ICA of Functional MRI Data: An Overview

1. ICA of Functional MRI Data:An Overview V.D. Calhoun, T. Adali, L.K. Hansen, et al., ICA 2003 Symposium Paper Presentation by Avshalom ElyadaFebruary 2004

2. Functional MRI • Non-invasively measure brain activity • Most popular method observes neuron activity indirectly by measuring Vascular and Hemodynamic signals • Change in blood flow and oxygenation (oxygenated vs. deoxygenated blood) in active brain areas is measured using MRI ICA of fMRI

3. Data Acquisition • Two orthogonal detectors capture MRI signal • This two channel input is put in complex form:f(t) + ig(t) • Discrete Fourier transform of this time-domain data yields complex image-space data • Usually magnitude only is used (but it is shown that ignoring phase loses significant data) • Data is in form of small intensity changes over time (contrast-to-noise ratio < 1) ICA of fMRI

4. Infomax BSS Algorithm • Widely used separation algorithm in fMRI • Neural Network viewpoint: • The algorithm is based on maximizing the output entropy (or information flow) of a neural network with non-linear outputs • Actually it is equivalent to Maximum-Likelihood, as we shall touch upon later ICA of fMRI

5. Signals of Interest • Task-related • Such as visual, visuomotor, … • Transiently task-related • Some components of brain response to task vary over time (stop before stimulation stops, change when repeated stimuli applied …) • Function-related • Several different transiently task-related signals may come from different areas when a certain function performed (e.g. correlation between opposite brain sides.) ICA of fMRI

6. Signals Not-of-interest • Physiology-related • Such as breathing, heart-rate • Motion-related • For instance when performing speaking experiment, signals due to mouth movement are detected ICA of fMRI

7. Noise • Magnetic resonance • Patient movement • Different from motion-related : here patient movement causes measurement noise • Physiological (heart-rate, breathing) • Again, note difference from prev. slide: here we refer to measurement noise and not the breathing related activity in the brain. ICA of fMRI

8. Visual Stimulation ICA Analysis Task related Heart beat & breathing related Low-freq. component possibly related to vasomotor oscillation Motion related “white noise” ICA of fMRI

9. Statistical Properties • For ICA, sources must be non-Gaussian with spatial & temporal independence • fMRI signals are typically focal and thus have sub-Gaussian spatial distribution • Noise generally non-Gaussian • If sources don’t have systematic overlap in time and/or space then considered independent ICA of fMRI

10. Spatial Correlation • The hemodynamic signal being measured is not the signal of interest itself, but an indirect indication • It has a spatial point spread function • Due to the hemodynamic properties themselves • Can be affected by choice of measurement parameters (sensitivity to blood flow and oxygenation, magnetic sensitivity) ICA of fMRI

11. Temporal Correlation • Can be introduced by rapid sampling, • By temporal hemodynamic point spread function, • Or by poorly understood temporal autocorrelations in the data ICA of fMRI

12. Spatial vs. Temporal • ICA is used to understand spatio-temporal structure of the fMRI signal • Factor the data into a product of a set of time courses and a set of spatial patterns • PCA: orthogonal time courses vs. orthogonal spatial patterns • ICA: neither are assumed a priori independent • Spatial ICA: Spatial independence is the leading assumption, followed by temporal • Temporal ICA: vice versa ICA of fMRI

13. ICA Block Model ICA of fMRI

14. Choice of Algorithm • Depends on assumptions about signals of interest • Spatial or temporal independence • Sub- or super-Gaussian sources • Evaluate effectiveness of algorithms, variants, preprocessing, check divergence to “true” distribution • Problem, since true distribution unknown • One method: Hybrid fMRI experiment. Superimposing a known source on the real fMRI data, check effectiveness of reconstructing known source (hybrid fMRI experiment). ICA of fMRI

15. Infomax • Entropy H • Mutual Information I • Infomax: minimize I between the sources • But minimizing I is hard • maximize entropy instead (both are indications of signal i.i.d) ICA of fMRI

16. Infomax (II) • Assume X is input to Neural Network, whose outputs are WiTX • Wi the weight vectors of the neurons • Infomax: maximize entropy of outputs • Plain max. not possible (-H can go to inf), maximize for gi(WiTX) , gi some non-linear scalar functions: H[g1(W1TX), … , gn(WnTX)] • This model can be used for ICA if gi are well-chosen ICA of fMRI

17. Connection Between Infomax and ML • The two approaches are equivalent • proof: “Infomax & ML for BSS” / JF Cardoso • Log-Likelihoodexpectation • If fi equal to actual dist. func., then first term above equal to ∑iH[WiTX] • Hence ML = -H + Constant, • Mazimize entropy  minimize likelihood • Choose gi close as possible to fi • As in ML, gi need not be known, only gaussianity ICA of fMRI

18. Group ICA • We aim to draw inferences about groups of signals, then plot them together • In ICA, different individuals in the group may have different time courses • An approach recently developed performs statistical comparison of individual maps trying to estimate the time-course parallelism ICA of fMRI

19. Non Task Related Left&right task-related to visual stimuli Sensitive to changes in stimuli (Transiently Task Related) ICA of fMRI

20. Comparisons • For example comparing a visual task with a visuo-motor task • Use a priori template to extract components of interest • Conjunctive ( & ), Subtractive ( - ) ICA of fMRI

21. Visual Vs. Visuomotor Comparison Conjunction V & VM:Visual areas appear Subtraction VM - V:Motor areas appear ICA of fMRI

22. Use of a priori Information • Provide improved separability • For example extract one component for selective analysis • ICA model make assumptions about the sources • A priori templates help assess impact of assumptions • Validation • Difficult, since sources are unknown • Hybrid fMRI experiment as mentioned earlier ICA of fMRI

23. Reference • ICA of functional MRI data: An Overview • Calhoun, Adali et. al, ICA2003 • Infomax and ML for BSS • Jean-Francois Cardoso • ICA Tutorial • Aapo Hyvärinen, Erkki Oja • www.cis.hut.fi/aapo/papers/IJCNN99_tutorialweb/IJCNN99_tutorial3.html ICA of fMRI