Dynamic modeling of neuronal responses in fMRI using cubature Kalman filtering

By Martin Havlicek, Karl J. Friston, Jirí Jan, Milan Brazdil, Vince D. Calhoun. 2011

182 citations recorded by the source corpus.

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.

Subfields: Cognitive Neuroscience, Signal Processing

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Citations in the corpus

Causal Discovery from Heterogeneous/Nonstationary Data (2019, background): “More speciﬁcally, it is believed that one of the basic properties of neural connections is their time-dependence (Havlicek et al., 2011).”
Causal Discovery from Nonstationary/Heterogeneous Data: Skeleton Estimation and Orientation Determination (2017, background): “More speciﬁcally, it is believed that one of the basic properties of the neural connections is their time-dependence [Havlicek et al. , 2011].”
Discovery and Visualization of Nonstationary Causal Models (2015, background): “More speciﬁcally, it is believed that one of the basic properties of the neural connections in the brain is its time-dependence [1].”
The brain basis of emotion: A meta-analytic review (2012, unknown): “Many refinements to GCA have been proposed, such as correlation-purged/dynamic/nonlinear GC (Deshpande et al. 2010; Marinazzo et al. 2008; Sato et al. 2006) and hemodynamic deconvolution (Havlicek et al. 2011; Ryali et al. 2011), which have increased the applicability of GCA to fMRI.”
The MVGC multivariate Granger causality toolbox: a new approach to Granger-causal inference. (2014, background): “Alternative promising approaches include estimation of state-space models which jointly parameterize functional connectivity and hemodynamic responses (Ryali et al., 2011) or blind deconvolution of the HRF to retrieve the underlying neuronal processes (Havlicek et al., 2011; Wu et al., 2013).”