Stochastic dynamic causal modelling of fMRI data: Should we care about neural noise?

Dynamic causal modelling (DCM) was introduced to study the effective connectivity among brain regions using neuroimaging data. Until recently, DCM relied on deterministic models of distributed neuronal responses to external perturbation (e.g., sensory stimulation or task demands). However, accounting for stochastic fluctuations in neuronal activity and their interaction with task-specific processes may be of particular importance for studying state-dependent interactions. Furthermore, allowing for random neuronal fluctuations may render DCM more robust to model misspecification and finesse problems with network identification. In this article, we examine stochastic dynamic causal models (sDCM) in relation to their deterministic counterparts (dDCM) and highlight questions that can only be addressed with sDCM. We also compare the network identification performance of deterministic and stochastic DCM, using Monte Carlo simulations and an empirical case study of absence epilepsy. For example, our results demonstrate that stochastic DCM can exploit the modelling of neural noise to discriminate between direct and mediated connections. We conclude with a discussion of the added value and limitations of sDCM, in relation to its deterministic homologue.

[1]  Karl J. Friston,et al.  Post hoc Bayesian model selection , 2011, NeuroImage.

[2]  L. Lemieux,et al.  Modelling large motion events in fMRI studies of patients with epilepsy. , 2007, Magnetic resonance imaging.

[3]  Karl J. Friston,et al.  DEM: A variational treatment of dynamic systems , 2008, NeuroImage.

[4]  Mark W. Woolrich,et al.  Network modelling methods for FMRI , 2011, NeuroImage.

[5]  Karl J. Friston,et al.  The Cortical Dynamics of Intelligible Speech , 2008, The Journal of Neuroscience.

[6]  Karl J. Friston,et al.  Comparing hemodynamic models with DCM , 2007, NeuroImage.

[7]  Karl J. Friston,et al.  Statistical parametric mapping , 2013 .

[8]  Karl J. Friston,et al.  Variational Bayesian identification and prediction of stochastic nonlinear dynamic causal models , 2009, Physica D. Nonlinear phenomena.

[9]  C. Degueldre,et al.  Functional neuroanatomy of hypnotic state , 1999, Biological Psychiatry.

[10]  Josef Hofbauer,et al.  Multiple limit cycles for three dimensional Lotka-Volterra equations , 1994 .

[11]  Klaas E. Stephan,et al.  Dynamic causal modelling: A critical review of the biophysical and statistical foundations , 2011, NeuroImage.

[12]  Derek Abbott,et al.  What Is Stochastic Resonance? Definitions, Misconceptions, Debates, and Its Relevance to Biology , 2009, PLoS Comput. Biol..

[13]  L. M. M.-T. Theory of Probability , 1929, Nature.

[14]  Karl J. Friston,et al.  Causal Hierarchy within the Thalamo-Cortical Network in Spike and Wave Discharges , 2009, PloS one.

[15]  Karl J. Friston,et al.  Variational free energy and the Laplace approximation , 2007, NeuroImage.

[16]  M. Steriade Sleep, epilepsy and thalamic reticular inhibitory neurons , 2005, Trends in Neurosciences.

[17]  Karl J. Friston,et al.  Dynamic causal modelling , 2003, NeuroImage.

[18]  Anthony A Grace,et al.  Gating of Hippocampal-Evoked Activity in Prefrontal Cortical Neurons by Inputs from the Mediodorsal Thalamus and Ventral Tegmental Area , 2003, The Journal of Neuroscience.

[19]  Kerstin Preuschoff,et al.  Optimizing Experimental Design for Comparing Models of Brain Function , 2011, PLoS Comput. Biol..

[20]  Karl J. Friston,et al.  Effective connectivity: Influence, causality and biophysical modeling , 2011, NeuroImage.

[21]  Karl J. Friston,et al.  Nonlinear Dynamic Causal Models for Fmri Nonlinear Dynamic Causal Models for Fmri Nonlinear Dynamic Causal Models for Fmri , 2022 .

[22]  Steven Laureys,et al.  Brain function in coma, vegetative state, and related disorders , 2004, The Lancet Neurology.

[23]  David L. Vaux,et al.  Bcl-2 gene promotes haemopoietic cell survival and cooperates with c-myc to immortalize pre-B cells , 1988, Nature.

[24]  Karl J. Friston,et al.  Nonlinear Responses in fMRI: The Balloon Model, Volterra Kernels, and Other Hemodynamics , 2000, NeuroImage.

[25]  G. Kraepelin,et al.  A. T. Winfree, The Geometry of Biological Time (Biomathematics, Vol.8). 530 S., 290 Abb. Berlin‐Heidelberg‐New‐York 1980. Springer‐Verlag. DM 59,50 , 1981 .

[26]  Vinod Menon,et al.  Functional connectivity in the resting brain: A network analysis of the default mode hypothesis , 2002, Proceedings of the National Academy of Sciences of the United States of America.

[27]  Alan C. Evans,et al.  Brain Connectivity , 2011, The Neuroscientist : a review journal bringing neurobiology, neurology and psychiatry.

[28]  D. James Surmeier,et al.  Thalamic Gating of Corticostriatal Signaling by Cholinergic Interneurons , 2010, Neuron.

[29]  Karl J. Friston,et al.  a K.E. Stephan, a R.B. Reilly, , 2007 .

[30]  Frédéric Grouiller,et al.  Characterization of the hemodynamic modes associated with interictal epileptic activity using a deformable model‐based analysis of combined EEG and functional MRI recordings , 2010, Human brain mapping.

[31]  John R. Huguenard,et al.  Thalamic synchrony and dynamic regulation of global forebrain oscillations , 2007, Trends in Neurosciences.

[32]  Karl J. Friston,et al.  Network discovery with DCM , 2011, NeuroImage.

[33]  Karl J. Friston,et al.  Behavioral / Systems / Cognitive Striatal Prediction Error Modulates Cortical Coupling , 2010 .

[34]  D. Contreras,et al.  Spike-wave complexes and fast components of cortically generated seizures. I. Role of neocortex and thalamus. , 1998, Journal of neurophysiology.

[35]  Max Kleiman-Weiner,et al.  A gain in GABAA receptor synaptic strength in thalamus reduces oscillatory activity and absence seizures , 2009, Proceedings of the National Academy of Sciences.

[36]  Karl J. Friston,et al.  EEG–fMRI of idiopathic and secondarily generalized epilepsies , 2006, NeuroImage.

[37]  N. Berglund,et al.  Noise-Induced Phenomena in Slow-Fast Dynamical Systems: A Sample-Paths Approach , 2005 .

[38]  Rainer Goebel,et al.  The identification of interacting networks in the brain using fMRI: Model selection, causality and deconvolution , 2011, NeuroImage.

[39]  M R Symms,et al.  Methodology: EEG-correlated fMRI. , 2000, Advances in neurology.

[40]  M. M. Tropper Ergodic and quasideterministic properties of finite-dimensional stochastic systems , 1977 .

[41]  Karl J. Friston,et al.  Modelling cardiac signal as a confound in EEG-fMRI and its application in focal epilepsy studies , 2006, NeuroImage.

[42]  S. Shipp,et al.  The functional logic of cortical connections , 1988, Nature.

[43]  D. Talay Numerical solution of stochastic differential equations , 1994 .

[44]  Karl J. Friston,et al.  Generalised filtering and stochastic DCM for fMRI , 2011, NeuroImage.

[45]  Michael Menzinger,et al.  On the local stability of limit cycles. , 1999, Chaos.

[46]  J. Daunizeau,et al.  Neural Mechanisms Underlying Motivation of Mental Versus Physical Effort , 2012, PLoS biology.