Quantitative evaluation of linear and nonlinear methods characterizing interdependencies between brain signals.

Brain functional connectivity can be characterized by the temporal evolution of correlation between signals recorded from spatially-distributed regions. It is aimed at explaining how different brain areas interact within networks involved during normal (as in cognitive tasks) or pathological (as in epilepsy) situations. Numerous techniques were introduced for assessing this connectivity. Recently, some efforts were made to compare methods performances but mainly qualitatively and for a special application. In this paper, we go further and propose a comprehensive comparison of different classes of methods (linear and nonlinear regressions, phase synchronization, and generalized synchronization) based on various simulation models. For this purpose, quantitative criteria are used: in addition to mean square error under null hypothesis (independence between two signals) and mean variance computed over all values of coupling degree in each model, we provide a criterion for comparing performances. Results show that the performances of the compared methods are highly dependent on the hypothesis regarding the underlying model for the generation of the signals. Moreover, none of them outperforms the others in all cases and the performance hierarchy is model dependent.

[1]  R. Quiroga,et al.  Learning driver-response relationships from synchronization patterns. , 1999, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[2]  A. W. Kemp,et al.  Kendall's Advanced Theory of Statistics. , 1994 .

[3]  F. D. Silva,et al.  Propagation of seizure activity in kindled dogs. , 1983 .

[4]  Juergen Kurths,et al.  Synchronization in a population of globally coupled chaotic oscillators , 1996 .

[5]  J. Martinerie,et al.  Comparison of Hilbert transform and wavelet methods for the analysis of neuronal synchrony , 2001, Journal of Neuroscience Methods.

[6]  J. Bhattacharya.  Reduced degree of long-range phase synchrony in pathological human brain. , 2001, Acta neurobiologiae experimentalis.

[7]  F. Wendling,et al.  Comparison of two estimators of time-frequency interdependencies between nonstationary signals: application to epileptic EEG , 2004, The 26th Annual International Conference of the IEEE Engineering in Medicine and Biology Society.

[8]  R. Burke,et al.  Detecting dynamical interdependence and generalized synchrony through mutual prediction in a neural ensemble. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[9]  Jürgen Kurths,et al.  Detection of n:m Phase Locking from Noisy Data: Application to Magnetoencephalography , 1998 .

[10]  J. Tukey,et al.  An algorithm for the machine calculation of complex Fourier series , 1965 .

[11]  Leon D. Iasemidis,et al.  Epileptic seizure prediction and control , 2003, IEEE Transactions on Biomedical Engineering.

[12]  M. Brazier.  Studies of the EEG activity of limbic structures in man. , 1968, Electroencephalography and clinical neurophysiology.

[13]  Lotfi Senhadji,et al.  Time-frequency characterization of interdependencies in nonstationary signals: application to epileptic EEG , 2005, IEEE Transactions on Biomedical Engineering.

[14]  J. Bendat,et al.  Random Data: Analysis and Measurement Procedures , 1987 .

[15]  M. Hénon.  A two-dimensional mapping with a strange attractor , 1976 .

[16]  Karl J. Friston,et al.  Evaluation of different measures of functional connectivity using a neural mass model , 2004, NeuroImage.

[17]  Fabrice Wendling,et al.  Relevance of nonlinear lumped-parameter models in the analysis of depth-EEG epileptic signals , 2000, Biological Cybernetics.

[18]  K Lehnertz,et al.  Non-linear time series analysis of intracranial EEG recordings in patients with epilepsy--an overview. , 1999, International journal of psychophysiology : official journal of the International Organization of Psychophysiology.

[19]  Fernando H. Lopes da Silva,et al.  Propagation of Electrical Activity: Nonlinear Associations and Time Delays between EEG Signals , 1993 .

[20]  F. H. Lopes da Silva,et al.  Propagation of seizure activity in kindled dogs. , 1983, Electroencephalography and clinical neurophysiology.

[21]  F. H. Lopes da Silva,et al.  Interdependence of EEG signals: Linear vs. nonlinear Associations and the significance of time delays and phase shifts , 2005, Brain Topography.

[22]  G Pfurtscheller,et al.  Event-Related changes of band power and coherence: methodology and interpretation. , 1999, Journal of clinical neurophysiology : official publication of the American Electroencephalographic Society.

[23]  O. Rössler.  An equation for continuous chaos , 1976 .

[24]  M A BRAZIER,et al.  A note on a correlator for electroencephalographic work. , 1954, Electroencephalography and Clinical Neurophysiology.

[25]  F. Mormann,et al.  Mean phase coherence as a measure for phase synchronization and its application to the EEG of epilepsy patients , 2000 .

[26]  P. Grassberger,et al.  A robust method for detecting interdependences: application to intracranially recorded EEG , 1999, chao-dyn/9907013.

[27]  Jürgen Kurths,et al.  SYNCHRONIZATION APPROACH TO ANALYSIS OF BIOLOGICAL SYSTEMS , 2004, The Random and Fluctuating World.

[28]  H. Saunders.  Literature Review : RANDOM DATA: ANALYSIS AND MEASUREMENT PROCEDURES J. S. Bendat and A.G. Piersol Wiley-Interscience, New York, N. Y. (1971) , 1974 .

[29]  C. Stam,et al.  Synchronization likelihood: an unbiased measure of generalized synchronization in multivariate data sets , 2002 .

[30]  Fraser,et al.  Independent coordinates for strange attractors from mutual information. , 1986, Physical review. A, General physics.

[31]  J. Bellanger,et al.  Interpretation of interdependencies in epileptic signals using a macroscopic physiological model of the EEG , 2001, Clinical Neurophysiology.

[32]  Grigory V. Osipov,et al.  PHASE SYNCHRONIZATION EFFECTS IN A LATTICE OF NONIDENTICAL ROSSLER OSCILLATORS , 1997 .

[33]  Ernesto Pereda,et al.  Comparing generalized and phase synchronization in cardiovascular and cardiorespiratory signals , 2005, IEEE Transactions on Biomedical Engineering.

[34]  R Quian Quiroga,et al.  Performance of different synchronization measures in real data: a case study on electroencephalographic signals. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[35]  Jürgen Kurths,et al.  Synchronization - A Universal Concept in Nonlinear Sciences , 2001, Cambridge Nonlinear Science Series.

[36]  A. Kraskov,et al.  On the predictability of epileptic seizures , 2005, Clinical Neurophysiology.

[37]  Piotr J. Franaszczuk,et al.  An autoregressive method for the measurement of synchronization of interictal and ictal EEG signals , 1999, Biological Cybernetics.

[38]  Joydeep Bhattacharya,et al.  Effective detection of coupling in short and noisy bivariate data , 2003, IEEE Trans. Syst. Man Cybern. Part B.

[39]  L. Cao.  Practical method for determining the minimum embedding dimension of a scalar time series , 1997 .

[40]  S. Haykin,et al.  Monitoring neuronal oscillations and signal transmission between cortical regions using time-frequency analysis of electroencephalographic activity , 1996, Proc. IEEE.