Identifying effective connectivity parameters in simulated fMRI: A direct comparison of switching linear dynamic system, stochastic dynamic causal, and multivariate autoregressive models

Frontiers in Neuroscience

Volumn , Issue 7 MAY, 2013, Pages

  Smith, Jason F ^a   Chen, Kewei ^b,c,d   Pillai, Ajay S ^e   Horwitz, Barry ^a  

^a NATIONAL INSTITUTE ON DEAFNESS AND OTHER COMMUNICATION DISORDERS   (United States)

^b BANNER GOOD SAMARITAN MEDICAL CENTER   (United States)

^c ARIZONA STATE UNIVERSITY   (United States)

^d ARIZONA ALZHEIMER S CONSORTIUM   (United States)

^e NATIONAL INSTITUTES OF HEALTH   (United States)

Author keywords

Effective connectivity; FMRI BOLD; Modeling and simulation; Parameter estimation

Indexed keywords

ACCURACY; ANALYTICAL PARAMETERS; ARTICLE; DYNAMIC CAUSAL MODEL; FUNCTIONAL MAGNETIC RESONANCE IMAGING; LINEAR DYNAMIC SYSTEM; MATHEMATICAL PHENOMENA; MULTIVARIATE ANALYSIS; MULTIVARIATE AUTOREGRESSIVE MODEL; SIMULATION; STOCHASTIC MODEL;

EID: 84879269843     PISSN: 16624548     EISSN: 1662453X     Source Type: Journal    
DOI: 10.3389/fnins.2013.00070     Document Type: Article

References (105)

1. Aguirre, G. K., Zarahn, E., and D'Esposito, M. (1998). The variability of human BOLD hemodynamic responses. Neuroimage 8, 360-369.
2. Alexander, G. E., and Moeller, J. R. (1994). Application of the scaled subprofile model to functional imaging in neuropsychiatric disorders: a principal component approach to modeling brain function and disease. Hum. Brain Mapp. 2, 79-94.
3. Åström, J. K. (1970). Introduction to Stochastic Control Theory. New York, NY: Academic Press.
4. Åström, J. K., and Wittenmark, B. (1996). Computer-Controlled Systems: Theory and Design. Upper Saddle River, NJ: Prentice-Hall.
5. Barber, D. (2006). Expectation correction for smoothed inference in switching linear dynamical systems. J. Mach. Learn. Res. 7, 2515-2540.
6. Barnet, L. C., and Seth, A. K. (2011). Behaviour of Granger causality under filtering: theoretical invariance and practical application. J. Neurosci. Methods 201, 404-419.
7. Bar-Shalom, Y., Li, X. R., and Kirubarajan, T. (2001). Estimation with Applications to Tracking and Navigation. New York, NY: John Wiley and Sons.
8. Bishop, C. M. (2006). Pattern Recognition and Machine Learning. Vol. 4. New York, NY: Springer.
9. Bokde, A. L. W., Ewers, M., and Hampel, H. (2009). Assessing neuronal networks: understanding Alzheimer's disease. Prog. Neurobiol. 89, 125-133.
10. Büchel, C., Coull, J. T., and Friston, K. J. (1999). The predictive value of changes in effective connectivity for human learning. Science 283, 1538-1541.
11. Bullmore, E. T., Long, C., Suckling, J., Fadili, J., Calvert, G., Zelaya, F., et al. (2001). Colored noise and computational inference in neurophysiological (fMRI) time series analysis: resampling methods in time and wavelet domains. Hum. Brain Mapp. 12, 61-78.
12. Bullmore, E. T., Rabe-Hesketh, S., Morris, R. G., Williams, S. C. R., Gregory, L., Gray, J. A., et al. (1996). Functional magnetic resonance image analysis of a large-scale neurocognitive network. Neuroimage 4, 16-23.
13. Buxton, R. B. (2012). Dynamic models of BOLD contrast. Neuroimage 62, 953-961.
14. Buxton, R. B., Wong, E. C., and Frank, L. R. (1998). Dynamics of blood flow and oxygenation changes during brain activation: the Balloon model. Magn. Reson. Med. 39, 855-864.
15. Calhoun, V. D., Adali, T., Pearlson, G. D., van Zijl, P. C. M., and Pekar, J. J. (2002). Independent component analysis of fMRI data in the complex domain. Magn. Reson. Med. 48, 180-192.
16. Chen, G., Saad, Z. S., Glen, D. R., Hamilton, J. P., Thomason, M. E., Gotlib, I. H., et al. (2011). Vector autoregression, structural equation modeling, and their synthesis in neuroimaging data analysis. Comput. Biol. Med. 41, 1142-1155.
17. Culver, W. J. (1966). On the existence and uniqueness of the real logarithm of a matrix. Proc. Am. Math. Soc. 17, 1146-1151.
18. Daunizeau, J., Friston, K. J., and Kiebel, S. J. (2009). Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models. Physica D 238, 2089-2118.
19. David, O., Guillemain, I., Saillet, S., Reyt, S., Deransart, C., Segebarth, C., and Depaulis, A. (2008). Identifying neural drivers with functional MRI: an electrophysiological validation. PLoS Biol. 6:e315. doi:10.1371/journal.pbio.0060315
20. Dempster, A. P., Laird, N. M., and Rubin, D. B. (1977). Maximum likelihood from incomplete data via the EM algorithm. J. R. Statist. Soc. Ser. B 39, 1-38.
21. Diamantaras, K. I., and Kung, S. Y. (1996). Principal Component Neural Networks: Theory and Applications. New York, NY: John Wiley and Sons.
22. Fisher, F. (1970). A correspondence principle for simultaneous equation models. Econometrica 28, 79-92.
23. Fox, E. B., Sudderth, E. B., Jordan, M. I., and Willsky, A. S. (2010). Bayesian nonparametric methods for learning Markov switching processes. IEEE Signal Process. Mag., 27, 43-54.
24. Franklin, G. F., Powell, D. J., and Workman, M. L. (1997). Digital Control of Dynamic Systems. Upper Saddle River, NJ: Prentice Hall.
25. Friston, K. J. (1994). Functional and effective connectivity in neuroimaging: a synthesis. Hum. Brain Mapp. 2, 56-78.
26. Friston, K. J., Harrison, L., and Penny, W. (2003). Dynamic causal modelling. Neuroimage 19, 1273-1302.
27. Friston, K. J., Jezzard, P., and Turner, R. (1994). Analysis of functional MRI time series. Hum. Brain Mapp. 1, 153-171.
28. Friston, K. J., Mechelli, A., Turner, R., and Price, C. J. (2000). Nonlinear responses in fMRI: the balloon model Volterra kernels, and other hemodynamics. Neuroimage 4, 466-477.
29. Friston, K. J., Stephan, K. E., Li, B., and Daunizeau, J. (2010). Generalized filtering. Math. Probl. Eng. 621670. doi: 10.1155/2010/621670
30. Ghahramani, Z., and Hinton, G. E. (1996). Parameter Estimation for Linear Dynamical Systems. Technical Report CRG-TR-96-92. Toronto, ON: University of Toronto.
31. Harrison, L., Penny, W. D., and Friston, K. (2003). Multivariate autoregressive modeling of fMRI time series. Neuroimage 19, 1477-1491.
32. Haken, H. (1996). Principles of Brain Functioning: A Synergetic Approach to Brain Activity, Behavior, and Cognition. Berlin: Springer.
33. Handwerker, D. A., Gonzalez-Castillo, J., D'Esposito, M., and Bandettini, P. A. (2012). The continuing challenge of understanding and modeling hemodynamic variation in fMRI Neuroimage 62, 1017-1023.
34. Handwerker, D. A., Ollinger, J. M., and D'Esposito, M. (2004). Variation of BOLD hemodynamic responses across subjects and brain regions and their effects on statistical analyses. Neuroimage 21, 1639-1651.
35. Havlicek, M., Friston, J. K., Jan, J., Brazdil, M., and Calhoun, V. D. (2011). Dynamic modeling of neural responses in fMRI using cubature Kalman filtering. Neuroimage 56, 2109-2128.
36. Havlicek, M., Jan, J., Brazdil, M., and Calhoun, V. D. (2010). Dynamic Granger causality based on Kalman filter for evaluation of functional network connectivity in fMRI data. Neuroimage 53, 65-77.
37. Haykin, S. (2002). Adaptive Filter Theory. Upper Saddle River, NJ: Prentice-Hall.
38. He, B., Dai, Y., Astolfi, L., Babiloni, F., Yuan, H., and Yang, L. (2011). eConnectome: a MATLAB toolbox for mapping and imaging of brain functional connectivity. J. Neurosci. Methods 195, 261-269.
39. Henson, R. (2003). "Analysis of fMRI timeseries: linear time-invariant model, event related fMRI and optimal experimental design," in Human Brain Function, eds R. S. J. Frackowiak, K. J. Friston, C. Frith, R. Dolan, C. J. Price, S. Zeki, J. Ashburner, and W. D. Penny (Academic Press).
40. Horwitz, B. (2003). The elusive concept of brain connectivity. Neuroimage 19, 466-470.
41. Horwitz, B., Grady, C. I., Haxby, J. V., Ungerleider, L. G., Schapiro, M. B., Mishkin, M., et al. (1992). Functional associations among posterior extrastriate brain region during object and spatial vision. J. Cogn. Neurosci. 4, 311-322.
42. Horwitz, B., and Rowe, J. B. (2011). Functional biomarkers for neurodegenerative disorders based on the network paradigm. Prog. Neurobiol. 95, 505-509.
43. Jolliffe, I. T. (1986). Principal Component Analysis. NewYork, NY: Springer-Verlag.
44. Kelso, J. A. S. (1995). Dynamic Patterns: The Self-Organization of Brain and Behavior. Cambridge, MA: MIT Press.
45. Kim, C. J. (1994). Dynamic linear models with Markov-switching. J. Econom. 60, 1-22.
46. Lacerda, G., Spirtes, P., Ramsey, J., and Hoyer, P. (2008). "Discovering cyclic causal models by independent components analysis," in Proceedings of the 24th Conference on Uncertainty in Artificial Intelligence (Helsinki).
47. Li, B., Daunizeau, J., Stephan, K. E., Penny, W., Hu, D., and Friston, K. J. (2011). Generalised filtering and stochastic DCM for fMRI. NeuroImage 58, 442-457.
48. Ljung, L., and Wills, A. G. (2010). Issues in sampling and estimating continuous-time models with stochastic disturbances. Automatica 46, 925-931.
49. Logothetis, N. K. (2008). What we can do and what we cannot do with fMRI. Nature 453, 869-878.
50. Logothetis, N. K., Pauls, J., Augath, M., Trinath, T., and Oeltermann, A. (2001). Neurophysiological investigation of the basis of the fMRI signal. Nature 412, 150-157.
51. Logothetis, N. K., and Pfeuffer, J. (2004). On the nature of the BOLD fMRI contrast mechanism. Magn. Reson. Imaging 22, 1517-1531.
52. Lütkepohl, H. (2007). New Introduction to Multiple Time Series Analysis. Berlin: Springer-Verlag.
53. Makni, S., Beckmann, C., Smith, S., and Woolrich, M. (2007). Bayesian deconvolution of fMRI data using bilinear dynamical systems. Neuroimage 42, 1381-1396.
54. Mandeville, J. B., Marota, J. J., Ayata, C., Zararchuk, G., Moskowitz, M. A., Rosen, B., et al. (1999). Evidence of a cerebrovascular postarteriole windkessel with delayed compliance. J. Cereb. Blood Flow Metab. 19, 679-689.
55. Marrelec, G., Krainik, A., Duffau, H., Pélégrini-Issac, M., Lehéricy, S., Doyon, J., et al. (2006). Partial correlation for functional brain interactivity investigation in functional MRI. Neuroimage 32, 228-237.
56. Martínez-Monts, E., Valdés-Sosa, P. A., Miwakeichi, F., Goldman, R. I., and Cohen, M. S. (2004). Concurrent EEG/fMRI analysis by multiway Partial Least Squares. Neuroimage 22, 1023-1034.
57. Marxen, M., Cassidy, R. J., Dawsom, T. L., Ross, B., and Graham, S. J. (2012). Transient and sustained components of the sensorimotor BOLD response in fMRI. Magn. Reson. Imaging 30, 837-847.
58. McIntosh, A. R. (1999). Mapping cognition to the brain through neural interactions. Memory 7, 523-548.
59. McIntosh, A. R. (2001). Towards a network theory of cognition. Neural Netw. 13, 861-876.
60. McIntosh, A. R., Bookstein, F. L., Haxby, J. V., and Grady, C. L. (1996). Spatial pattern analysis of functional brain images using partial least squares. Neuroimage 3, 143-157.
61. McIntosh, A. R., and Gonzalez-Lima, F. (1994). Structural equation modeling and its application to network analysis in functional brain imaging. Hum. Brain Mapp. 2, 2-22.
62. McKeown, M. J., Makeig, S., Brown, G. G., Jung, T. P., Kindermann, S. S., Bell, A. J., et al. (1998). Analysis of fMRI data by blind separation into independent spatial components. Hum. Brain Mapp. 6, 160-188.
63. Mechelli, A., Penny, W. D., Price, C. J., Gitelman, D. R., and Friston, K. J. (2002). Effective connectivity and intersubject variability: using a multisubject network to test differences and commonalities. Neuroimage 17, 1459-1469.
64. Minka, T. (2000). Bayesian Linear Regression. Technical report. Cambridge MA: MIT.
65. Moeller, J. R., and Strother, S. C. (1991). A regional covariance approach to the analysis of functional patterns in positron emission tomographic data. J. Cereb. Blood Flow Metab. 11, A121-A135.
66. Murphy, K. (1998). Learning Switching Kalman Filter Models. Cambridge MA: Compaq Cambridge Research Lab Tech Report 98-10.
67. Neumaier, A., and Schneider, T. (2001). Estimation of parameters and eigenmodes of multivariate autoregressive models. ACM Trans. Math. Softw. 27, 27-57.
68. Patel, R. S., Bowman, F. D., and Rilling, J. K. (2006). A Bayesian approach to determining connectivity of the human brain. Hum. Brain Mapp. 27, 267-276.
69. Penny, W. D., Ghahramani, Z., and Friston, K. J. (2005). Bilinear dynamical systems. Philos. Trans. R. Soc. Lond. B Biol. Sci. 360, 983-993.
70. Penny, W. D., Stephan, K. E., Mechelli, A., and Friston, K. J. (2004). Modeling functional integration: a comparison of structural equation and dynamic causal models. Neuroimage 23(Suppl. 1), S264-S274.
71. Rajapakse, J. C., and Zhou, J. (2007). Learning effective brain connectivity with dynamic Bayesian networks. Neuroimage 37, 749-760.
72. Raol, J. R., Puthenpura, S., and Sinha, N. K. (1987). Algorithms for transformation of multivariable discrete-time models to continuous-time models. Adv. Model. Simul. 6, 52-62.
73. Richardson, T. (1996). "A discovery algorithm for directed cyclic graphs," in Proceedings of the 12th Conference on Uncertainty in Artificial Intelligence (Portland, OR).
74. Riera, J. J., Watanabe, J., Kazuki, I., Naoki, M., Aubert, E., Ozaki, T., et al. (2004). A state space model of the hemodynamic approach: nonlinear filtering of BOLD signals. Neuroimage 21, 547-567.
75. Roebroeck, A., Formisano, E., and Goebel, R. (2005). Mapping directed influence over the brain using Granger causality and fMRI. Neuroimage 25, 230-242.
76. Roebroeck, A., Formisano, E., and Goebel, R. (2011). The identification of interacting networks in the brain using fMRI: model selection, causality and deconvolution. Neuroimage 58, 296-302.
77. Rowe, J. B. (2010). Connectivity analysis is essential to understand neurological disorders. Front. Syst. Neurosci. 4:144. doi: 10.3389/fnsys.2010.00144
78. Roweis, S., and Ghahramani, Z. (1999). A unifying review of linear Gaussian models. Neural Comput. 11, 305-346.
79. Rubio-Ramírez, J. F., Waggoner, D. F., and Zha, T. (2010). Structural vector autoregressions: theory of indentification and algorithms for inference. Rev. Econ. Stud. 77, 665-696.
80. Ryali, S., Supekar, K., Chen, T., and Menon, V. (2011). Multivariate dynamical systems models for estimating causal interactions in fMRI. Neuroimage 54, 807-823.
81. Schneider, T., and Neumaier, A. (2001). Algorithm 808: ARfit-A Matlab package for the estimation of parameters and eigenmodes of multivariate autoregressive models. ACM Trans. Math. Softw. 27, 58-65.
82. Seth, A. K. (2005). Causal connectivity of evolved neural networks during behavior. Network 16, 35-54.
83. Seth, A. K. (2010). A MATLAB toolbox for Granger causal connectivity analysis. J. Neurosci. Methods 186, 262-273.
84. Seth, A. K., Chorley, P., and Barnet, L. C. (2013). Granger causality analysis of fMRI BOLD signals is invariant to hemodynamic convolution but not downsampling. Neuroimage 65, 540-555.
85. Shimizu, S., Hoyer, P., Hyvärien, A., and Kerminen, A. (2006). A linear non-gaussian acyclic model for causal discovery. J. Mach. Learn. Res. 7, 2003-2030.
86. Shumway, R. H., and Stoffer, D. S. (1982). An approach to time series smoothing and forecasting using the EM algorithm. J. Time Ser. Anal. 3, 253-264.
87. Sims, C. A. (1980). Macroeconomics and reality. Econometrica 48, 1-48.
88. Sims, C. A., and Zha, T. (1998). Bayesian methods in dynamic multivariate models. Int. Econ. Rev. 39, 949-968.
89. Smith, J. F., Chen, K., Johnson, S., Morrone-Strupinsky, J., Reiman, E. M., Nelson, A., et al. (2006). Network analysis of single subject fMRI during a finger opposition task. Neuroimage 32, 325-332.
90. Smith, J. F., Pillai, A. S., Chen, K., and Horwitz, B. (2010). Identification and validation of effective connectivity networks in functional magnetic resonance imaging using switching linear dynamic systems. Neuroimage 52, 1027-1040.
91. Smith, S. M., Miller, K. L., Salimi-Khorshidi, G., Webster, M., Beckmann, C. F., Nichols, T. E., et al. (2011a). Network modeling methods for FMRI. Neuroimage 54, 875-891.
92. Smith, J. F., Pillai, A., Chen, K., and Horwitz, B. (2011b). Effective connectivity modeling for fMRI: Six issues and possible solutions using linear dynamic systems. Front. Syst. Neurosci. 5:104. doi: 10.3389/fnsys.2011.00104
93. Stewart, G. W. (1987). Collinearity and least squares regression. Stat. Sci. 2, 68-84.
94. Storkey, A. J., Simonotto, E., Whalley, H., Lawrie, S., Murray, L., and McGonigle, D. (2007). "Learning structural equation models for fmri," in Advances in Neural Information Processing Systems, Vol. 19, eds B. Schölkopf, J. Platt, and T. Hoffman (Cambridge, MA: MIT Press), 1329-1336.
95. Sun, F. T., Miller, L. M., and D'Esposito, M. (2004). Measuring interregional functional connectivity using coherence and partial coherence analyses of fMRI data. Neuroimage 21, 647-658.
96. Tipping, M. E., and Bishop, C. M. (1999). Probabilistic principal component analysis. J. R. Statist. Soc. Ser. B 61, 611-622.
97. Valdés-Sosa, P. A. (2004). Spatio-temporal autoregressive models defined over brain manifolds. Neuroinformatics 2, 239-250.
98. Valdés-Sosa, P. A., Roebroeck, A., Daunizeau, J., and Friston, K. (2011). Effective connectivity: influence, causality and biophysical modelling. Neuroimage 58, 339-361.
99. Valdés-Sosa, P. A., Sanchez-Bornot, J. M., Lage-Castellanos, A., Vega-Hernandez, M., Bosch-Bayard, J., Melie-Garcia, L., et al. (2005). Estimating brain functional connectivity with sparse multivariate autoregression. Philos. Trans. R. Soc. Lond. B Biol. Sci. 360, 969-981.
100. Wan, E. A., and van der Merwe, R. (2001). "The unscented Kalman filter," in Kalman Filtering and Neural Networks, ed S. Hayken (New York, NY: Wiley Publishing), 221-280.
101. Whalley, H. C., Steele, J. D., Mukherjee, P., Romaniuk, L., McIntosh, A. M., Hall, J., et al. (2009). Connecting the brain and new drug targets for schizophrenia. Curr. Pharm. Des. 15, 2615-2631.
102. Wills, A., Ninness, B., and Gibson, S. (2009). Maximum likelihood estimation of state space models from frequency domain data. IEEE Trans. Automat. Contr. 54, 19-33.
103. Wold, H. (1996). "Estimation of principal components and related models by iterative least squares," in Multivariate Analysis, ed P. R. Krishnaiah (New York, NY: Academic Press), 391-420.
104. Wold, S., Esbensen, K., and Geladi, P. (1987). Principal component analysis. Chemometr. Intell. Lab. 2, 37-52.
105. Yesilyurt, B., Ugurbil, K., and Uludag, K. (2008). Dynamics and nonlinearities of the BOLD response at very short stimulus durations. Magn. Reson. Imaging 26, 853-862.