ANALYSIS OF fMRI DATA BASED 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 O 2 Blood vessels dilate bringing more blood highly oxygenated fMRI signal increases in this area, detecting the change in the oxygenation level of the blood fMRI Measures 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) 680–697 J. Riera, J. Bosch, O. Yamashita, R. Kawashima, N. Sadato, T. Okada,e and T. Ozaki Continuos-time model

MAIN FEATURES Dynamical Model Spatial dependency x x x x t x Equations of the NN-ARx Model AR term Nearest Neighbors eXogenous variable Innovations

AR term Nearest Neighbors eXogenous variable MAIN FEATURES Dynamical Model Spatial dependency Innovations analysis Long-range conectivity analysis Innovations Connection between y(v1) & y(v2) ?   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

Correlations between two voxels based on innovations Instantaneous Lagged * ● v w Notation ● * ● * ● *

AR term Nearest Neighbors eXogenous variable MAIN FEATURES Dynamical Model Spatial dependency Innovations analysis Long-range conectivity analysis Innovations Connection between y(v1) & y(v2) ?   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 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. for all positive and negative lags. 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.

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