Dynamic filtering of static dipoles in magnetoencephalography

We consider the problem of estimating neural activity from measurements of the magnetic fields recorded by magnetoencephalography. We exploit the temporal structure of the problem and model the neural current as a collection of evolving current dipoles, which appear and disappear, but whose locations are constant throughout their lifetime. This fully reflects the physiological interpretation of the model. In order to conduct inference under this proposed model, it was necessary to develop an algorithm based around state-of-the-art sequential Monte Carlo methods employing carefully designed importance distributions. Previous work employed a bootstrap filter and an artificial dynamic structure where dipoles performed a random walk in space, yielding nonphysical artefacts in the reconstructions; such artefacts are not observed when using the proposed model. The algorithm is validated with simulated data, in which it provided an average localisation error which is approximately half that of the bootstrap filter. An application to complex real data derived from a somatosensory experiment is presented. Assessment of model fit via marginal likelihood showed a clear preference for the proposed model and the associated reconstructions show better localisation.

[1]  C. Campi,et al.  A Rao–Blackwellized particle filter for magnetoencephalography , 2008 .

[2]  R. Ilmoniemi,et al.  Magnetoencephalography-theory, instrumentation, and applications to noninvasive studies of the working human brain , 1993 .

[3]  Michele Piana,et al.  Particle filtering, beamforming and multiple signal classification for the analysis of magnetoencephalography time series: A comparison of algorithms , 2010 .

[4]  Polina Golland,et al.  A distributed spatio-temporal EEG/MEG inverse solver , 2009, NeuroImage.

[5]  Tian Wang,et al.  Improved Particle Filter , 2014, CIT 2014.

[6]  Zhimin Li,et al.  A spatio-temporal solution for the EEG/MEG inverse problem using group penalization methods , 2011 .

[7]  Sergey M. Plis,et al.  Spatiotemporal Bayesian inference dipole analysis for MEG neuroimaging data , 2005, NeuroImage.

[8]  W. Drongelen,et al.  Localization of brain electrical activity via linearly constrained minimum variance spatial filtering , 1997, IEEE Transactions on Biomedical Engineering.

[9]  S. Taulu,et al.  Suppression of Interference and Artifacts by the Signal Space Separation Method , 2003, Brain Topography.

[10]  F Mauguière,et al.  Activation of a distributed somatosensory cortical network in the human brain: a dipole modelling study of magnetic fields evoked by median nerve stimulation. Part II: Effects of stimulus rate, attention and stimulus detection. , 1997, Electroencephalography and clinical neurophysiology.

[11]  Nicholas G. Polson,et al.  Particle Filtering , 2006 .

[12]  P. Fearnhead,et al.  Improved particle filter for nonlinear problems , 1999 .

[13]  Roman Holenstein,et al.  Particle Markov chain Monte Carlo , 2009 .

[14]  E. Somersalo,et al.  Non-stationary magnetoencephalography by Bayesian filtering of dipole models , 2003 .

[15]  Lauri Parkkonen,et al.  Dynamical MEG source modeling with multi‐target Bayesian filtering , 2009, Human brain mapping.

[16]  M. Scherg,et al.  Evoked dipole source potentials of the human auditory cortex. , 1986, Electroencephalography and clinical neurophysiology.

[17]  Pierre Del Moral,et al.  Feynman-Kac formulae , 2004 .

[18]  A. Doucet,et al.  A Tutorial on Particle Filtering and Smoothing: Fifteen years later , 2008 .

[19]  Antonio Hernando,et al.  Comparison and improvements of LCMV and MUSIC source localization techniques for use in real clinical environments , 2012, Journal of Neuroscience Methods.

[20]  Eric Moulines,et al.  Comparison of resampling schemes for particle filtering , 2005, ISPA 2005. Proceedings of the 4th International Symposium on Image and Signal Processing and Analysis, 2005..

[21]  M. Piana,et al.  Highly Automated Dipole EStimation , 2010 .

[22]  Richard M. Leahy,et al.  Source localization using recursively applied and projected (RAP) MUSIC , 1997, Conference Record of the Thirty-First Asilomar Conference on Signals, Systems and Computers (Cat. No.97CB36136).

[23]  R. Ilmoniemi,et al.  Interpreting magnetic fields of the brain: minimum norm estimates , 2006, Medical and Biological Engineering and Computing.

[24]  Simona Temereanca,et al.  STATE-SPACE SOLUTIONS TO THE DYNAMIC MAGNETOENCEPHALOGRAPHY INVERSE PROBLEM USING HIGH PERFORMANCE COMPUTING. , 2011, The annals of applied statistics.

[25]  Jun S. Liu,et al.  Sequential Imputations and Bayesian Missing Data Problems , 1994 .

[26]  J. Sarvas.  Basic mathematical and electromagnetic concepts of the biomagnetic inverse problem. , 1987, Physics in medicine and biology.

[27]  A. Gramfort,et al.  Mixed-norm estimates for the M/EEG inverse problem using accelerated gradient methods , 2012, Physics in medicine and biology.

[28]  Gene H. Golub,et al.  Matrix computations , 1983 .

[29]  Michele Piana,et al.  Highly Automated Dipole EStimation (HADES) , 2011, Comput. Intell. Neurosci..

[30]  M. Li,et al.  Particle Markov chain Monte Carlo methods , 2015 .

[31]  Qiao Shi-dong.  An Improved Particle Filter , 2008 .

[32]  A. Lee Swindlehurst,et al.  Efficient Dipole Parameter Estimation in EEG Systems With Near-ML Performance , 2012, IEEE Transactions on Biomedical Engineering.

[33]  J.C. Mosher,et al.  Multiple dipole modeling and localization from spatio-temporal MEG data , 1992, IEEE Transactions on Biomedical Engineering.

[34]  Ba-Ngu Vo,et al.  A Consistent Metric for Performance Evaluation of Multi-Object Filters , 2008, IEEE Transactions on Signal Processing.

[35]  Arnaud Doucet,et al.  An overview of sequential Monte Carlo methods for parameter estimation in general state-space models , 2009 .

[36]  P. Moral.  Feynman-Kac Formulae: Genealogical and Interacting Particle Systems with Applications , 2004 .

[37]  A. Doucet,et al.  Particle Markov chain Monte Carlo methods , 2010 .

[38]  Alberto Sorrentino,et al.  Particle Filters for Magnetoencephalography , 2010 .

[39]  W. Gilks,et al.  Following a moving target—Monte Carlo inference for dynamic Bayesian models , 2001 .

[40]  Anders M. Dale,et al.  Cortical Surface-Based Analysis I. Segmentation and Surface Reconstruction , 1999, NeuroImage.

[41]  E. Somersalo,et al.  Visualization of Magnetoencephalographic Data Using Minimum Current Estimates , 1999, NeuroImage.

[42]  P. Fearnhead,et al.  An improved particle filter for non-linear problems , 1999 .

[43]  D. Cohen,et al.  Demonstration of useful differences between magnetoencephalogram and electroencephalogram. , 1983, Electroencephalography and clinical neurophysiology.

[44]  N. Chopin.  Central limit theorem for sequential Monte Carlo methods and its application to Bayesian inference , 2004, math/0508594.

[45]  E.N. Brown,et al.  Large Scale Kalman Filtering Solutions to the Electrophysiological Source Localization Problem- A MEG Case Study , 2006, 2006 International Conference of the IEEE Engineering in Medicine and Biology Society.

[46]  Uang,et al.  A TWO-WAY REGULARIZATION METHOD FOR MEG SOURCE RECONSTRUCTION , 2011 .

[47]  V. Jousmäki,et al.  Activation of a distributed somatosensory cortical network in the human brain. A dipole modelling study of magnetic fields evoked by median nerve stimulation. Part I: Location and activation timing of SEF sources. , 1997, Electroencephalography and clinical neurophysiology.

[48]  Nicolas Chopin,et al.  SMC2: an efficient algorithm for sequential analysis of state space models , 2011, 1101.1528.

[49]  Simon J. Godsill,et al.  On sequential Monte Carlo sampling methods for Bayesian filtering , 2000, Stat. Comput..

[50]  Seppo P. Ahlfors,et al.  Assessing and improving the spatial accuracy in MEG source localization by depth-weighted minimum-norm estimates , 2006, NeuroImage.

[51]  A. Doucet,et al.  Sequential Monte Carlo methods for multitarget filtering with random finite sets , 2005, IEEE Transactions on Aerospace and Electronic Systems.

[52]  E. Halgren,et al.  Dynamic Statistical Parametric Mapping Combining fMRI and MEG for High-Resolution Imaging of Cortical Activity , 2000, Neuron.

[53]  A. Doucet,et al.  Smoothing algorithms for state–space models , 2010 .

[54]  Polina Golland,et al.  A Distributed Spatio-temporal EEG/MEG Inverse Solver , 2008, MICCAI.

[55]  J. Geweke,et al.  Bayesian Inference in Econometric Models Using Monte Carlo Integration , 1989 .