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 Elyada February 2004

2. Avshalom ElyadaICA of fMRI2 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

3. Avshalom ElyadaICA of fMRI3 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)

4. Avshalom ElyadaICA of fMRI4 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

5. Avshalom ElyadaICA of fMRI5 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.)

6. Avshalom ElyadaICA of fMRI6 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

7. Avshalom ElyadaICA of fMRI7 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.

8. Avshalom ElyadaICA of fMRI8 Visual Stimulation ICA Analysis Task related Heart beat & breathing related Low-freq. component possibly related to vasomotor oscillation Motion related “white noise”

9. Avshalom ElyadaICA of fMRI9 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

10. Avshalom ElyadaICA of fMRI10 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)

11. Avshalom ElyadaICA of fMRI11 Temporal Correlation Can be introduced by rapid sampling, By temporal hemodynamic point spread function, Or by poorly understood temporal autocorrelations in the data

12. Avshalom ElyadaICA of fMRI12 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

13. Avshalom ElyadaICA of fMRI13 ICA Block Model

14. Avshalom ElyadaICA of fMRI14 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).

15. Avshalom ElyadaICA of fMRI15 Entropy H Mutual Information I Infomax Infomax: minimize I between the sources –But minimizing I is hard –maximize entropy instead (both are indications of signal i.i.d)

16. Avshalom ElyadaICA of fMRI16 Infomax (II) Assume X is input to Neural Network, whose outputs are W i T X W i the weight vectors of the neurons Infomax: maximize entropy of outputs Plain max. not possible (-H can go to inf), maximize for g i (W i T X), g i some non-linear scalar functions: H[g 1 (W 1 T X), …, g n (W n T X)] This model can be used for ICA if g i are well- chosen

17. Avshalom ElyadaICA of fMRI17 The two approaches are equivalent –proof: “Infomax & ML for BSS” / JF Cardoso Log-Likelihood expectation If f i equal to actual dist. func., then first term above equal to ∑ i H[W i T X] Hence ML = -H + Constant, Mazimize entropy  minimize likelihood Choose g i close as possible to f i –As in ML, g i need not be known, only gaussianity Connection Between Infomax and ML

18. Avshalom ElyadaICA of fMRI18 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

19. Avshalom ElyadaICA of fMRI19 Left&right task-related to visual stimuli Sensitive to changes in stimuli (Transiently Task Related) Non Task Related

20. Avshalom ElyadaICA of fMRI20 Comparisons For example comparing a visual task with a visuo-motor task Use a priori template to extract components of interest Conjunctive ( & ), Subtractive ( - )

21. Avshalom ElyadaICA of fMRI21 Visual Vs. Visuomotor Comparison Conjunction V & VM: Visual areas appear Subtraction VM - V: Motor areas appear

22. Avshalom ElyadaICA of fMRI22 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

23. Avshalom ElyadaICA of fMRI23 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_tutorialw eb/IJCNN99_tutorial3.html