Bilinear dynamical systems

In this paper, we propose the use of bilinear dynamical systems (BDS)s for model-based deconvolution of fMRI time-series. The importance of this work lies in being able to deconvolve haemodynamic time-series, in an informed way, to disclose the underlying neuronal activity. Being able to estimate neuronal responses in a particular brain region is fundamental for many models of functional integration and connectivity in the brain. BDSs comprise a stochastic bilinear neurodynamical model specified in discrete time, and a set of linear convolution kernels for the haemodynamics. We derive an expectation-maximization (EM) algorithm for parameter estimation, in which fMRI time-series are deconvolved in an E-step and model parameters are updated in an M-Step. We report preliminary results that focus on the assumed stochastic nature of the neurodynamic model and compare the method to Wiener deconvolution.

[1]  A. Weigend,et al.  Time Series Prediction: Forecasting the Future and Understanding the Past , 1994 .

[2]  T. Sejnowski,et al.  Dynamic Brain Sources of Visual Evoked Responses , 2002, Science.

[3]  Karl J. Friston,et al.  Dynamic causal modelling , 2003, NeuroImage.

[4]  G. Glover Deconvolution of Impulse Response in Event-Related BOLD fMRI1 , 1999, NeuroImage.

[5]  C. Büchel,et al.  Modulation of connectivity in visual pathways by attention: cortical interactions evaluated with structural equation modelling and fMRI. , 1997, Cerebral cortex.

[6]  Zoubin Ghahramani,et al.  Propagation Algorithms for Variational Bayesian Learning , 2000, NIPS.

[7]  S Makeig,et al.  Analysis of fMRI data by blind separation into independent spatial components , 1998, Human brain mapping.

[8]  John R. Terry,et al.  NONLINEAR INTERDEPENDENCE IN NEURAL SYSTEMS: MOTIVATION, THEORY, AND RELEVANCE , 2002, The International journal of neuroscience.

[9]  Karl J. Friston,et al.  The choice of basis functions in event-related fMRI , 2001, NeuroImage.

[10]  Karl J. Friston,et al.  Bayesian Estimation of Dynamical Systems: An Application to fMRI , 2002, NeuroImage.

[11]  Bruno A. Olshausen,et al.  Book Review , 2003, Journal of Cognitive Neuroscience.

[12]  Karl J. Friston,et al.  Human Brain Function , 1997 .

[13]  Karl J. Friston,et al.  Comparing dynamic causal models , 2004, NeuroImage.

[14]  Tohru Ozaki,et al.  A solution to the dynamical inverse problem of EEG generation using spatiotemporal Kalman filtering , 2004, NeuroImage.

[15]  S. Haykin Adaptive Filter Theory , 1986 .

[16]  Juan C. Jiménez,et al.  Nonlinear EEG analysis based on a neural mass model , 1999, Biological Cybernetics.

[17]  Geoffrey E. Hinton,et al.  Parameter estimation for linear dynamical systems , 1996 .

[18]  Tohru Ozaki,et al.  Recursive penalized least squares solution for dynamical inverse problems of EEG generation , 2004, Human brain mapping.

[19]  N. Logothetis,et al.  Neurophysiological investigation of the basis of the fMRI signal , 2001, Nature.

[20]  Karl J. Friston,et al.  A neural mass model for MEG/EEG: coupling and neuronal dynamics , 2003, NeuroImage.

[21]  William H. Press,et al.  Numerical recipes in C , 2002 .

[22]  Karl J. Friston,et al.  Correcting for non-sphericity in imaging data using classical and Bayesian approaches , 2001, NeuroImage.

[23]  Peter Dayan,et al.  Theoretical Neuroscience: Computational and Mathematical Modeling of Neural Systems , 2001 .

[24]  D. Rubin,et al.  Maximum likelihood from incomplete data via the EM - algorithm plus discussions on the paper , 1977 .

[25]  Karl J. Friston,et al.  Modeling regional and psychophysiologic interactions in fMRI: the importance of hemodynamic deconvolution , 2003, NeuroImage.

[26]  L. Ingber Statistical mechanics of multiple scales of neocortical interactions , 1995 .

[27]  Richard M. Leahy,et al.  Electromagnetic brain mapping , 2001, IEEE Signal Process. Mag..

[28]  Karl J. Friston,et al.  Biophysical models of fMRI responses , 2004, Current Opinion in Neurobiology.

[29]  Richard M. Leahy,et al.  Electromagnetic brain mapping - IEEE Signal Processing Magazine , 2001 .

[30]  Karl J. Friston,et al.  Psychophysiological and Modulatory Interactions in Neuroimaging , 1997, NeuroImage.

[31]  Dale Borowiak,et al.  Linear Models, Least Squares and Alternatives , 2001, Technometrics.

[32]  Naoki Miura,et al.  A state-space model of the hemodynamic approach: nonlinear filtering of BOLD signals , 2004, NeuroImage.

[33]  Zoubin Ghahramani,et al.  A Unifying Review of Linear Gaussian Models , 1999, Neural Computation.

[34]  Andreas S. Weigend,et al.  Time Series Prediction: Forecasting the Future and Understanding the Past , 1994 .

[35]  Karl J. Friston,et al.  Statistical parametric maps in functional imaging: A general linear approach , 1994 .

[36]  R. Buxton,et al.  Dynamics of blood flow and oxygenation changes during brain activation: The balloon model , 1998, Magnetic resonance in medicine.