Abstract
Complex processes resulting from interaction of multiple elements can rarely be understood by analytical scientific approaches alone; additional, mathematical models of system dynamics are required. This insight, which disciplines like physics have embraced for a long time already, is gradually gaining importance in the study of cognitive processes by functional neuroimaging. In this field, causal mechanisms in neural systems are described in terms of effective connectivity. Recently, dynamic causal modelling (DCM) was introduced as a generic method to estimate effective connectivity from neuroimaging data in a Bayesian fashion. One of the key advantages of DCM over previous methods is that it distinguishes between neural state equations and modality-specific forward models that translate neural activity into a measured signal. Another strength is its natural relation to Bayesian model selection (BMS) procedures. In this article, we review the conceptual and mathematical basis of DCM and its implementation for functional magnetic resonance imaging data and event-related potentials. After introducing the application of BMS in the context of DCM, we conclude with an outlook to future extensions of DCM. These extensions are guided by the long-term goal of using dynamic system models for pharmacological and clinical applications, particularly with regard to synaptic plasticity.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
Abbreviations
- AIC:
-
Akaike information criterion
- BF:
-
Bayes factor
- BIC:
-
Bayesian information criterion
- BMS:
-
Bayesian model selection
- DCM:
-
dynamic causal modelling
- EEG:
-
electroencephalography
- ERPs:
-
event-related potentials
- fMRI:
-
functional magnetic resource imaging
- IFG:
-
interior frontal gyrus
- MEG:
-
magnetoencephalography
- SPC:
-
superior parietal cortex.
References
Aertsen A and Preißl H 1991 Dynamics of activity and connectivity in physiological neuronal Networks; in Non linear dynamics and neuronal networks (ed.) H G Schuster (New York: VCH Publishers) pp 281–302
Bitan T, Booth J R, Choy J, Burman D D, Gitelman D R and Mesulam M M 2005 Shifts of effective connectivity within a language network during rhyming and spelling; J. Neurosci. 25 5397–5403
Breakspear M, Terry J R and Friston K J 2003 Modulation of excitatory synaptic coupling facilitates synchronization and complex dynamics in a biophysical model of neuronal dynamics; Network: Comput. Neural Sys. 14 703–732
Büchel C and Friston K J 1997 Modulation of connectivity in visual pathways by attention: cortical interactions evaluated with structural equation modelling and fMRI; Cerebral Cortex 7 768–778
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
David O and Friston K J 2003 A neural mass model for MEG/EEG: coupling and neuronal dynamics; NeuroImage 20 1743–1755
David O, Harrison L M and Friston K J 2005 Modelling event-related responses in the brain; NeuroImage 25 756–770
David O, Kiebel S J, Harrison L M, Mattout J, Kilner J M and Friston K J 2006 Dynamic causal modeling of evoked responses in EEG and MEG; NeuroImage 30 1255–1272
Dempster A P, Laird N M and Rubin D B 1977 Maximum likelihood from incomplete data via the EM algorithm; J. R. Stat. Soc. Series B: Stat. Methodol. 39 1–38
Friston K J 1994 Functional and effective connectivity in neuroimaging: a synthesis; Hum. Brain Mapping 2 56–78
Friston K J 1998 The disconnection hypothesis; Schizophrenia Res. 30 115–125
Friston K J 2002a Beyond phrenology: What can neuroimaging tell us about distributed circuitry; Annu. Rev. Neurosci. 25 221–250
Friston K J 2002b Bayesian estimation of dynamical systems: An application to fMRI; NeuroImage 16 513–530
Friston K J, Harrison L and Penny W 2003 Dynamic causal modelling; NeuroImage 19 1273–1302
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 12 466–477
Goebel R, Roebroeck A, Kim D S and Formisano E 2003 Investigating directed cortical interactions in time-resolved fMRI data using vector autoregressive modeling and Granger causality mapping; Magn. Reson. Imaging 21 1251–1261
Gottesman I I and Gould T D 2003 The endophenotype concept in psychiatry: etymology and strategic intentions; Am. J. Psychiatry 160 636–645
Harrison L M, Penny W and Friston K J 2003 Multivariate autoregressive modeling of fMRI time series; NeuroImage 19 1477–1491
Harrison L M, David O and Friston K J 2005 Stochastic models of neuronal dynamics; Philos. Trans. R. Soc. London B Biol. Sci. 360 1075–1091
Honey G D, Suckling J, Zelaya F, Long C, Routledge C, Jackson S, Ng V, Fletcher P C, Williams S C R and Brown J and Bullmore E T 2003 Dopaminergic drug effects on physiological connectivity in a human cortico-striato-thalamic system; Brain 126 1767–1281
Honey G and Bullmore E 2004 Human pharmacological MRI; Trends Pharmacol. Sci. 25 366–374
Jansen B H and Rit V G 1995 Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns; Biol. Cybernetics 73 357–366
Jirsa V K 2004 Connectivity and dynamics of neural information processing; Neuroinformatics 2 183–204
Kiebel S J, David O and Friston K J 2006 Dynamic causal modelling of evoked responses in EEG/MEG with lead-field parameterization; NeuroImage 30 1273–1284
Mechelli A, Price C J, Noppeney U and Friston K J 2003 A dynamic causal modeling study on category effects: bottom-up or top-down mediation?; J. Cognitive Neurosci. 15 925–934
McIntosh A R and Gonzalez-Lima F 1994 Structural equation modeling and its application to network analysis in functional brain imaging; Hum. Brain Mapping 2 2–22
Penny W D, Stephan K E, Mechelli A and Friston K J 2004a Comparing dynamic causal models; NeuroImage 22 1157–1172
Penny W D, Stephan K E, Mechelli A and Friston K J 2004b Modelling functional integration: a comparison of structural equation and dynamic causal models; NeuroImage 23 S264–S274
Pitt M A and Myung I J 2002 When a good fit can be bad; Trends Cognitive Neurosci. 6 421–425
Raftery A E 1995 Bayesian model selection in social research; in Sociological methodology (ed.) P V Marsden (Cambridge, MA: Cambridge University Press) pp 111–196
Robinson P A, Rennie C J, Wright J J, Bahramali H, Gordon E and Rowe D L 2001 Prediction of electroencephalographic spectra from neurophysiology; Phys. Rev. E63 021903
Schultz W and Dickinson A 2000 Neuronal coding of prediction errors; Annu. Rev. Neurosci, 23 473–500
Smith A P R, Stephan K E, Rugg M D and Dolan R J 2006 Task and content modulate amygdala-hippocampal connectivity in emotional retrieval; Neuron 49 631–638
Stephan K E 2004 On the role of general system theory for functional neuroimaging; J. Anat. 205 443–470
Stephan K E, Baldeweg T and Friston K J 2006 Synaptic plasticity and dysconnection in schizophrenia; Biol. Psychiatry 59 929–939
Stephan K E, Penny W D, Marshall J C, Fink G R and Friston K J 2005 Investigating the functional role of callosal connections with dynamic causal models; Ann. N. Y. Acad. Sci. 1064 16–36
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Stephan, K.E., Harrison, L.M., Kiebel, S.J. et al. Dynamic causal models of neural system dynamics: current state and future extensions. J Biosci 32, 129–144 (2007). https://doi.org/10.1007/s12038-007-0012-5
Published:
Issue Date:
DOI: https://doi.org/10.1007/s12038-007-0012-5