title: Bilinear dynamical systems.
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.
authors.affiliation: Wellcome Department of Imaging Neuroscience, University College, London WC1N 3BG, UK. wpenny@fil.ion.ucl.ac.uk
authors.forename: W
authors.initials: W
authors.lastname: Penny
authors.forename: Z
authors.initials: Z
authors.lastname: Ghahramani
authors.forename: K
authors.initials: K
authors.lastname: Friston
mesh_terms: D000465:Algorithms; D001921:Brain / Q000033:anatomy & histology / Q000502:physiology*; D001931:Brain Mapping / Q000379:methods*; D003198:Computer Simulation; D003627:Data Interpretation, Statistical; D006801:Humans; D016014:Linear Models; D008279:Magnetic Resonance Imaging / Q000379:methods*; D008959:Models, Neurological; D009474:Neurons / Q000502:physiology; D013269:Stochastic Processes; D013997:Time Factors