fMRI resting state data analysis - McGill University · to resting state. • Spontaneous BOLD is...

Statistical Analysis Aspects of Resting State Functional

Connectivity

Biswal’s result (1995)

Correlations between RS Fluctuations of left and right motor areas

Why studying resting state?

• Human Brain = 2% Total Body Mass

but consumes 20% of the body energy.

• Task-related increases are small (<5%) relativeto resting state.

• Spontaneous BOLD is not random noise:

It is spatially/functionally organized

A model for resting state?• Task-response studies:

Bold(t) = s(t)*HRF(t) + noise(t)

Spontaneous BOLD signal has been viewed as noise and its effects is minimized through averaging.

• Resting state studies:

Bold = noise? “Wrong model”

Bold(t) = Organized RS Fluctuations (t) + noise(t)

More on the model• Bold = Organized RS Fluctuations + noise

Can we model RS Fluctuations? Ideal

What to do?

• To model noise as best as possible and remove it out from the data

“Clean” Bold ~ Organized RS Fluctuations

• How to model and remove “noise” from resting state BOLD signals?

Noise components• Physiological noise:

Oscillatory fluctuations due to respiration andcardiac pulsation.

• Low frequency drift:

Mainly due to hardware instabilities.

• Movements effects.

• White noise.

Preprocessing steps : NIAK?

• Motion correction between and within runs.

• Slice timing correction.

• Co-registration of functional and anatomical images.

• Removal of physiological noise.

• Band pass filtering at [0.01 0.1] Hz.

• Re-sampling to MNI space

• Spatial smoothing.

Importance of physiological noise

• Fluctuations of fMRI resting data occurs at thesame frequency rate of fluctuations induced byphysiological noise (i.e. respiratory rhythms,cardiac beats).

• Physiologic-related fluctuations may increasetemporal variance in fMRI data

Reduction of sensitivity in correlation maps.

Reduction of sensitivity in correlation

. .Bold RSF Phy Noise White NoiseVar Var Var Var= + +

Bold = RS Fluctuations + Physiological noise + White noise.Assumption: Independence between each pair of components (Validated by most ICA-based studies)

1 2

'1 2

1 2( , )s s

s ss sρσ σ

=1 2

'1 2

1 2. .

( , )( )( )s Phy Noise s Phy Noise

s ss sρσ σ σ σ

=+ +

Methods for removal of physiological noise

1. Measuring physiological parameters duringBOLD acquisition and remove them out bylinear regression (RETROICOR).

2. Removal of average signal obtained fromnon-gray matter regions (ventricles, whitematter).

3. SVD-type procedures for isolating noisecomponents (PCA, ICA, PICA).

4. CORSICA: combination of 3) and 2).

5. Removal of global average signal.

Recent Improvements• Correction by the respiration volume per time (RVT):

breath to breath variations in the depth and ratebreathing (same frequencies and spatial location ofRS fluctuations). Birn, et.al, 2008, HBM.

Signal changes correlated with RVT

Signal changes correlated with a PCC seed

• Correction by time-shifted cardiac rate timecourses (HR), Shmueli et. al, 2007,NeuroImage.

• Use of Respiration Response Function (RRF,Birn, et.al, 2008, NeuroImage) and CardiacResponse Function (CRF, Chang, et.al, 2009,NeuroImage) in the model (similar to HRF):

Bold = RS Fluctuations + RVT*RRF + HR*CRF +White noise.

Data for correlation analysis

• 17 subjects from BS002 database (Fox et.al, 2007 ), 4 runs each.

• TR = 2.16 sec.

• 190 time frames after pre-processing.

• Dimensions: 79 x 95 x 69 voxels of 2x2x2 mm each.

Methods for functional connectivity

1. SVD-based exploratory techniques such as PCA, ICA, PICA.

2. Seed correlations.

3. Iterated seed-correlations.

4. Hierarchical clustering.

5. All cross-correlations.

6. All cross-correlations based on ROIs.

Principal Components Analysis (PCA)

• Friston et. al, 1993: find spatial and temporalcomponents that capture as much as possibleof the variability of the data.

• Singular Value Decomposition of time x spacematrix:

Y = U D V’ (U’U = I, V’V = I, D = diag)

• Regions with high score on a spatialcomponent (column of V) are correlated or‘connected’

PCA on a single subject after basic pre-processing (keeping most of the

sources of noise)

PCA after slice timing and motion correction

0 50 100 150 200-4.5

-4

-3.5

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-Com

pone

nt

Frame

Temporal components (sd, % variance explained)

0.53, 28.2%

0.29, 8.4%

0.21, 4.6%

0.19, 3.6%

Slice (0 based)

Com

pone

nt

Spatial components

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Global effect explaining 28.2% of total variance in the 1st component

PCA after removal of global average

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0.38, 14.4%

0.24, 5.9%

0.22, 4.9%

0.2, 4.1%

Slice (0 based)

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pone

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Spatial components

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Linear trend effect explaining 14.4% of total variance in the 1st component

PCA after removal of linear trend

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0.28, 7.7%

0.24, 5.8%

0.23, 5.3%

0.22, 4.7%

Slice (0 based)

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pone

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Spatial components

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Resting state connectivity on these components?

PCA on the same subject after full pre-processing (NIAK)

PCA after removal of global average and linear trend

0 50 100 150 200-4.5

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0.34, 11.5%

0.27, 7.4%

0.26, 6.5%

0.24, 5.5%

Slice (0 based)

Com

pone

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Spatial components

0 5 10 15 20 25 30

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Resting state connectivity are enhanced?

Seed connectivity analysis on the same subject

Posterior Cingulate/Precuneus (PCC)

[-2 -36 37] (Task Negative Network)

Z=37

z = [42 35 28 21 14] Threshold = 4.99

Negative correlations revealed after removal of global averageNegative correlations: Task positive networkPositive correlations: Task negative network

Which is better?

Thresholding correlations,

or

PCA

Comparison of methods

1. PCA• Lack of meaningful statistical hypothesis testing.

• Require interpretation and characterization of components.

• Useful for extensive correlated regions.

2. Seed correlations.• How to choose the seed?

• Allows modeling of the time courses.

• Useful for focal correlated regions.

3. All cross-correlations based on ROIs.

Summary of analysis

• A global effect is captured by PCA.

• Removal of global effect facilitates interpretationof specific RS correlations.

• What is the origin of this effect? Is it neuronallyinduced or just a remaining noise component?

• What are the implications of this global effect forconnectivity analysis.

• How to effectively remove this global effect?

What is the origin of this effect?• It could be related to a vascular process

(unrelated to neuronal function) due to theinfluence of arterial carbon dioxide fluctuations(Wise et al. 2004, NeuroImage).

• It can be related to changes in the breathedvolume (respiration volume over time) (Birn etal. 2006, NeuroImage).

• These sources of noise are not usuallycorrected by ICA-type methods.

How to remove a global effect?• Regressing out the global average signal from

every voxel in the brain (Fox et al. 2005, Procc. Natl. Acad. Sci. U.S.A)

Implications:

• Not all voxels contribute equally to the globalaverage.

• This technique may introduces SpuriousNegative Correlations (Murphy et al. 2009,Neuroimage).

• Reported negative correlations are possibly theresult of the global average removal.

Why regression of the global average may introduces negative correlations?

• How to regress out a confound z from a variable y: (Pz)y, where

• What happens to the correlation C(x,y) after regressing out z from both x and y?

• if an only if z is uncorrelated to both x and y.

• Neither x nor y are uncorrelated to z=(x+y)/2

1( ( ' ) ')zP I z z z z−= −

( , ) ( , ) ( , )( , )1 ( , ) 1 ( , )z z

C x y C x z C y zC P x P yC x z C y z

−=

− −

( , ) ( , )z zC P x P y C x y=

How to effectively remove the global effect?

Our proposal (Abstract submitted to HBM 2010)

1. PCA decomposition.

2. Selection of the PC most correlated to the global average signal.

3. Removal of the selected component.

Rationale of the method

1. PCA decomposition:

• PCA captures a global effect in one of its components (namely, the 1st PC)

• Additive model in PCA:

Bold = Global Effect + RS Fluctuations

Bold ~ 1st PC + (2nd PC +....+ Last PC)

• Regression of the 1st PC results in specific functional connectivity RS fluctuations

Implementation

• PCA decomposition.

• Computation of the correlation coefficientbetween each temporal component and theglobal average signal.

• Selection of the component corresponding tothe maximum absolute value of thosecorrelation coefficients.

• Removal of this principal component.

How to remove the PC?

• Each PC is composed of

- Eigenimage (Spatial component)

- Time course (Temporal component)

Component = Eigenimage X Time Course

Standard Regression: Removal of temporal PC

Our method: Removal of combined eigenimageand temporal PC

PC ~ Weighted global average

Properties of the method

• Removes most of the variability associated with the global average signal.

• Does not change the correlation structure of the RS fluctuations.

- The removed PC is orthogonal to the remaining data (RS Fluctuations)

Go back to examples

Relationship between global average and PC

High correlation/coherence between global average and PCThis value increases with pre-processing improvement

z = [42 35 28 21 14] Threshold = 4.99

Negative correlations more extended with removal of global average

fMRI resting state data analysis - McGill University · to resting state. • Spontaneous BOLD is...

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