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

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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

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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)

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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

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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.)

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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

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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.

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Visual Stimulation

ICA Analysis

Task related

Heart beat & breathing related

Low-freq. component possibly related to vasomotor

oscillation

Motion related “white noise”

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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

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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)

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Temporal Correlation

• Can be introduced by rapid sampling,

• By temporal hemodynamic point spread function,

• Or by poorly understood temporal autocorrelations in the data

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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

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ICA Block Model

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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).

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• 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)

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Infomax (II)

• Assume X is input to Neural Network, whose outputs are Wi

TX

• 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(Wn

TX)]

• This model can be used for ICA if gi are well-chosen

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• 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[Wi

TX]

• 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

Connection Between Infomax and ML

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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

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Left&right task-related to visual stimuli

Sensitive to changes in stimuli (Transiently Task Related)

Non Task

Related

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Comparisons

• For example comparing a visual task with a visuo-motor task

• Use a priori template to extract components of interest

• Conjunctive ( & ), Subtractive ( - )

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Visual Vs. Visuomotor ComparisonConjunction V & VM:

Visual areas appearSubtraction VM - V:Motor areas appear

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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

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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