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
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•Dynamical Model
•Spatial dependencyxx
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Equations of the NN-ARx Model
AR termNearest Neighbors
eXogenous variable Innovations
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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.Realigning
Correcting 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 slicing
Correcting 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
1
1
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