HERMES: Towards an Integrated Toolbox to Characterize Functional and Effective Brain Connectivity

The analysis of the interdependence between time series has become an important field of research in the last years, mainly as a result of advances in the characterization of dynamical systems from the signals they produce, the introduction of concepts such as generalized and phase synchronization and the application of information theory to time series analysis. In neurophysiology, different analytical tools stemming from these concepts have added to the ‘traditional’ set of linear methods, which includes the cross-correlation and the coherency function in the time and frequency domain, respectively, or more elaborated tools such as Granger Causality.This increase in the number of approaches to tackle the existence of functional (FC) or effective connectivity (EC) between two (or among many) neural networks, along with the mathematical complexity of the corresponding time series analysis tools, makes it desirable to arrange them into a unified-easy-to-use software package. The goal is to allow neuroscientists, neurophysiologists and researchers from related fields to easily access and make use of these analysis methods from a single integrated toolbox.Here we present HERMES (http://hermes.ctb.upm.es), a toolbox for the Matlab® environment (The Mathworks, Inc), which is designed to study functional and effective brain connectivity from neurophysiological data such as multivariate EEG and/or MEG records. It includes also visualization tools and statistical methods to address the problem of multiple comparisons. We believe that this toolbox will be very helpful to all the researchers working in the emerging field of brain connectivity analysis.

[1]  J. Bendat,et al.  Random Data: Analysis and Measurement Procedures , 1971 .

[2]  Richard M. Leahy,et al.  Brainstorm: A User-Friendly Application for MEG/EEG Analysis , 2011, Comput. Intell. Neurosci..

[3]  P. A. Blight.  The Analysis of Time Series: An Introduction , 1991 .

[4]  A. Kraskov,et al.  Bivariate surrogate techniques: necessity, strengths, and caveats. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[5]  Karl J. Friston.  Functional and effective connectivity in neuroimaging: A synthesis , 1994 .

[6]  Theiler,et al.  Spurious dimension from correlation algorithms applied to limited time-series data. , 1986, Physical review. A, General physics.

[7]  Klaus Lehnertz,et al.  Identifying phase synchronization clusters in spatially extended dynamical systems. , 2006, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

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

[10]  Robert Oostenveld,et al.  FieldTrip: Open Source Software for Advanced Analysis of MEG, EEG, and Invasive Electrophysiological Data , 2010, Comput. Intell. Neurosci..

[11]  Cesare Furlanello,et al.  minerva and minepy: a C engine for the MINE suite and its R, Python and MATLAB wrappers , 2012, Bioinform..

[12]  Y. Benjamini,et al.  Controlling the false discovery rate: a practical and powerful approach to multiple testing , 1995 .

[13]  C. Stam,et al.  Phase lag index: Assessment of functional connectivity from multi channel EEG and MEG with diminished bias from common sources , 2007, Human brain mapping.

[14]  Kurths,et al.  Phase synchronization of chaotic oscillators. , 1996, Physical review letters.

[15]  T. Schreiber,et al.  Surrogate time series , 1999, chao-dyn/9909037.

[16]  Karl J. Friston,et al.  Combining Spatial Extent and Peak Intensity to Test for Activations in Functional Imaging , 1997, NeuroImage.

[17]  Jürgen Kurths,et al.  Recurrence plots for the analysis of complex systems , 2009 .

[18]  Ernesto Pereda,et al.  Assessment of changing interdependencies between human electroencephalograms using nonlinear methods , 2001 .

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

[20]  Arnold Neumaier,et al.  Estimation of parameters and eigenmodes of multivariate autoregressive models , 2001, TOMS.

[21]  Jürgen Kurths,et al.  Eigenvalue Decomposition as a Generalized Synchronization Cluster Analysis , 2007, Int. J. Bifurc. Chaos.

[22]  K. Pawelzik,et al.  Mutual information and global strange attractors in Taylor-Couette flow , 1994 .

[23]  M. Hallett,et al.  Identifying true brain interaction from EEG data using the imaginary part of coherency , 2004, Clinical Neurophysiology.

[24]  Cristian S. Calude.  The mathematical theory of information , 2007 .

[25]  Hualou Liang,et al.  Short-window spectral analysis of cortical event-related potentials by adaptive multivariate autoregressive modeling: data preprocessing, model validation, and variability assessment , 2000, Biological Cybernetics.

[26]  A. Louisa,et al.  コロイド混合体における有効力 空乏引力から集積斥力へ | 文献情報 | J-GLOBAL 科学技術総合リンクセンター , 2002 .

[27]  Gordon Pipa,et al.  Transfer entropy—a model-free measure of effective connectivity for the neurosciences , 2010, Journal of Computational Neuroscience.

[28]  Schreiber,et al.  Measuring information transfer , 2000, Physical review letters.

[29]  L. Tsimring,et al.  Generalized synchronization of chaos in directionally coupled chaotic systems. , 1995, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[30]  Arnold Neumaier,et al.  Algorithm 808: ARfit—a matlab package for the estimation of parameters and eigenmodes of multivariate autoregressive models , 2001, TOMS.

[31]  Rodrigo Quian Quiroga,et al.  Nonlinear multivariate analysis of neurophysiological signals , 2005, Progress in Neurobiology.

[32]  A. Kraskov,et al.  Estimating mutual information. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[33]  Cornelis J. Stam,et al.  Go with the flow: Use of a directed phase lag index (dPLI) to characterize patterns of phase relations in a large-scale model of brain dynamics , 2012, NeuroImage.

[34]  Holger Kantz,et al.  Practical implementation of nonlinear time series methods: The TISEAN package. , 1998, Chaos.

[35]  Jürgen Kurths,et al.  Quantifying Causal Coupling Strength: A Lag-specific Measure For Multivariate Time Series Related To Transfer Entropy , 2012, Physical review. E, Statistical, nonlinear, and soft matter physics.

[36]  M. Corbetta,et al.  Large-scale cortical correlation structure of spontaneous oscillatory activity , 2012, Nature Neuroscience.

[37]  Stefan Haufe,et al.  A critical assessment of connectivity measures for EEG data: A simulation study , 2013, NeuroImage.

[38]  Arnaud Delorme,et al.  EEGLAB, SIFT, NFT, BCILAB, and ERICA: New Tools for Advanced EEG Processing , 2011, Comput. Intell. Neurosci..

[39]  D. Smirnov,et al.  Estimation of interaction strength and direction from short and noisy time series. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[40]  Koichi Sameshima,et al.  Using partial directed coherence to describe neuronal ensemble interactions , 1999, Journal of Neuroscience Methods.

[41]  Cornelis J. Stam,et al.  Synchronization likelihood with explicit time-frequency priors , 2006, NeuroImage.

[42]  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.

[43]  Robert Oostenveld,et al.  An improved index of phase-synchronization for electrophysiological data in the presence of volume-conduction, noise and sample-size bias , 2011, NeuroImage.

[44]  Arnaud Delorme,et al.  EEGLAB: an open source toolbox for analysis of single-trial EEG dynamics including independent component analysis , 2004, Journal of Neuroscience Methods.

[45]  Y. Benjamini,et al.  THE CONTROL OF THE FALSE DISCOVERY RATE IN MULTIPLE TESTING UNDER DEPENDENCY , 2001 .

[46]  Michael Mitzenmacher,et al.  Detecting Novel Associations in Large Data Sets , 2011, Science.

[47]  Rolando J. Biscay-Lirio,et al.  Assessing interactions in the brain with exact low-resolution electromagnetic tomography , 2011, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences.

[48]  Olaf Sporns,et al.  Complex network measures of brain connectivity: Uses and interpretations , 2010, NeuroImage.

[49]  O. Sporns,et al.  Complex brain networks: graph theoretical analysis of structural and functional systems , 2009, Nature Reviews Neuroscience.

[50]  D Curran-Everett,et al.  Multiple comparisons: philosophies and illustrations. , 2000, American journal of physiology. Regulatory, integrative and comparative physiology.

[51]  Sang Joon Kim,et al.  A Mathematical Theory of Communication , 2006 .

[52]  M. D. Ernst.  Permutation Methods: A Basis for Exact Inference , 2004 .

[53]  Thomas E. Nichols,et al.  Nonparametric permutation tests for functional neuroimaging: A primer with examples , 2002, Human brain mapping.

[54]  Thomas E. Nichols,et al.  Thresholding of Statistical Maps in Functional Neuroimaging Using the False Discovery Rate , 2002, NeuroImage.

[55]  F. Takens.  Detecting strange attractors in turbulence , 1981 .

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

[57]  S. Frenzel,et al.  Partial mutual information for coupling analysis of multivariate time series. , 2007, Physical review letters.

[58]  F. Varela,et al.  Measuring phase synchrony in brain signals , 1999, Human brain mapping.

[59]  Wesley K. Thompson,et al.  MATLAB toolbox for functional connectivity , 2009, NeuroImage.

[60]  Reinhold Kliegl,et al.  Twin surrogates to test for complex synchronisation , 2006 .

[61]  N. Castellanos,et al.  Early dysfunction of functional connectivity in healthy elderly with subjective memory complaints , 2012, AGE.

[62]  Prashant Parikh.  A Theory of Communication , 2010 .

[63]  E. Beckenbach,et al.  Modern mathematics for the engineer , 1958 .

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

[65]  G. Schwarz.  Estimating the Dimension of a Model , 1978 .

[66]  Tobias Otto,et al.  The Biopsychology-Toolbox: A free, open-source Matlab-toolbox for the control of behavioral experiments , 2008, Journal of Neuroscience Methods.

[67]  H. Abarbanel,et al.  Determining embedding dimension for phase-space reconstruction using a geometrical construction. , 1992, Physical review. A, Atomic, molecular, and optical physics.

[68]  Daniel Chicharro,et al.  Reliable detection of directional couplings using rank statistics. , 2009, Physical review. E, Statistical, nonlinear, and soft matter physics.

[69]  Carsten Allefeld,et al.  Detecting synchronization clusters in multivariate time series via coarse-graining of Markov chains. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

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

[71]  A. Bruns.  Fourier-, Hilbert- and wavelet-based signal analysis: are they really different approaches? , 2004, Journal of Neuroscience Methods.

[72]  Karl J. Friston.  Functional and Effective Connectivity: A Review , 2011, Brain Connect..

[73]  J. Tukey.  The Philosophy of Multiple Comparisons , 1991 .

[74]  C. Granger.  Investigating causal relations by econometric models and cross-spectral methods , 1969 .

[75]  D. Gabor,et al.  Theory of communication. Part 1: The analysis of information , 1946 .

[76]  J. Bhattacharya,et al.  High-Learners Present Larger Mid-Frontal Theta Power and Connectivity in Response to Incorrect Performance Feedback , 2013, The Journal of Neuroscience.

[77]  T. Speed.  A Correlation for the 21st Century , 2011, Science.

[78]  C. Stam,et al.  The organization of physiological brain networks , 2012, Clinical Neurophysiology.

[79]  James Theiler,et al.  Testing for nonlinearity in time series: the method of surrogate data , 1992 .

[80]  Katarzyna J. Blinowska,et al.  A new method of the description of the information flow in the brain structures , 1991, Biological Cybernetics.

[81]  Gordon Pipa,et al.  Assessing coupling dynamics from an ensemble of time series , 2010, Entropy.

[82]  R. Oostenveld,et al.  Nonparametric statistical testing of EEG- and MEG-data , 2007, Journal of Neuroscience Methods.

[83]  Anil K. Seth,et al.  A MATLAB toolbox for Granger causal connectivity analysis , 2010, Journal of Neuroscience Methods.

[84]  M. Rosenblum,et al.  Identification of coupling direction: application to cardiorespiratory interaction. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[85]  Swinney,et al.  Information transport in spatiotemporal systems. , 1988, Physical review letters.

[86]  H. Akaike.  A new look at the statistical model identification , 1974 .

[87]  Luiz A. Baccalá,et al.  Partial directed coherence: a new concept in neural structure determination , 2001, Biological Cybernetics.

[88]  Jürgen Kurths,et al.  Escaping the curse of dimensionality in estimating multivariate transfer entropy. , 2012, Physical review letters.

[89]  C. Autermann,et al.  崩壊Bs0→Ds(*)Ds(*) , 2007 .

[90]  Jan Khre,et al.  The Mathematical Theory of Information , 2012 .

[91]  Heidelberg,et al.  Encircling an exceptional point. , 2004, Physical review. E, Statistical, nonlinear, and soft matter physics.

[92]  M. Rosenblum,et al.  Detecting direction of coupling in interacting oscillators. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[93]  K. Müller,et al.  Robustly estimating the flow direction of information in complex physical systems. , 2007, Physical review letters.

[94]  J. Geweke,et al.  Measurement of Linear Dependence and Feedback between Multiple Time Series , 1982 .

[95]  Barry Horwitz,et al.  The elusive concept of brain connectivity , 2003, NeuroImage.

[96]  H. Kantz,et al.  Nonlinear time series analysis , 1997 .