Stochastic Dynamic Causal Modelling of fMRI Data with Multiple-Model Kalman Filters

Summary

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 de terministic 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.

Keywords

Stochastic - DCM - fMRI - Multiple-Model Kalman Filter

• References

• 1 Valdes-Sosa PA, Roebroeck A, Daunizeau J, Friston K. Effective connectivity: Influence, causality and biophysical modeling. NeuroImage. 2011
• 2 Friston KJ, Harrison L, Penny WD. Dynamic Causal Modelling. NeuroImage 2003; 19 (04) 1273-1302.
• 3 Buxton RB, Wong EC, Frank LR. Dynamics of blood flow and oxygenation changes during brain activation: the balloon model. Magn Reson Med 1998; 39 (06) 855-864. Available from http://view.ncbi.nlm.nih.gov/pubmed/9621908.
• 4 Friston KJ, Mechelli A, Turner R, Price CJ. Non-linear responses in fMRI: The Balloon model, Volterra kernels and other hemodynamics. NeuroImage 2000; 12: 466-477.
• 5 Li B, Daunizeau J, Stephan K, Penny W, Friston K. Stochastic DCM and generalized filtering. NeuroImage. 2011
• 6 Friston K, Trujillo-Barreto N, Daunizeau J. DEM: a variational treatment of dynamic systems. NeuroImage 2008; 41 (03) 849-885.
• 7 Friston K, Stephan K, Li B, Daunizeau J. Generalised filtering. Mathematical Problems in Engineering 2010; 2010 Article ID 621670 1-35.
• 8 Kalman RE. A New Approach to Linear Filtering and Prediction Problems. Transactions of the ASME-Journal of Basic Engineering 1960; 82 Series D 35-45.
• 9 Athans M, Falb PL. Optimal control: an introduction to the theory and its applications. New York: McGraw-Hill; 1966
• 10 Murray-Smith R, Johansen TA. editors Multiple Model Approaches to Modelling and Control. Taylor and Francis systems and control book series. London, UK: Taylor and Francis; 1997. Available from http://eprints.gla.ac.uk/34147/.
• 11 Baram Y, Sandell N. An information theoretic approach to dynamical systems modeling and identification. IEEE Trans on Automatic Control 1978; 23 (01) 61-66.
• 12 Penny WD, Stephan KE, Mechelli PS, Friston KJ. Comparing Dynamic Causal Models. Neuroimage 2004; 22: 1157-1172.
• 13 Murta T, Leal A, Garrido I M, Figueiredo P. Dynamic Causal Modelling of epileptic seizure propagation pathways: A combined EEG/fMRI study. NeuroImage 2012; 62 (03) 1634-1642.
• 14 Griffanti L, Baglio F, Lagan MM, Pret MG, Cecconi P, Clerici M. et al. Individual Thresholding of Voxel-based Functional Connectivity Maps. Estimation of Random Errors by Means of Surrogate Time Series. Methods Inf Med 2014; 53: 4.
• 15 Daunizeau J, Stephan KE, Friston KJ. Stochastic dynamic causal modelling of fMRI data: Should we care about neural noise?. NeuroImage 2012; 62 (01) 464-481.
• 16 Hamandi K, Powell HWR, Laufs H, Symms MR, Barker GJ, Parker GJM. et al. Combined EEG-fMRI and tractography to visualise propagation of epileptic activity. Journal of Neurology, Neurosurgery and Psychiatry 2008; 79 (05) 594-597.
• 17 David O, Guillemain I, Saillet S, Reyt S, Deransart C, Segebarth C. et al. Identifying neural drivers with functional MRI: an electrophysiological validation. PLoS Biol 2008; 6 (12) 2683-2697.
• 18 Vaudano A, Laufs H, Kiebel S, Carmichael D, Hamandi K, Guye M. et al. Causal hierarchy within the thalamo-cortical network in spike and wave discharges. PLoS One 2008; 4 (08) e6475.
• 19 Bastos-Leite AJ, Ridgway GR, Silveira C, Norton A, Reis S, Friston KJ. Dysconnectivity within the Default Mode in First-Episode Schizophrenia: A Stochastic Dynamic Causal Modeling Study with Functional Magnetic Resonance Imaging. Schizophrenia Bulletin. 2014
• 20 Havlicek M, Friston KJ, Jan J, Brazdil M, Calhoun VD. Dynamic modeling of neuronal responses in fMRI using cubature Kalman filtering. Neuro-Image.
• 21 Silvestre C, Figueiredo P, Rosa P. Multiple-Model Set-Valued Observers: A new tool for HRF model selection in fMRI. Conf Proc IEEE Eng Med Biol Soc 2010; 1: 5704-5707. Available from http://www.biomedsearch.com/nih/Multiple-Model-Set-Valued-Observers/21097322.html.