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Bilinear dynamical systems.

W Penny·Z Ghahramani·K Friston
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Abstract

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.

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AlgorithmsBrainBrain MappingComputer SimulationData Interpretation, StatisticalHumansLinear ModelsMagnetic Resonance ImagingModels, NeurologicalNeuronsStochastic ProcessesTime FactorsComparative StudyJournal ArticleResearch Support, Non-U.S. Gov't

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W Penny, Z Ghahramani, K Friston. 2005-05-29. Bilinear dynamical systems.. https://doi.org/10.1098/rstb.2005.1642

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