FMRI data: Independent Component Analysis (GIFT) & Connectivity Analysis (FNC)

Transcription

1 FMRI data: Independent Component Analysis (GIFT) & Connectivity Analysis (FNC) Software: Matlab Toolbox: GIFT & FNC Yingying Wang, Ph.D. in Biomedical Engineering th, 2014 PI: Dr. Nadine Gaab

2 Outline Introduction [Independent component analysis & connectivity analysis] Toolbox: GIFT Toolbox: FNC Demo & Hands-on

3 Independent Component Analysis Data Driven Multivariate Model-free The goal of ICA is to separate sources from a linear mixture. Assumptions: Linear mixing, independence, Non-gaussian ICA finds the independent components (also called factors, latent variables or sources) by maximizing the statistical independence of the estimated components. The form of ICA depends on the way to define independence. Minimization mutual information (infomax, Bell and Sejnowski, 1995) Maximization of non-gaussianity (FastICA, Hyvarinen et al., 2001) A simple example: the cocktail party problem

4 Two people talking Microphones at different distances from speakers Voice #1 (source) How can we separate the two speakers voice? X M mic #1 (detector) Y Y = M X 2 k k Voice #2 (source) mic #2 (detector)

5 Matlab Demo (Please download the data and code from our training website: Voice #1 >> [x1,fs]=audioread('x1.wav'); >> plot(x1) Voice #2 >> [x2,fs]=audioread('x2.wav'); >> plot(x2) A real Cocktail Party Effect. Two Speakers have been recorded speaking simultaneously. Speaker 1 says the digits from one to ten in English and speaker 2 counts at the same time the digits in Spanish (uno dos... ) The recording has been done in a normal office room. The distance between the speakers and the microphones is about 60cm in a square ordering (sampling rate 16kHz). (All files are in 16kHz wav-format). Data file:

6 Mic #1 >> [y1,fs]=audioread( y1.wav'); >> plot(y1) Mic #2 >> [y2,fs]=audioread( y2.wav'); >> plot(y2) Data file:

7 y () t m x m x y () t m x m x m ij...depends on the distances of the microphones from the speakers Noise-free ICA definition Use a statistical latent variables system Drop the time index, random variables Y is linear mixture of n independent components: y j m j1x1... m jnxn for all j Y = MX M --- basis functions, also called mixing matrix (unknown) X --- independent components, are latent variables which mean that they cannot be directly observed (unknown) GOAL: Estimate M and X using only the observable random variables Y

8 To solve this problem, some assumptions are needed: The components x i are statistically independent. x i The components have non-gaussian distributions. (if only one IC is gaussian, the estimation is still possible) For simplicity, mixing matrix M is square (can be sometimes relaxed) and can be inverted. The number of ICs equals the number of observable mixtures. Also for simplicity, we omit any noise term and illustrate using a noise-free ICA model. Note: (1) we cannot determine the variances of the independent components. (2) we cannot determine the order of the independent components.

9 Solution >>x=[x1,x2] ; >>r=fastica(x); >>subplot(2,1,1); >>plot(r(1,:), r ); >>hold on; >>plot(x2, y ); >>subplot(2,1,2); >>plot(r(2,:), r ); >>hold on; >>plot(x1, y ); Download cocktail_problem.zip

10 PCA-PCs uncorrelated: E PC PC E PC E PC Note: uncorrelated random variables are not necessarily independent. ICA-ICs independent: Pr( IC IC ) Pr IC Pr IC ICA v.s. PCA Principle component Analysis: find the components which can explain the maximum amount of variance possible presented in the observed data. Both are subspace projection techniques. Basic goal of PCA is to decorrelate the signal by projecting the data onto orthogonal axes, while the goal of ICA is to find statistically independent components from the signal. PCA: minimize the reprojection error from compressed data; ICA: minimize the statistical dependence between the ICs. PCs are orthogonal and ranked in order; ICs are statistical independent, but not orthogonal to each other and not ranked. There is no closed form expression to find M (iterative algorithms). Important property: the new sets of components are uncorrelated with each other (thus PCA is often used in the pre-processing procedure of ICA).

11 PCA reduces the dimensionality (the number of variables) of a data set by maintaining as much as variance as possible) PCA finds directions of maximal variance using second order statistics. ICA finds directions which maximize independence using higher order statistics

12 Summary PCA is good for Gaussian noise separation ICA is good for non-gaussian noise separation PCs have obvious meaning highest energy components ICA derived sources: arbitrary scaling/inversion & ordering --- need energy-independent heuristic to identify signals/noise Order of ICs change IC space is derived from the data -- PC space only changes if SNR changes. ICA assumes linear mixing matrix ICA assumes stationary mixing and ICA requires as many sensors as sources (like EEG, MEG inverse problem).

13 Application in fmri data analysis Relying on the intrinsic structure of the data, no assumptions about the form of the hemodynamic response function (HRF) which is needed for generalized linear modeling (GLM). GOAL: to identify a number of unknown sources of signal, ICA assumes that these sources are mutually and statistically independent in space (sica) or time (tica). For fmri data analysis, sica is preferred because temporal points (few hundreds, corresponding to each occurrence of a functional image acquisition) are small compared to spatial locations (more than millions voxels in a functional image).

14 sica Task Non task-related activations (e.g. Arousal) System Noise Measured Signal Pulsations Assumption: spatial pattern from sources of variability is unrelated (independent).

15 Figure source:

16 ICA Software Packages GIFT ( Matlab, multiple ICA algorithms (infomax, fastica, etc.) Graphic User Interface (GUI) and sorting options AnalyzeFMRI ( R, FastICA BrainVoyager ( Commercial (not free, but FDA approved), FastICA ICALAB Matlab, many ICA algorithms, no user-friendly fmri data display FSL melodic ( C, FastICA

17 GIFT Demo for single subject Installation of the toolbox (1) You need to have Matlab installed in your laptop. (2) Download GIFT toolbox from (3) >>pathtool >>addpath( c:\icatb\ ); >>gift

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19 Choose a folder to put your ICA results in. Download: single_subject_ica.zip Then, click OK

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21 Number of ICs Too many over-splitting Too few over-clumping How to choose? Between 20 and 40 appears to be a reasonable choice for typical fmri experiment Tools for estimating this number are available in GIFT (AIC/MDL/BIC) (make decision based upon the complexity or information content of data) Akaike s information criterion (AIC) Minimum description length (MDL) Bayesian information criterion (BIC) Note: See more in V.D. Calhoun, et al. (2001) HBM, vol.14:

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25 Preprocessing Centering (subtract the mean to create a zero mean signal) Simplify the ICA analysis (zero mean variable so ICs are zeromean too according to the equation [take expectations on both sides of the Y=MX equation). Whitening (transform Y linearly so that new Y is white) and dimension reduction can be achieved using Principle Component Analysis or Singular Value Decomposition (to make sure its components are uncorrelated and their variances equal unity).

26 Scaling Z-score: each image and time course are divided by its standard deviation Percent signal change Time courses are regressed onto original data at voxels which are maximal for a given IC. Scaled to reflect percent signal change from the mean. Images are also scaled such that the maximal voxel value contains the maximal percent signal change value.

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29 Run ICA

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38 Sorting Temporal sorting Correlation Multiple regression Frequency power spectra, etc Spatial sorting Correlation with mask or prior knowledge Maximum value with in mask Multiple regression Multivariate sorting Support Vector Machine

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41 Group ICA Sub 1 Sub N ICA ICA? Figure source:

42 Group ICA Figure source:

43 Group ICA Data ICA Back-reconstruction Subject 1 A 1 A i 1 Subject i S i X A S_agg Subject N A N Figure source:

44 Group ICA Download cocktail_problem.zip

45 If each subject went through multiple sessions, you can put the preprocessed fmri data into the sub-folder.

46 ICASSO Consistency and Clustering of ICs

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50 Our example only has one session, so choose No here. Then click OK.

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52 Change to 10, we let ICA run 10 times, each time starts with random initial value.

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62 Run analysis using commands:

63 Different useful tools, like Write Talairach Table to get the IC s Talairach coordinates, etc.

64 After sica, Functional Network Connectivity (FNC) Functional Connectivity Effective Connectivity Structural Connectivity Pic source:

65 Functional Network Connectivity (FNC) FNC is a Matlab toolbox which finds and displays temporal relations amongst components. This can help determine causal relations in the brain. Using GIFT to preprocess the raw data for FNC is recommended. Webpage: Documentation: Publications:

66 Functional Network Connectivity (between groups) Key: : ρ patient > ρ control : ρ control > ρ patient A: Default G: Temporal B: Parietal F: Frontal C: L. & M. Visual Cortical Areas E: Frontal Parietal Subcortical D: Frontal Temporal Parietal

67 Start FNC >> fnctb

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71 Let s pick Com9, 11, 16, 27

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78 The End Thank you