Tutorial MICCAI'04. fmri data analysis: state of the art and future challenges. Jean-Baptiste Poline Philippe Ciuciu Alexis Roche

Transcription

1 Tutorial MICCAI'04 fmri data analysis: state of the art and future challenges Jean-Baptiste Poline Philippe Ciuciu Alexis Roche CEA/SHFJ, Orsay (France)

2 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

3 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

4 Introduction: what are fmri data? I. II. 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 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

5 fmri data: What are they used for? Experimental Paradigm time 64x64x32x1000 time Localize brain regions involved in the realization of sensori, motor, or cognitive processes

6 Neo-phrenology?

7 A new multi-disciplinary field Neurobiology Neurosciences (cellular) Physiology MRI Physic, Bio-physic Electronics Electromagnetic Neuroimaging Data analysis Modeling Applied Mathematics Cognitive Sciences Cognitive Neurosciences Neuropsychology Neurology, Psychiatry

8 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

9 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,

10 The growth of neuroimaging in general and of fmri in particular Number of published papers Papers that contain fmri in their title Source : pubmed

11 : Standard analyses Part I The truth about fmri data Modelling the experimental paradigm Univariate ii. Multivariate The Multiple comparison problem i.

12 : 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,

13 : The truth about fmri data V. They are big and are getting bigger T=1 T=16 T=2 T=1 T=2 T=30 1 brain volume (64x64x30) in 3 sec (TR =1) T=1 T=2 T=30 T=30 TR =200 This is ONE run; often 3-8 runs X 15 subjects 6D Data (~20 Go)

14 : 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

15 Design matrix Adjusted data Your question: a contrast Spatial filter images realignment & coregistration smoothing General Linear Model Random Field Theory Linear fit normalisation Statistical Map AnatomicalUncorrected p-values Reference Corrected p-values

16 Realignment : spatial & temporal T=1 T=2 1st eigenimage : loads of variance on the border T=1 T=30 T=16 T=2 T=30 A B Original Distorted C Rotated, distorted D E and realigned B-D

17 Inter-subjects normalization Subj 1 Subj 2 Subj 3 Subj 4 Subj 5 Subj 6 Template / canonical brain

18 Voxel by voxel fmri response analysis model specification Time parameter estimation hypothesis statistic Ti m e Intensity Passive word listening versus rest; one session single voxel time series SPM

19 Regression model ε ~ N (0, σ I ) Time = β1 Intensity + β2 x1 Question: Is there a change in the BOLD response between listening and rest? + x2 error 2 ε Error: normal and independently and identically distributed or more complex models Hypothesis test: β 1 = 0? (using t-statistic)

20 Design matrix = y = X βˆ1 βˆ 2 + β + εˆ

21 Modeling low frequency drift X: Three different models The good: All sort of effect (measured or assumed) can be added The bad: We don t know which one should be in The ugly: Models are rarely checked, assumed constant across voxels, assumed linearity

22 Confounds, noise and signal modelled BOLD response BOLD response Linear and non linear Scanner drift Cardiacrespiratory cycle head movements non-modelled neuronal events HRF shape different UNKNOWN Low freq regressors movementrelated regressors y = Xβ + ε temporal correlation Parameter Estimation with OLS T 1 T ˆ β = (X X ) X y

23 Inference - t- and F statistics c = c= c T βˆ t= T ˆ ˆ St d ( c β ) additional variance accounted for F = by tested error effects variance estimate SPM{F}

24 Real life design matrix for real life experiments C1 C1 C2 C2 C3 C3 Factorial Design 2x2 V A V A V A C1 V C2 C3 C1 C2 A C3

25 Convolution model Design and contrast SPM(t) or SPM(F) Fitted and adjusted data

26 Mass-univariate approach y = Xβ + ε K p K (voxels) β p = N (time) y K N X + N εˆ 2 ˆ ε

27 voxels data matrix scans = design matrix Residual analysis parameter estimates + resid uals ^ β + e Y = X Variance(e) = V1 voxels scans E V2 U1 = s1 U2 + s / E / std = normalised residuals

28 Normalized residual of a language study: first spatial component Temporal pattern difficult to interpret

29 voxels data matrix = scans design matrix Partial Least Square Multivariate Linear Models Y = X parameter estimates + residu als ^ β + e Variance(e) = V1 V2 U1 parameter estimates = s1 [U S V] = U2 APPROX. OF Y + s2 APPROX. OF Y SVD (X Y) OR in the space defined by a contrast +...

30 Multivariate Linear Models: first component on a calculus study U1 V1

31 Other Multivariate methods I. ICA II. Probabilistic ICA III. Functional Clustering IV. Anatomo-functional clustering V. Many others Riesmann et al., 04

32 The multiple comparison problem: Where s the signal? High Threshold Med. Threshold Low Threshold t > 5.5 t > 3.5 t > 0.5 Good Specificity Poor Specificity (risk of false positives) Poor Power (risk of false negatives) Good Power...but why threshold?!

33 The MC problem: dependence on the number of tests and on the images smoothness 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 ) N? - Dependence? 5mm 10mm Independent : a = 1- (1-a)1/N Completely dependant : a = a Dependant :a=? 15mm

34 Random Field Theory solution FWHM 1- Estimate field roughness Λ with the Cov of the spatial derivatives Autocorrelation Function 2- Cut the field at threshold u 3- Compute expected Euler characteristics that approximate prob. of the field to cross u: E(u) λ (Ω) Λ 1/2 (u2-1) exp(-u2/2) / (2π )2 Can be applied on t, F, X,.. Fields; can be used to get probability of the size of a cluster

35 Level of inference, power and regional specificity This EPS image does not contain a screen preview. It will print correctly to a PostScript printer. File Name : recap_tests.eps Title : recap_tests.eps Creator : CLARIS EPSF Export Filter V1.0 CreationDate : 5/12/96 2:13:30 p.m.

36 False Detection Rate The idea: To control the number of false positive as a proportion q of the number of detected voxels (JRSS, 95; Genovese p(i) i/v q i/v q The method: 0 p(i) p-value 02) i/v

37 Control of Per Comparison 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 Familywise Error Rate at 10% FWE Control of False Discovery Rate at 10% 6.7% 10.4% 14.9% 9.3% 16.2% 13.8% 14.0% 10.5% 12.2% 8.7% Courtesy of T. Nichols

38 Permutation testing 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 Threshold 5% of the

39 Bayesian Inference: Posterior Probability Maps p (θ y ) p ( y θ ) p(θ ) Posterior γ PPMs Likelihood Prior SPMs p (t θ = 0) u Infer on what DID NOT elicit a response p (θ y ) θ rest [2.06] Separate effectsize and effectvariability t = f ( y) rest contrast(s) < < SPMmip [0, 0, 0] < SPM{T SPMresults:C:\home\spm\analysis_PET Height threshold T = 5.50 Extent threshold k = 0 voxels Bayesian approach is yet1 to be 4 7 accepted by medical/biol ogy litterature 34 3 < For hgh thresholds have intrinsically high specificity Design matrix PPM>2) >.95 P(E SPMresults:C:\home\spm\analysis_PET Height threshold P = 0.95 Extent threshold k = 0 voxels 2.06 P-values don t change with 1 search volume 4 contrast(s) 4 < SPMmip [0, 0, 0] < computation ally demanding } Design matrix

40 I: Emerging themes in fmri I 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

41 I Anatomical and functional integration : cortical surface mapping (Andrade et al, 2001) Theory of random fields Distorsion correction for 3T field General Linear Models Inflation algorithm for visualisation

42 RETINOTOPIC AREA (Courtesy of Michel Dojat et al, Grenoble) I

43 I EEG-fMRI simultaneous recording and fusion (Lahaye et al, 2004) Fusion Algorithm

44 Friston & Buchel (2000) PNAS I Harrison et al (2003) NeuroImage Laufs et al (2003) PNAS Grady et al (2001) J Neurosci

45 Predicting manual responses I right hand > left hand Lateralized BOLD Response left hand > right hand Response Side L R L L L R L R R L R L L R R R L R L R R Dehaene et al, Nature neurosciences

46 Emerging themes in methods ( ) I 1. Wavelets Bayesian Wavelet & fmri Permutation Bayesian & fmri Permuation & frmi

47 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

48 THANKS TO. F. Kherif M. Lavielle J.-B. Poline et P. Valdes Sosa G. Flandin S. Dodel Salima Makni A. Roche L. Hugueville et D. Schwartz S. Mériaux P. Ciuciu B. Thirion P.-J. Lahaye L. Garnero et X