift2. Cardiac-

respiratory cycle3. head

movements4. non-modelled

neuronal events5. HRF shape

different6. UNKNOWN

BOLD responseLinear and non

linear

εβ += Xy

modelled BOLD response

Low freq regressors

movement-related

regressors

yXXX TT 1)(ˆ −=βParameter Estimation with OLS

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Inference - t- and F statistics

c = 1 0 0 0 0 0 0 0 0 0 0

)ˆ(ˆ

ˆ

ββ

T

T

cdtS

ct =

0 0 1 0 0 0 0 0 0 0 0 0 0 0 1 0 0 0 0 0 0 00 0 0 0 1 0 0 0 0 0 00 0 0 0 0 1 0 0 0 0 00 0 0 0 0 0 1 0 0 0 00 0 0 0 0 0 0 1 0 0 0

c =

SPMF

F = error

varianceestimate

additionalvariance

accounted for

by tested effects

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Real life design matrix for real life experiments

V A V A V A

C1 C1 C2 C2 C3 C3

V

A

C1

C2

C3

C1

C2

C3

Factorial Design2x2

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Convolution model

Design andcontrast

SPM(t) orSPM(F)

Fitted andadjusted data

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=

Mass-univariate approach

+

β

ε

N

p

p

K

εβ += Xy

K

N

y XN (time)

K (voxels)

∑ 2ε

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E

voxelsvoxels

scansscans

e

= +Y X

data matrix

desi

gn

matr

ix

+= ×voxelsvoxels

scansscans

β^

residuals

parameterestimates

Variance(e) =

= ss11

VV11

UU11

+ ss22

VV22

UU22

+ ...

/

E / std = normalised residuals

Residual analysis Part II

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Temporal pattern difficult to interpret

Normalized residual of a language study: first spatial componentPart II

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e

= +Y X

data matrix

des

ign

mat

rix

+=voxelsvoxels

scansscans

β^

residuals

parameterestimates

Variance(e) =

= APPROX. APPROX.

OF YOF Yss11

VV11

UU11

+ APPROX. APPROX. OF YOF Y

ss22

VV22

UU22

+ ...parameterestimates

[U S V] = SVD (X’Y)

OR in the space defined by a contrast

Partial Least Square – Multivariate Linear ModelsPart II

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UU11

VV11

Multivariate Linear Models: first component on a calculus studyPart II

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Other Multivariate methods

I. ICA

II. Probabilistic ICA

III. Functional Clustering

IV. Anatomo-functional clustering

V. Many others

Part II

Riesmann et al., 04

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The multiple comparison problem: Where’s the signal?

t > 0.5t > 3.5t > 5.5

High Threshold Med. Threshold Low Threshold

Good Specificity

Poor Power(risk of false negatives)

Poor Specificity(risk of false positives)

Good Power

...but why threshold?!

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5mm 10mm 15mm

Suppose N independent tests for voxel. Let a be the threshold such that P(max(ti) > ta) = a (eg : a = 5%, N = 50000)P(max(ti) > ta) = 1 - (1-a)N

=> a = 1 - (1-a)1/N =~ a/N (eg : a = 10-6 )

Independent : a = 1- (1-a)1/N

Completely dependant : a = aDependant : a = ?

N ? - Dependence ?

The MC problem: dependence on the number of tests and on the images smoothnessPart II

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Random Field Theory solution

Autocorrelation Function

FWHM

1- Estimate field roughness Λwith the Cov of the spatial derivatives

2- Cut the field at threshold u

E(u) ≈ λ (Ω) |Λ|1/2 (u2 -1) exp(-u2/2) / (2π )2

3- Compute expected Euler characteristics that approximate prob. of the field to cross u :

Can be applied on t, F, X, .. Fields; can be used to get probability of the size of a cluster

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Level of inference, power and regional specificityPart II

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False Detection Rate

p(i) ≤ i/V × q

p(i)

i/V

i/V × qp-v

alu

e

0 1

01

The idea:To control the number of false positive as a proportion q of the number of detected voxels (JRSS, 95; Genovese 02) The method:

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FWE

6.7% 10.4% 14.9% 9.3% 16.2% 13.8% 14.0% 10.5% 12.2% 8.7%

Control of Familywise Error Rate at 10%

11.3% 11.3% 12.5% 10.8% 11.5% 10.0% 10.7% 11.2% 10.2% 9.5%

Control of Per Comparison Rate at 10%

Control of False Discovery Rate at 10%

Courtesy of T. Nichols

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Permutation testing

Threshold 5% of the

I. The idea:

– The experimentator knows which scans are condition A and which are conditions B

– Under the null hypothesis, same sort of results if A and B are randomly labelled

II.The method:

– Construct the distribution of the max under N re-labelling and compare the value obtained under the true labelling

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LikelihoodLikelihood PriorPriorPosteriorPosterior

SPMsSPMsPPMsPPMs

γ

θ

u

)(yft =

)0|( =θtp

)|( yp θ

Bayesian Inference: Posterior Probability Maps

)()|()|( θθθ pypyp ∝SP

Mm

ip[0

, 0, 0

]

<

< <

PPM2.06

rest [2.06]

SPMresults:C:\home\spm\analysis_PET

Height threshold P = 0.95

Extent threshold k = 0 voxels

Design matrix1 4 7 10 13 16 19 22

147

1013161922252831343740434649525560

contrast(s)

4

SPM

mip

[0, 0, 0]

<

< <

SPMT39.0

rest

SPMresults:C:\home\spm\analysis_PET

Height threshold T = 5.50

Extent threshold k = 0 voxels

Design matrix1 4 7 10 13 16 19 22

147

1013161922252831343740434649525560

contrast(s)

3

Infer on what DID NOT elicit a response

Separate effect-size and effect-variability

P-values don’t change with search volume

For hgh thresholds have intrinsically high specificity

computationally demanding

Bayesian approach is yet to be accepted by medical/biology litterature

P(E >2) > .95

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Part III: Emerging themes in fMRI

I. How to analyze ALL the data ? Multimodal fusion

– Integrating anatomical information

– Other temporal information (Cardiac, MEEG, …)

– Subjects information

II. Bayesian Analyses

III. Connectivity analyses

– Multivariate analyses; SOM, …

– Region based + graph theory

– Region based + SEM/Others

IV. Parceling / Clustering

V. Prediction

Part III

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Anatomical and functional integration :cortical surface mapping (Andrade et al, 2001)

Theory of randomfields

General Linear Models

Distorsion correction for 3T field

Inflation algorithm for visualisation

Part III

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RETINOTOPIC AREA (Courtesy of Michel Dojat et al, Grenoble)Part III

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EEG-fMRI simultaneous recording and fusion (Lahaye et al, 2004)

Fusion Algorithm

Part III

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Harrison et al (2003) NeuroImage

Friston & Buchel (2000) PNAS

Laufs et al (2003) PNAS

Grady et al (2001)

J Neurosci

Part III

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LateralizedBOLD

Response-3

0

3

L R L L L R L R R L R L L R R R L R L R RResponse Side

right hand > left hand left hand > right hand

Predicting manual responses

Dehaene et al, Nature neurosciences

Part III

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Emerging themes in methods (1990-2004)

0

1

2

3

4

5

6

90 92 94 96 98 0 2

Permuation &fRMI

02468

101214161820

90 92 94 96 98 0 2

Wavelet & fMRI

0

2

46

810

1214

16

18

90 92 94 96 98 0 2

Bayesian &fMRI

1. Wavelets1. Wavelets

3. Permutation3. Permutation2. Bayesian2. Bayesian

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Conclusion: why are we failing to have an impact on the field ?

why most used sofware are developed by psychiatrists?

I. Because we don’t know enough of the questions asked to the data

II. Because we miss part of the problems during acquisition and context of acquisition of the data (movement, etc…)

III. Because we don’t keep up with the advances in cognitive neurosciences

IV. Because we don’t keep up with the technological advances of the scanners

BECAUSES NEUROSCIENCES AND IMAGE/SIGNAL PROCESSING WORLDS ARE TOO DISCONNECTED

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A. Roche

F. Kherif

S. Mériaux

P. Ciuciu

G. Flandin

S. Dodel

P.-J. Lahaye

M. Lavielle J.-B. Poline et P. Valdes Sosa

L. Hugueville et D. Schwartz

L. Garnero et X

B. Thirion

Salima Makni

THANKS TO …. www.madic.org