The W matrix can be estimated using “Maximum Entropy Method” an adaptive learning algorithm based on information theoretic approach (Bell and Sejnowski, 1995). Maximum entropy method is based on blind source separation. Mutual information (cross-over) between two random variables is hard to minimize and therefore maximum entropy approach is more commonly used in fMRI analyses. For mathematical algorithm on the W (unmixing matrix) estimation, refer to “ICA method for Blind Source Separation of Instantaneous Mixtures: A Case Study” by Das et al., 2007 and to “An information maximisation approach to blind separation and blind deconvolution.” by Bell and Sejnowski, 1995.

ICA PCA GLM

Data-driven Data-driven Model-based (and heavily based on the correctness of

hypothesis)

Multivariate Multivariate Univariate

No constraints on the shape of the hemodynamic response

No constraints on the shape ofthe hemodynamic response

Assumptions on the uniform shape of the hemodynamic

response in every brain region

Separates independent spatial components with respective

fMRI time courses

Separates orthogonal components ranked on maximal

variance contributions

Calculates Parameter estimates of a particular condition of

interest for every voxel

Devoid of spatial correlation issue

Devoid of spatial correlation issue

Does not deal with spatial correlation issue due to its univariate-based approach

Encodes higher order statistics (such as Kurtosis) and deals

more efficiently with fMRI signal which is often sub-gaussian

(negative kurtosis) and possible noise which is often super-gaussian (positive kurtosis)

Encode only second order statistics by finding the direction of maximal variance and it does

not work efficiently on non-gaussian data

Encodes the 1st-order and 2nd order statistics (mean and

variance) for every voxel and calculates t-statistics for every

voxel

Deconvolution of DMN component more efficient with adaptive separation method

based on higher-order statistics

Deconvolution of DMN component less efficient due to

lack of sufficient information obtained from the

components based on variance

Deconvolution in GLM more complex if there is multiple cross-talking especially in a

rapid-event fMRI design

METHODS FOR DMN IDENTIFICATIONGeneral Linear Model (GLM): Univariate

(one voxel a time), heavy model and hypothesis based assumptions.Y = Xβ + ε where Y = Observed data for each voxel i.e. hemodynamic signal at each time point. X = Design matrix that includes indicators of onset of stimuli, duration of stimuli, possible covariates, etc. that explains the observed data. β = Summary statistics based on least squares procedure e.g., β = 1.15 indicates a 15% increase in the hemodynamic signal from a relative baseline due to a particular stimulus.ε = Error assumed gaussian, independent and non-spherical in nature. GLM performs ANOVAs estimating t-

statistics for the significance of activation level at each voxel.

Principal Component Analysis (PCA): Transformation method in which the data is expressed as a linear combination of its basis vectors. Y = PX where X = observed data set and Y = representative data set and P = linear transformation.

PCA assumes large variances have important dynamics like high signal to noise ratio and lower variances represent noise.

The task of PCA is to find principal components which are orthogonal and are then ranked as per their variance contributions.

Independent Component Analysis (ICA): similar to PCA; it abandons assumptions considered in PCA except linearity. ICA finds direction of maximal independence of non-Gaussian data.

Goal of ICA is to separate sources S (components) from a linear mixture X (fMRI hemodynamic signal) using the blind separation method. For example, ICA works well on the “Cocktail Party” problem where a particular voice could be separated from a mixtures of voices from different sources.

Assume X= AS, Where X = linear mixture of neuronal signals, S = independent sources contributing to the mixture and A is the mixing matrix.

Y = WX where, W is the unmixing matrix, Y = estimate of the vector S of the source signals.

The task of ICA is to recover the original sources by finding W, which is theoretically equal to the inverse of the unknown matric A. i.e., W = A-1 , so that Y is as close as possible to S.

Examining Brain’s Default Mode Differences Using Group Independent Component AnalysisM.S. Dalwani1, J.R. Tregellas1, J.R. Andrews-Hanna2, J.T. Sakai1, S.K. Mikulich-Gilbertson1, M. T. Banich1, 2 , T. J. Crowley1 1U Colo Denver School of Medicine and 2U Colo Boulder, CO, USA.

DEFINITIONSDefault Mode Network (DMN): is one of

the “resting state networks” that is associated with mind wandering, day-dreaming, self-referential mental activity, collection and evaluation of information and extraction of episodic memory.

Functional Magnetic Resonance Imaging (fMRI): is a technique to detect changes in blood flow in the brain.

Independent Component Analysis (ICA): is a statistical technique based on blind separation method to separate a linear mixture into independent components.

Rapid-Event fMRI: fMRI design (or

task) with short inter-stimulus interval e.g. “Colorado Balloon Game” task used for this experiment included 4 second stimulus such as decisions, outcomes (wins and losses) separated by short intervals (2-4 second fixations).

Voxel: Subdivision of brain into thousands of small cubic regions (i.e. “voxels”) with respective three dimensional (x,y,z) co-ordinates for atlas labeling.

Data processed separately for two groups: patient boys and control boys (Figure 3 and 4)For each of the two study groups the toolbox performed the analysis in three stages:

(i) data reduction (Figure 2; phase 1), (ii) application of the ICA algorithm (Figure 2 and Figure 3) and (iii) back-reconstruction for each individual subject (Figure 2 and Figure 3)

DMN component was identified by selecting the component with the highest spatial correlation to a default network mask (Garrity et al., 2007) (see Figure 2 and Figure 3)

The mask included the lateral posterior parietal cortex, precuneus, posterior cingulate cortex, frontal pole, and occipitotemporal junction, as defined anatomically from the WFU Pickatlas http://www.fmri/wfubmc.edu).

Note that typical DMN activity as the one showed in figure 1a was obtained in both groups.

DMN selection from each subject was obtained and then averaged within groups. The within groups DMN activity are shown in Figure 5a and Figure 5b.

DISCUSSION ICA-data driven approach “Killer” Application in Noise and Artifact removal Identify different networks incl. DMN (Figure 5a and 5b) DMN identification validated by examining frequency and time

course of DMN time course (Figure 6 and 7)

The authors have no financial relationships that relate to the topic of this presentation

Figure 3 Group ICA: Data Analyses Pipeline

Figure 4 (Group ICA Flowchart as applied to this study; Calhoun et al., 2004; printed with permission)

Figure 5a Controls: Average DMN Activity Figure 5b Patients: Average DMN Activity

LIMITATIONS Over- or Under- Splitting Some prior knowledge needed to identify networksOrder of the independent components can not be determined as A and S

are unknown in the basic model

CONCLUSION ICA useful in identifying resting state network such as DMN and can

be applied on a Rapid Event Design

REFERENCES Beckmann CF. Modelling with independent components. Neuroimage. 2012. Bell AJ and Sejnowski TJ. An information maximisation approach to blind separation and blind

deconvolution. Neural Computation. 1995; 7, 6, 1129-1159 Calhoun VD, Adali T, Pearlson GD, Pekar JJ. Spatial and temporal independent component analysis of

functional MRI data containing a pair of task-related waveforms. Hum Brain Mapp. 2001;13:43–53 Calhoun VD, Adali T, Pekar JJ. A method for comparing group fMRI data using independent component

analysis: Application to visual, motor and visuomotor tasks. Magn Reson Imaging. 2004; 22:1181–1191. Calhoun VD, Kiehl KA, and Pearlson GD. Modulation of temporally coherent brain networks estimated

using ICA at rest and during cognitive tasks. Hum Brain Mapp. 2008; 29, 7: 828-38. Calhoun VD, Liu J, Adalı T. A review o group ICA for fMRI data and ICA for joint inference of imaging,

genetic, and ERP data. NeuroImage. 2009;45(1, Supplement 1):S163–S172. Crowley TJ, Dalwani M, Mikulich-Gilbertson SK, Du YP, Lejuez C, Raymond KM, Banich MT. Risky

Decisions and Their Consequences: Neural Processing by Antisocial Substance-Dependent Boys. PLoS One. 2010; 5(9):e12835

Das, N, Routray, A, Dash PK. ICA methods for blind source separation of instantaneous mixtures: A case study. Neural Information Processing -Letters and Reviews 2007.

Sambataro F, Blasi G, Fazio L, Caforio G, Taurisano P, Romano R, et al. Treatment with olanzapine is associated with modulation of the default mode network in patients with Schizophrenia. Neuropsychopharmacology. 2010;35:904–912.

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fMRI DataRapid-event fMRI design “Colorado Balloon Game” involving several cognitive stimuli

(decision, wins, losses) spaced closely in time to simulate real-life “decision-making” & “risk-taking” experience.

Preprocessing (or pre-whitening) included Motion correction, coregistration to structural image, normalization to standard Montreal Neurological Institute (MNI) space and smoothing with a 6mm FWHM Gaussian filter as shown in Figure 3 (Phase 1).

Funding Source: NIDA grants DA009842, DA011015 and DA024104, and the Kane Family Foundation. The author would like to thank the travel funds committee at Colorado School of Public Health for their travel support to the WNAR.

MOTIVATIONTo detect default mode network (DMN) in a rapid-event functional MRI (fMRI) experiment using the spatial independent component analysis (ICA) method.

TYPICAL DMN ACTIVITY

ICA ON FUNCTIONAL MRI DATA

GROUP INDEPENDENT COMPONENT ANALYSES

ICA ANALYSES RESULTS

Figure 6: Spectral Analyses of DMN

DMN VALIDATION: SPECTRAL AND TIME COURSE ANALYSES

Figure 7: Time Course Analyses of DMN

b

a

NOVELTYICA has been applied on resting state, block or traditional (slow) event fMRI design to detect DMN. This study is novel because ICA is applied to a rapid-event fMRI design to detect DMN.

ICA WORKS BEST FOR DMN IDENTIFICATION

Figure 2 Schematic presentation of spatial ICA (Printed from Beckmann 2012 with permission)

X A=W-1S

MAXMIMUM ENTROPY METHOD

DMN has been shown to occur at low frequencies (<0.05 Hz). Spectral analyses confirmed that the DMN components had most spectral power at low frequency bins in both groups and there was no significant difference between the two groups as shown Figure 6.

DMN is one of the resting state network and the time course activity in both groups showed that DMN activity was higher when there was minimal or no stimulus and minimal when the subjects were required to engage in other cognitive activity. Figure 7 below shows the DMN activity in control subjects which is similar to pattern observed in 1b.

D “MN OFF” when Stimulus is “ON” D “MN ON” when Stimulus is “OFF”

Figure 1a: Typical DMN spatial activity from a fMRI design; Figure 1b: DMN time course “on” when task stimuli is “off”; Sambataro et al. 2010; printed with permission