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##### ANALYSIS OF fMRI DATA BASED ON NN-ARx MODELING

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**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**fMRI: Functional Magnetic Resonance Imaging**Provides functional information about the state of the brain Measuresthe brain blood oxygenation level at some specific instant of time. fMRI Stimulus Blood vessels dilate bringing more blood highly oxygenated Neuronal activity demands more glucose and O2 Brain Activation fMRI signal increases in this area, detecting the change in the oxygenation level of the blood Metabolism**Standard continuous-time modelfor theBOLD signal**U(t) neuronal sinaptic activity X1(t) inducing signal X2(t) blood flow X3(t) blood volume X4(t) de-oxyhemoglobine Friston et al (2000) Riera et al (2004) Buxton et al (1998) BOLD signal**Continuos-time model**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**Equations of the NN-ARx Model**eXogenous variable Nearest Neighbors Innovations AR term MAIN FEATURES • Dynamical Model • Spatial dependency x x x x x t**Equation of the NN-ARx Model**eXogenous variable Nearest Neighbors Innovations AR term Whiteness Gaussianity Variance MAIN FEATURES • Dynamical Model • Spatial dependency • Innovations analysis • Long-range conectivity analysis Connection between y(v1) & y(v2) ? v1 v2**Before Starting the Analysis. fMRI preprocessing**• 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. • 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).**Visual experiment**Task :Visual stimulus by black and white shuffled check board Data provided by Prof. N. Sadato, (National Institute of Physiological Sciences) Sampling frequency: 3s Resolution: 64× 64 × 36 # of time points : 60 3 T**Map of the innovations variance**Double Click**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 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 2 and 3 (2-3)Are these activations**significative? T2 test for Condition 1**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**v**● w * Correlations between two voxels based on innovations Instantaneous ● * Lagged ● * ● * Notation**Equation of the NN-ARx Model**eXogenous variable Nearest Neighbors Innovations AR term Whiteness Gaussianity Variance MAIN FEATURES • Dynamical Model • Spatial dependency • Innovations analysis • Long-range conectivity analysis Connection between y(v1) & y(v2) ? v1 v2**Regional Correlations**• Calculate the vector of all possible correlations between all voxels v in region V vs. all voxels w in region W, pair to pair. • Take the square of the correlations in order to capture both positive and negative correlations. • Summarize the correlation between the two regions by the upper 90th percentile of the values in for all positive and negative lags. • Further, summarize the lagged correlations by: • 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 notimply causal connectivity. • The neurophysiological meaningof innovations in NN-Arx modeling should be further elucidated in the context of fMRI experiments to aid interpretaion of findings.