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Stochastic dynamic causal modelling of FMRI data with multiple-model Kalman filters.

INTRODUCTION
This article is part of the Focus Theme of Methods of Information in Medicine on "Biosignal Interpretation: Advanced Methods for Neural Signals and Images".


BACKGROUND
Dynamic Causal Modelling (DCM) is a generic formalism to study effective brain connectivity based on neuroimaging data, particularly functional Magnetic Resonance Imaging (fMRI). Recently, there have been attempts at modifying this model to allow for stochastic disturbances in the states of the model.


OBJECTIVES
This paper proposes the Multiple-Model Kalman Filtering (MMKF) technique as a stochastic identification model discriminating among different hypothetical connectivity structures in the DCM framework; moreover, the performance compared to a similar deterministic identification model is assessed.


METHODS
The integration of the stochastic DCM equations is first presented, and a MMKF algorithm is then developed to perform model selection based on these equations. Monte Carlo simulations are performed in order to investigate the ability of MMKF to distinguish between different connectivity structures and to estimate hidden states under both deterministic and stochastic DCM.


RESULTS
The simulations show that the proposed MMKF algorithm was able to successfully select the correct connectivity model structure from a set of pre-specified plausible alternatives. Moreover, the stochastic approach by MMKF was more effective compared to its deterministic counterpart, both in the selection of the correct connectivity structure and in the estimation of the hidden states.


CONCLUSIONS
These results demonstrate the applicability of a MMKF approach to the study of effective brain connectivity using DCM, particularly when a stochastic formulation is desirable.