ANALYSIS OF fMRI DATABASED ON NN-ARx MODELING

Biscay-Lirio, R: Inst. of Cybernetics, Mathematics and Physics, Cuba

Bosch-Bayard, J.: Cuban Neuroscience Center, Havana, Cuba

Riera-Diaz, J.: NICHe, Tohoku University, Sendai, Japan

Biscay-Lirio,R.: Inst. of Cybernetics, Mathematics and Physics, Havana, Cuba

Galka, A.: Inst. of Experim. and Applied Physics, University of Kiel, Germany

Sadato, N.: National Institute for Physiological Science, Okazaki, Japan

Valdes-Sosa, P.: Cuban Neuroscience Center, Havana, Cuba

Ozaki, Tohru: The Institute of Statistical Mathematics, Tokyo, Japan

THE NN-ARx MODEL

fMRI: Functional Magnetic Resonance Imaging

Provides functional information about the state of the brain

Stimulus

Brain Activation Metabolism

Neuronal activity demands more glucose and O2

Blood vessels dilate bringing more blood highly oxygenated

fMRI signal increases in this area, detecting the change in the oxygenation level of the blood

fMRIMeasures the brain blood oxygenation level at some specific instant of time.

Standard continuous-time model for the BOLD signal

U(t) neuronal sinaptic activity

X1(t) inducing signal

X2(t) blood flow

X3(t) blood volume

X4(t) de-oxyhemoglobine

BOLD signal

Buxton et al(1998)

Friston et al (2000)

Riera et al (2004)

NN-ARx model

fMRI activation maps based on the NN-ARx model. NeuroImage 23 (2004) 680–697J. Riera, J. Bosch, O. Yamashita, R. Kawashima, N. Sadato, T. Okada,e and T. Ozaki

Continuos-time model

1( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

1 1

q p d mv v v v v v v vt t k t k k t k k t k t

k k k d

y y s

Lxt( i, j,k ) x t

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(xt( i1, j,k ) x t

( i 1, j ,k ) x t( i, j1,k ) x t

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( )

0

gv v kt k

k

t

( ) ( )v vt tLx y MAIN FEATURES

•Dynamical Model

•Spatial dependencyxxx

x

t

x

Equations of the NN-ARx Model

AR termNearest Neighbors

eXogenous variable Innovations

1( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

1 1

q p d mv v v v v v v vt t k t k k t k k t k t

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(xt( i1, j,k ) x t

( i 1, j ,k ) x t( i, j1,k ) x t

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( i, j ,k1))

( )

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gv v kt k

k

t

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AR termNearest Neighbors

eXogenous variable

MAIN FEATURES

•Dynamical Model

•Spatial dependency

•Innovations analysis

•Long-range conectivity analysis

Innovations

Connection between y(v1) & y(v2) ?

( 2)vt

( 1)vt

v1

v2

Whiteness

Gaussianity

Variance

Equation of the NN-ARx Model

ACTIVATION ANALYSIS BASED ON NN-ARx MODELING

Before Starting the Analysis. fMRI preprocessing

1.RealigningCorrecting the fMRI scans for possible head movements, so the time series we see in one voxel over time corresponds approximately to the same site in the brain.

2.Time slicingCorrecting the time shifting introduced among slices while taking one fMRI scan.

We perform these two preprocessing using the SPM software (Statistical Parametric Mapping, by Friston et al).

Some exploratory tools for NN-ARx model fitting

Task : Visual stimulus

by black and white shuffled check board

Sampling frequency: 3s

Resolution: 64× 64 × 36

# of time points : 60

3 T

Visual experiment

Data provided by Prof. N. Sadato,(National Institute of Physiological Sciences)

HRF activation for a visual experiment

Model fitting for a voxel in the calcarine

HRF in detail for the selected voxel

Map of the innovations variance

Double Click

Map of autocorrelations at a selected voxel

Correlation maps for different voxels Lag 0

Cerebelum

R = 0.5

Vermix

R = 0.7

Lingual

R = 0.6

Experiment from Sassa et al, IDAC. Tohoku University

1-Talk to a familiar person

2-Talk to an unfamiliar person

3-Listen from familiar person

4-Listen from unfamiliar person

5-Say an object name

HRF for a voxel at the Hippocampus

HRF for a voxel at the Cunneus

Left Click here

Testing for activation

Fitted NN-ARx model

T2 statistics at each voxel

Permutation tests based on all T2 statistics

Difference of Conditions 1 and 2 (1-2)

Difference of Conditions 1 and 3 (1-3)

Difference of Conditions 2 and 3 (2-3)Are these activations significative?

T2 test for Condition 1

T2 test for Condition 3

REGIONAL CONNECTIVITY ANALYSIS

Some methodological issues

• Functional connectivity (observed dependencies) vs effective connectivity (causal relations).

• In general, causal relations can not be inferred from observational data.

Some approaches for connectivity analysis

• Standard (zero-lag) correlation analysis

• Structural equation modeling

• Dynamic causal modeling

,0 ,v w v w

t tR corr

Correlations between two voxels based on innovations

Instantaneous

, ,w v v wl t l tR corr

Lagged

*

●v

w

, ,v w w vl t l tR corr

, , , , and v w v w v w w vl l l lR R R R

Notation

● *

● *

● *

1( ) ( ) ( ) ( ) ( ) ( ) ( ) ( )

1 1

q p d mv v v v v v v vt t k t k k t k k t k t

k k k d

y y s

Lxt( i, j,k ) x t

( i, j ,k ) 16

(xt( i1, j,k ) x t

( i 1, j ,k ) x t( i, j1,k ) x t

( i, j 1,k ) xt( i, j,k 1) x t

( i, j ,k1))

( )

0

gv v kt k

k

t

( ) ( )v vt tLx y

AR termNearest Neighbors

eXogenous variable

MAIN FEATURES

•Dynamical Model

•Spatial dependency

•Innovations analysis

•Long-range conectivity analysis

Innovations

Connection between y(v1) & y(v2) ?

( 2)vt

( 1)vt

v1

v2

Whiteness

Gaussianity

Variance

Equation of the NN-ARx Model

3. Summarize the correlation between the two regions by the upper 90th percentile of the values in

Regional Correlations

2, ,v w v wl lS R

, ,v w V Wl lS U

1. Calculate the vector of all possible correlations between all voxels v in region V vs. all voxels w in region W, pair to pair.

2. Take the square of the correlations in order to capture both positive and negative correlations.

, ,0 and - v w v w

lR R k l k

for all positive and negative lags.

, ,

0

11

LV W V W

ll

U UL

0, ,1

1V W V W

ll L

U UL

5. Further, summarize the lagged correlations by:

6. For statistical significance we use the bootstrap technique.

Results. Significant correlations for a group of subjects under a visual task

Results. Significant correlations for a group of subjects performing a motor task

Results. Significant correlations for a blind subject under a tactile discrimination task

Some concluding remarks• NN-ARx modeling offers a dynamic approach for the

analysis of both activation and connectivity from fMRI data.

• Connectivity analysis based on innovations permits to clean the data from short-range connections and focus on long-range connections.

• Regional connectivity measures that do not involved spatial averaging may be defined to atenue the confounding effects of lack of homogeneity within each region and of errors in brain segmentation.

But…some limitations and cautions

• fMRI has low time resolution (in comparison with neural time scale).

• Flexibility in defining regional connectivity measures without spatial averaging is achieved at the expense of computer-intensive algorithms for statistical testing.

• A high correlation between the past of a region and the future of another region does not imply causal connectivity.

• The neurophysiological meaning of innovations in NN-Arx modeling should be further elucidated in the context of fMRI experiments to aid interpretaion of findings.

THANKS