Dynamic modeling of neuronal responses in fMRI using cubature Kalman filtering

NeuroImage

Volumn 56, Issue 4, 2011, Pages 2109-2128

  Havlicek, Martin ^a,b,d   Friston, Karl J ^c   Jan, Jiri ^a   Brazdil, Milan ^e,f   Calhoun, Vince D ^b,d  

^a BRNO UNIVERSITY OF TECHNOLOGY   (Czech Republic)

^b MIND RESEARCH NETWORK   (United States)

^c WELLCOME TRUST CENTRE FOR NEUROIMAGING   (United Kingdom)

^d UNIVERSITY OF NEW MEXICO   (United States)

^e MASARYK UNIVERSITY   (Czech Republic)

^f ST ANNE S UNIVERSITY HOSPITAL   (Czech Republic)

Author keywords

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

Indexed keywords

ALGORITHM; ARTICLE; BAYES THEOREM; BRAIN ELECTROPHYSIOLOGY; BRAIN FUNCTION; CUBATURE KALMAN FILTER; ELECTROENCEPHALOGRAM; EVOKED BRAIN STEM RESPONSE; FUNCTIONAL MAGNETIC RESONANCE IMAGING; HEMODYNAMIC PARAMETERS; MATHEMATICAL MODEL; NERVE CELL; NONLINEAR SYSTEM; PRIORITY JOURNAL; STATISTICAL ANALYSIS;

ALGORITHMS; BRAIN; HEMODYNAMICS; HUMANS; IMAGE INTERPRETATION, COMPUTER-ASSISTED; MAGNETIC RESONANCE IMAGING; MODELS, NEUROLOGICAL; MONTE CARLO METHOD; NEURAL PATHWAYS; NEURONS;

EID: 79957479620     PISSN: 10538119     EISSN: 10959572     Source Type: Journal    
DOI: 10.1016/j.neuroimage.2011.03.005     Document Type: Article

References (68)

1. Aguirre G.K., Zarahn E., D'esposito M. The variability of human, BOLD hemodynamic responses. Neuroimage 1998, 8:360-369.
2. Arasaratnam I., Haykin S. Nonlinear Bayesian filters for training recurrent neural networks. MICAI 2008: Advances in Artificial Intelligence 2008, 12-33.
3. Arasaratnam I., Haykin S. Cubature Kalman filters. IEEE Trans. Autom. Control 2009, 54:1254-1269.
4. Attwell D., Buchan A.M., Charpak S., Lauritzen M., MacVicar B.A., Newman E.A. Glial and neuronal control of brain blood flow. Nature 2010, 468:232-243.
5. Berns G.S., Song A.W., Mao H. Continuous functional magnetic resonance imaging reveals dynamic nonlinearities of "dose-response" curves for finger opposition. J. Neurosci. 1999, 19:1-6.
6. Birn R.M., Saad Z.S., Bandettini P.A. Spatial heterogeneity of the nonlinear dynamics in the FMRI BOLD response. Neuroimage 2001, 14:817-826.
7. Biscay R., Jimenez J.C., Riera J.J., Valdes P.A. Local linearization method for the numerical solution of stochastic differential equations. Ann. Inst. Stat. Math. 1996, 48:631-644.
8. Biswal B., Yetkin F.Z., Haughton V.M., Hyde J.S. Functional connectivity in the motor cortex of resting human brain using echo-planar MRI. Magn. Reson. Med. 1995, 34:537-541.
9. Bucy R.S., Senne K.D. Digital synthesis of non-linear filters. Automatica 1971, 7:287-298.
10. Buxton R.B., Wong E.C., Frank L.R. Dynamics of blood flow and oxygenation changes during brain activation: the balloon model. Magn. Reson. Med. 1998, 39:855-864.
11. Buxton R.B., Uludag K., Dubowitz D.J., Liu T.T. Modeling the hemodynamic response to brain activation. Neuroimage 2004, 23:S220-S233.
12. David, O., in press. fMRI connectivity, meaning and empiricism Comments on: Roebroeck et al. The identification of interacting networks in the brain using fMRI: Model selection, causality and deconvolution. Neuroimage.
13. David O., Guillemain I., Saillet S., Reyt S., Deransart C., Segebarth C., Depaulis A. Identifying neural drivers with functional MRI: an electrophysiological validation. PLoS Biol. 2008, 6:2683-2697.
14. Deneux T., Faugeras O. Using nonlinear models in fMRI data analysis: model selection and activation detection. Neuroimage 2006, 32:1669-1689.
15. Doucet A., De Freitas N., Gordon N. Sequential Monte Carlo methods in practice 2001, Springer Verlag.
16. Fernandez-Prades C., Vila-Valls J. Bayesian nonlinear filtering using quadrature and cubature rules applied to sensor data fusion for positioning. Proceeding of IEEE International Conference on Communications 2010, 1-5.
17. Friston K.J. Bayesian estimation of dynamical systems: an application to fMRI. Neuroimage 2002, 16:513-530.
18. Friston K. Variational filtering. Neuroimage 2008, 41:747-766.
19. Friston K.J. Hierarchical models in the brain. PLoS Comput. Biol. 2008, 4:e1000211.
20. Friston, K., in press. Dynamic casual modeling and Granger causality Comments on: the identification of interacting networks in the brain using fMRI: Model selection, causality and deconvolution. Neuroimage.
21. Friston K.J., Mechelli A., Turner R., Price C.J. Nonlinear responses in fMRI: the Balloon model, Volterra kernels, and other hemodynamics. Neuroimage 2000, 12:466-477.
22. Friston K.J., Harrison L., Penny W. Dynamic causal modelling. Neuroimage 2003, 19:1273-1302.
23. Friston K.J., Trujillo-Barreto N., Daunizeau J. DEM: a variational treatment of dynamic systems. Neuroimage 2008, 41:849-885.
24. Friston K.J., Stephan K.E., Daunizeau J. Generalised filtering. Mathematical Problems in Engineering 2010 2010.
25. Gitelman D.R., Penny W.D., Ashburner J., Friston K.J. Modeling regional and psychophysiologic interactions in fMRI: the importance of hemodynamic deconvolution. Neuroimage 2003, 19:200-207.
26. Handwerker D., Ollinger J., D'Esposito M. Variation of BOLD hemodynamic responses across subjects and brain regions and their effects on statistical analyses. Neuroimage 2004, 21:1639-1651.
27. Haykin S.S. Kalman Filtering and Neural Networks 2001, Wiley Online Library.
28. Hinton G.E., van Camp D. Keeping the neural networks simple by minimizing the description length of the weights. Proceedings of COLT-93 1993, 5-13. ACM.
29. Hu Z., Zhao X., Liu H., Shi P. Nonlinear analysis of the BOLD signal. EURASIP J. Adv. Signal Process. 2009, 2009:1-13.
30. Iadecola C. CC commentary: intrinsic signals and functional brain mapping: caution, blood vessels at work. Cereb. Cortex 2002, 12:223-224.
31. Ito K., Xiong K. Gaussian filters for nonlinear filtering problems. IEEE Trans. Automatic Control 2002, 45:910-927.
32. Jaakkola T.S. Tutorial on variational approximation methods. Advanced mean field methods: theory and practice 2000, 129-159.
33. Jacobsen D., Hansen L., Madsen K. Bayesian model comparison in nonlinear BOLD fMRI hemodynamics. Neural Comput. 2008, 20:738-755.
34. Ji Z., Brown M. Joint state and parameter estimation for biochemical dynamic pathways with iterative extended Kalman filter: comparison with dual state and parameter estimation. Open Automation Control Syst. J. 2009, 2:69-77.
35. Jimenez J.C. A simple algebraic expression to evaluate the local linearization schemes for stochastic differential equations 1. Appl. Math. Lett. 2002, 15:775-780.
36. Jimenez J.C., Ozaki T. Local linearization filters for non-linear continuous-discrete state space models with multiplicative noise. Int. J. Control 2003, 76:1159-1170.
37. Jimenez J.C., Shoji I., Ozaki T. Simulation of stochastic differential equations through the local linearization method. A comparative study. J. Stat. Phys. 1999, 94:587-602.
38. Johnston L.A., Duff E., Mareels I., Egan G.F. Nonlinear estimation of the BOLD signal. Neuroimage 2008, 40:504-514.
39. Julier S., Uhlmann J., Durrant-Whyte H.F. A new method for the nonlinear transformation of means and covariances in filters and estimators. IEEE Trans. Automatic Control 2002, 45:477-482.
40. Kalman R.E. A new approach to linear filtering and prediction problems. J. Basic Eng. 1960, 82:35-45.
41. Kaminski P., Bryson A., Schmidt S. Discrete square root filtering: a survey of current techniques. IEEE Trans. Automatic Control 1971, 16:727-736.
42. Kloeden P.E., Platen E. Numerical Solution of Stochastic Differential Equations, Stochastic Modeling and Applied Probability, 3rd editon 1999, Springer.
43. Krüger G., Glover G.H. Physiological noise in oxygenation sensitive magnetic resonance imaging. Magn. Reson. Med. 2001, 46:631-637.
44. Lauritzen M. Relationship of spikes, synaptic activity, and local changes of cerebral blood flow. J. Cereb. Blood Flow Metab. 2001, 21:1367-1383.
45. Li P., Yu J., Wan M., Huang J. The augmented form of cubature Kalman filter and quadrature Kalman filter for additive noise. IEEE Youth Conference on Information, Computing and Telecommunication, YC-ICT '09 2009, 295-298. IEEE.
46. Ljung L., Söderström T. Theory and Practice of Recursive Identification 1983, MIT Press, Cambridge, MA.
47. Logothetis N.K. The neural basis of the blood-oxygen-level-dependent functional magnetic resonance imaging signal. Philos. Trans. R. Soc. Lond. B Biol. Sci. 2002, 357:1003.
48. MacKay D.J.C. Developments in probabilistic modelling with neural networks-ensemble learning. Proceedings of 3rd Annual Symposium on Neural Networks, Nijmegen, Netherlands 1995, 191-198.
49. Magistretti P., Pellerin L. Cellular mechanisms of brain energy metabolism and their relevance to functional brain imaging. Philos. Trans. R. Soc. Lond. B Biol. Sci. 1999, 354:1155-1163.
50. Mandeville J.B., Marota J.J.A., Ayata C., Zaharchuk G., Moskowitz M.A., Rosen B.R., Weisskoff R.M. Evidence of a cerebrovascular postarteriole windkessel with delayed compliance. J. Cereb. Blood Flow Metab. 1999, 19:679-689.
51. Mechelli A., Price C., Friston K. Nonlinear coupling between evoked rCBF and BOLD signals: a simulation study of hemodynamic responses. Neuroimage 2001, 14:862-872.
52. Miller K.L., Luh W.M., Liu T.T., Martinez A., Obata T., Wong E.C., Frank L.R., Buxton R.B. Nonlinear temporal dynamics of the cerebral blood flow response. Hum. Brain Mapp. 2001, 13:1-12.
53. Murray L., Storkey A. Continuous time particle filtering for fMRI. Adv. Neural Inf. Process. Syst. 2008, 20.
54. Nelson, A.T., 2000. Nonlinear estimation and modeling of noisy time-series by dual Kalman filtering methods. Ph.D thesis, Oregon Graduate Institute of Science and Technology.
55. Norgaard M., Poulsen N.K., Ravn O. New developments in state estimation for nonlinear systems. Automatica 2000, 36:1627-1638.
56. Ozaki T. A bridge between nonlinear time series models and nonlinear stochastic dynamical systems: a local linearization approach. Stat. Sin. 1992, 2:113-135.
57. Riera J., Watanabe J., Kazuki I., Naoki M., Aubert E., Ozaki T., Kawashima R. A state-space model of the hemodynamic approach: nonlinear filtering of BOLD signals. Neuroimage 2004, 21:547-567.
58. Robbins H., Monro S. A stochastic approximation method. Ann. Math. Stat. 1951, 22:400-407.
59. Roebroeck, A., Formisano, E., Goebel, R., in press-a. Reply to Friston and David: After comments on: The identification of interacting networks in the brain using fMRI: Model selection, causality and deconvolution. Neuroimage.
60. Roebroeck, A., Formisano, E., Goebel, R., in press-b. The identification of interacting networks in the brain using fMRI: model selection, causality and deconvolution. Neuroimage.
61. Särkkä S., Nummenmaa A. Recursive noise adaptive Kalman filtering by variational Bayesian approximations. IEEE Trans. Automatic Control 2009, 54:596-600.
62. Simandl M., Dunik J. Design of derivative-free smoothers and predictors. Proceeding of the 14th IFAC Symposium on System Identification, SYSID06 2006, 1240-1245.
63. Sitz A., Schwarz U., Kurths J., Voss H.U. Estimation of parameters and unobserved components for nonlinear systems from noisy time series. Phys. Rev. E 2002, 66:1-9.
64. Sotero R.C., Trujillo-Barreto N.J., Jiménez J.C., Carbonell F., Rodríguez-Rojas R. Identification and comparison of stochastic metabolic/hemodynamic models (sMHM) for the generation of the BOLD signal. J. Comput. Neurosci. 2009, 26:251-269.
65. Stephan K.E., Kasper L., Harrison L.M., Daunizeau J., den Ouden H.E.M., Breakspear M., Friston K.J. Nonlinear dynamic causal models for fMRI. Neuroimage 2008, 42:649-662.
66. Valdes Sosa P.A., Sanchez Bornot J.M., Sotero R.C., Iturria Medina Y., Aleman Gomez Y., Bosch Bayard J., Carbonell F., Ozaki T. Model driven EEG/fMRI fusion of brain oscillations. Hum. Brain Mapp. 2009, 30:2701-2721.
67. Van der Merwe, R., 2004. Sigma-point Kalman filters for probabilistic inference in dynamic state-space models. Ph.D. thesis, Oregon Graduate Institute of Science and Technology.
68. Wu Y., Hu D., Wu M., Hu X. Unscented Kalman filtering for additive noise case: augmented vs. non-augmented. IEEE Signal Process Lett. 2005, 12:357-359.