Bayesian deconvolution fMRI data using bilinear dynamical systems

Makni, Salima; Beckmann, Christian F.; Smith, Stephen M.; Woolrich, Mark W.

doi:10.1016/j.neuroimage.2008.05.052

Cited by 36 publications

(32 citation statements)

References 21 publications

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“…Penny et al (2005) used difference equations to furnish a bilinear state-space model for fMRI time series and estimated its parameters and states using expectation maximisation (EM). This work was extended by Makni et al (2008), who used a Variational Bayes inversion scheme that allowed for priors over model parameters and enabled model comparison (Penny et al, 2004). More recently, Daunizeau et al (2009) introduced a general variational Bayesian approach for approximate inference on nonlinear models based on stochastic differential equations.…”

Section: Introductionmentioning

confidence: 99%

“…This affords a model of state-noise that is not restricted to Wiener processes or Markovian assumptions. Furthermore, we will consider DCMs that comprise a network of regions (see also Valdés-Sosa et al, 2005), instead of the single regions considered previously (Penny et al, 2005;Makni et al, 2008). Our work in this area has focused on schemes that simplify the inversion problem, using various assumptions about the posterior or conditional density on unknown quantities in the model.…”

Section: Introductionmentioning

confidence: 99%

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Generalised filtering and stochastic DCM for fMRI

et al. 2011

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Section: Introductionmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Generalised filtering and stochastic DCM for fMRI

et al. 2011

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“…The SLM is implicitly Bayesian, in that the state equation is equivalently a prior on the signal dynamics, and the resultant estimation algorithm optimises in a maximum a posteriori sense for the best state and parameter estimates given the observed data. Our approach differs to Bayesian models in the literature, for example [14,10], in that we have not placed prior distributions governed by hyperparameters on the signal and noise parameters. Such prior distributions can be added at the cost of computational expense.…”

Section: Discussionmentioning

confidence: 99%

“…It is of interest to compare in future the SLM with methods in which parameterised, deterministic HRFs are estimated [14], or those in which the HRF is constrained to be a smoothly varying function [3]. Similarly, in future work we will compare the stochastic linear model with nonlinear extended balloon models of the BOLD signal [8] and their estimation strategies, and alternative stochastic modelling approaches such as BDS [10,12].…”

Section: Discussionmentioning

confidence: 99%

“…Unlike the methods of Ciuciu et al, our model is stochastic and parameterised, with the BOLD signal estimated voxelwise along with the activation weight. The SLM is a state space model, similar in form to the bilinear dynamical systems (BDS) proposed by [12] and recently extended by [10]. The key difference between the SLM and BDS is that BDS models the supposed neuronal activity via stochastic state dynamics, which are then convolved with HRF kernels to form the BOLD signal.…”

Section: Introductionmentioning

confidence: 99%

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A Stochastic Linear Model for fMRI Activation Analyses

Johnston

Egan

2011

Lecture Notes in Computer Science

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Abstract. Purpose:The debate regarding how best to model variability of the hemodynamic response function in fMRI data has focussed on the linear vs. nonlinear nature of the optimal signal model, with few studies exploring the deterministic vs. stochastic nature of the dynamics. We propose a stochastic linear model (SLM) of the hemodynamic signal and noise dynamics to more robustly infer fMRI activation estimates. Methods: The SLM models the hemodynamic signal by an exogenous input autoregressive model driven by Gaussian state noise. Activation weights are inferred by a joint state-parameter iterative coordinate descent algorithm based on the Kalman smoother. Results: The SLM produced more accurate parameter estimates than the GLM for event-design simulated data. In application to block-design experimental visuo-motor task fMRI data, the SLM resulted in more punctate and well-defined motor cortex activation maps than the GLM, and was able to track variations in the hemodynamics, as expected from a stochastic model. Conclusions: We demonstrate in application to both simulated and experimental fMRI data that in comparison to the GLM, the SLM produces more flexible, consistent and enhanced fMRI activation estimates.

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State–Space Models of Mental Processes from fMRI

Janoos

Singh

Machiraju

et al. 2011

Lecture Notes in Computer Science

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In addition to functional localization and integration, the problem of determining whether the data encode some information about the mental state of the subject, and if so, how this information is represented has become an important research agenda in functional neuroimaging. Multivariate classifiers, commonly used for brain state decoding, are restricted to simple experimental paradigms with a fixed number of alternatives and are limited in their representation of the temporal dimension of the task. Moreover, they learn a mapping from the data to experimental conditions and therefore do not explain the intrinsic patterns in the data. In this paper, we present a data–driven approach to building a spatio–temporal representation of mental processes using a state–space formalism, without reference to experimental conditions. Efficient Monte Carlo algorithms for estimating the parameters of the model along with a method for model–size selection are developed. The advantages of such a model in determining the mental–state of the subject over pattern classifiers are demonstrated using an fMRI study of mental arithmetic.

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Bayesian deconvolution fMRI data using bilinear dynamical systems

Cited by 36 publications

References 21 publications

Generalised filtering and stochastic DCM for fMRI

Generalised filtering and stochastic DCM for fMRI

A Stochastic Linear Model for fMRI Activation Analyses

State–Space Models of Mental Processes from fMRI

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