Dynamic modeling of neuronal responses in fMRI using cubature Kalman filtering

Martin Havlicek, Karl J. Friston, Jiri Jan, Milan Brazdil, Vince D. Calhoun

Research output: Contribution to journalArticlepeer-review

125 Scopus citations


This paper presents a new approach to inverting (fitting) models of coupled dynamical systems based on state-of-the-art (cubature) Kalman filtering. Crucially, this inversion furnishes posterior estimates of both the hidden states and parameters of a system, including any unknown exogenous input. Because the underlying generative model is formulated in continuous time (with a discrete observation process) it can be applied to a wide variety of models specified with either ordinary or stochastic differential equations. These are an important class of models that are particularly appropriate for biological time-series, where the underlying system is specified in terms of kinetics or dynamics (i.e., dynamic causal models). We provide comparative evaluations with generalized Bayesian filtering (dynamic expectation maximization) and demonstrate marked improvements in accuracy and computational efficiency. We compare the schemes using a series of difficult (nonlinear) toy examples and conclude with a special focus on hemodynamic models of evoked brain responses in fMRI. Our scheme promises to provide a significant advance in characterizing the functional architectures of distributed neuronal systems, even in the absence of known exogenous (experimental) input; e.g., resting state fMRI studies and spontaneous fluctuations in electrophysiological studies. Importantly, unlike current Bayesian filters (e.g. DEM), our scheme provides estimates of time-varying parameters, which we will exploit in future work on the adaptation and enabling of connections in the brain.

Original languageEnglish (US)
Pages (from-to)2109-2128
Number of pages20
Issue number4
StatePublished - Jun 15 2011
Externally publishedYes


  • Blind deconvolution
  • Cubature Kalman filter
  • Dynamic expectation maximization
  • FMRI
  • Hemodynamic modeling
  • Neuronal
  • Nonlinear
  • Smoother
  • Stochastic

ASJC Scopus subject areas

  • Neurology
  • Cognitive Neuroscience


Dive into the research topics of 'Dynamic modeling of neuronal responses in fMRI using cubature Kalman filtering'. Together they form a unique fingerprint.

Cite this