DCM, Conductance Based Models and Clinical Applications

This chapter reviews some recent advances in dynamic causal modelling (DCM) of electrophysiology, in particular with respect to conductance based models and clinical applications. DCM addresses observed responses of complex neuronal systems by looking at the neuronal interactions that generate them and how these responses reflect the underlying neurobiology. DCM is a technique for inferring the biophysical properties of cortical sources and their directed connectivity based on distinct neuronal and observation models. The DCM framework uses mathematical formalisms of neural masses, neural fields and mean-fields as forward or generative models for observed neuronal activity. We here consider conductance based neural mass, mean-field and field models—and review their latest technical developments. We use dynamically rich conductance based models to generate responses in laminar-specific populations of excitatory and inhibitory cells. These models allow for the evaluation of neuronal connections and high-order statistics of neuronal states, using Bayesian estimation and inference. We also discuss recent clinical applications of DCM for convolution based neural mass models, in particular for the study of Parkinson’s disease. We present a study of data from Parkinsonian patients, and model the large-scale network changes underlying the pathological excess of beta oscillations that characterise the Parkinsonian state.

[1]  Ben H. Jansen,et al.  Electroencephalogram and visual evoked potential generation in a mathematical model of coupled cortical columns , 1995, Biological Cybernetics.

[2]  Karl J. Friston,et al.  Modelling event-related responses in the brain , 2005, NeuroImage.

[3]  S. Braeutigam,et al.  Abnormal intrinsic and extrinsic connectivity within the magnetic mismatch negativity brain network in schizophrenia: A preliminary study , 2012, Schizophrenia Research.

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

[5]  Karl J. Friston,et al.  Behavioral / Systems / Cognitive Connectivity Changes Underlying Spectral EEG Changes during Propofol-Induced Loss of Consciousness , 2012 .

[6]  Ralf Deichmann,et al.  Resting state fMRI reveals increased subthalamic nucleus–motor cortex connectivity in Parkinson's disease , 2011, NeuroImage.

[7]  Peter A. Tass,et al.  Impact of acoustic coordinated reset neuromodulation on effective connectivity in a neural network of phantom sound , 2013, NeuroImage.

[8]  Raymond J. Dolan,et al.  Consistent spectral predictors for dynamic causal models of steady-state responses , 2011, NeuroImage.

[9]  Fabrice Wendling,et al.  Relevance of nonlinear lumped-parameter models in the analysis of depth-EEG epileptic signals , 2000, Biological Cybernetics.

[10]  Karl J. Friston,et al.  Extracting novel information from neuroimaging data using neural fields , 2014, EPJ Nonlinear Biomedical Physics.

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

[12]  Karl J. Friston,et al.  Preserved Feedforward But Impaired Top-Down Processes in the Vegetative State , 2011, Science.

[13]  Henry C. Tuckwell,et al.  Analytical and Simulation Results for Stochastic Fitzhugh-Nagumo Neurons and Neural Networks , 1998, Journal of Computational Neuroscience.

[14]  James B. Rowe,et al.  Reorganisation of brain networks in frontotemporal dementia and progressive supranuclear palsy☆ , 2013, NeuroImage: Clinical.

[15]  B. Ermentrout Neural networks as spatio-temporal pattern-forming systems , 1998 .

[16]  C. Morris,et al.  Voltage oscillations in the barnacle giant muscle fiber. , 1981, Biophysical journal.

[17]  Oleg Korzyukov,et al.  Modulation of effective connectivity during vocalization with perturbed auditory feedback , 2013, Neuropsychologia.

[18]  J. Cowan,et al.  Excitatory and inhibitory interactions in localized populations of model neurons. , 1972, Biophysical journal.

[19]  Raymond J. Dolan,et al.  Dynamic causal models of steady-state responses , 2009, NeuroImage.

[20]  S. Zeki,et al.  Parallelism in the brain's visual form system , 2013, The European journal of neuroscience.

[21]  Raymond J. Dolan,et al.  Network reconfiguration and working memory impairment in mesial temporal lobe epilepsy , 2013, NeuroImage.

[22]  Karl J. Friston,et al.  Dynamic causal modelling of evoked responses in EEG/MEG with lead field parameterization , 2006, NeuroImage.

[23]  Esther Florin,et al.  Dopamine Replacement Modulates Oscillatory Coupling Between Premotor and Motor Cortical Areas in Parkinson's Disease , 2013, Cerebral cortex.

[24]  H. Spekreijse,et al.  Electrophysiological Correlate of Binocular Depth Perception in Man , 1970, Nature.

[25]  H. Tuckwell,et al.  Statistical properties of stochastic nonlinear dynamical models of single spiking neurons and neural networks. , 1996, Physical review. E, Statistical physics, plasmas, fluids, and related interdisciplinary topics.

[26]  Karl J. Friston,et al.  Changing meaning causes coupling changes within higher levels of the cortical hierarchy , 2009, Proceedings of the National Academy of Sciences.

[27]  J. Duncan,et al.  Lateral Prefrontal Cortex Subregions Make Dissociable Contributions during Fluid Reasoning , 2010, Cerebral cortex.

[28]  Karl J. Friston,et al.  Modeling ketamine effects on synaptic plasticity during the mismatch negativity. , 2013, Cerebral cortex.

[29]  Marcus T. Wilson,et al.  General Anesthetic-induced Seizures Can Be Explained by a Mean-field Model of Cortical Dynamics , 2006, Anesthesiology.

[30]  E. Haskell,et al.  Population density methods for large-scale modelling of neuronal networks with realistic synaptic kinetics: cutting the dimension down to size , 2001 .

[31]  Karl J. Friston,et al.  The functional anatomy of the MMN: A DCM study of the roving paradigm , 2008, NeuroImage.

[32]  S. Nelson,et al.  An emergent model of orientation selectivity in cat visual cortical simple cells , 1995, The Journal of neuroscience : the official journal of the Society for Neuroscience.

[33]  Karl J. Friston,et al.  Dynamic causal modeling of evoked responses in EEG and MEG , 2006, NeuroImage.

[34]  Emmanuel Maby,et al.  Impaired pitch perception and memory in congenital amusia: the deficit starts in the auditory cortex. , 2013, Brain : a journal of neurology.

[35]  Lawrence Sirovich,et al.  On the Simulation of Large Populations of Neurons , 2004, Journal of Computational Neuroscience.

[36]  Karl J. Friston,et al.  Neural masses and fields in dynamic causal modeling , 2013, Front. Comput. Neurosci..

[37]  Karl J. Friston,et al.  Neural Fields, Masses and Bayesian Modelling , 2014 .

[38]  Karl J. Friston,et al.  Dynamic causal modeling for EEG and MEG , 2009, Human brain mapping.

[39]  Karl J. Friston,et al.  An In Vivo Assay of Synaptic Function Mediating Human Cognition , 2011, Current Biology.

[40]  Jonathan Touboul,et al.  Finite-size and correlation-induced effects in mean-field dynamics , 2010, Journal of Computational Neuroscience.

[41]  T. Sejnowski,et al.  Neurocomputational models of working memory , 2000, Nature Neuroscience.

[42]  Karl J. Friston,et al.  Population dynamics under the Laplace assumption , 2009, NeuroImage.

[43]  Karl J. Friston,et al.  Stochastic models of neuronal dynamics , 2005, Philosophical Transactions of the Royal Society B: Biological Sciences.

[44]  C. Segebarth,et al.  Identifying Neural Drivers with Functional MRI: An Electrophysiological Validation , 2008, PLoS biology.

[45]  N. Gorelova,et al.  Dopamine D1/D5 receptor activation modulates a persistent sodium current in rat prefrontal cortical neurons in vitro. , 2000, Journal of neurophysiology.

[46]  Hideo Hasegawa,et al.  Dynamical mean-field theory of spiking neuron ensembles: response to a single spike with independent noises. , 2002, Physical review. E, Statistical, nonlinear, and soft matter physics.

[47]  D. Liley,et al.  Modeling the effects of anesthesia on the electroencephalogram. , 2005, Physical review. E, Statistical, nonlinear, and soft matter physics.

[48]  Karl J. Friston,et al.  Dynamic Causal Models for phase coupling , 2009, Journal of Neuroscience Methods.

[49]  Marcus T. Wilson,et al.  Progress in Modeling EEG Effects of General Anesthesia: Biphasic Response and Hysteresis , 2011 .

[50]  J. Bolam,et al.  Dopamine regulates the impact of the cerebral cortex on the subthalamic nucleus–globus pallidus network , 2001, Neuroscience.

[51]  John R. Terry,et al.  Conditions for the Generation of Beta Oscillations in the Subthalamic Nucleus–Globus Pallidus Network , 2010, The Journal of Neuroscience.

[52]  Karl J. Friston,et al.  Contrast gain control and horizontal interactions in V1: A DCM study , 2014, NeuroImage.

[53]  Asla Pitkänen,et al.  Simultaneous BOLD fMRI and local field potential measurements during kainic acid–induced seizures , 2012, Epilepsia.

[54]  Karl J. Friston,et al.  The effect of prior visual information on recognition of speech and sounds. , 2008, Cerebral cortex.

[55]  W Rall,et al.  Changes of action potential shape and velocity for changing core conductor geometry. , 1974, Biophysical journal.

[56]  Hartwig R. Siebner,et al.  Task-specific modulation of effective connectivity during two simple unimanual motor tasks: A 122-channel EEG study , 2012, NeuroImage.

[57]  Pablo Campo,et al.  Anterobasal Temporal Lobe Lesions Alter Recurrent Functional Connectivity within the Ventral Pathway during Naming , 2013, The Journal of Neuroscience.

[58]  F. Blankenburg,et al.  Recurrent Neural Processing and Somatosensory Awareness , 2012, The Journal of Neuroscience.

[59]  Anatol C. Kreitzer,et al.  Regulation of parkinsonian motor behaviours by optogenetic control of basal ganglia circuitry , 2010, Nature.

[60]  Karl J. Friston,et al.  Bayesian model selection for group studies (vol 46, pg 1005, 2009) , 2009 .

[61]  Danai Dima,et al.  Impaired top-down processes in schizophrenia: A DCM study of ERPs , 2010, NeuroImage.

[62]  L. Kristiansson,et al.  Performance of a model for a local neuron population , 1978, Biological Cybernetics.

[63]  Lawrence Sirovich,et al.  A Population Study of Integrate-and-Fire-or-Burst Neurons , 2002, Neural Computation.

[64]  Xiao-Jing Wang,et al.  Erratum to: Effects of neuromodulation in a cortical network model of object working memory dominated by recurrent inhibition , 2014, Journal of Computational Neuroscience.

[65]  Perambur S. Neelakanta,et al.  Stochastical aspects of neuronal dynamics: Fokker-Planck approach , 1993, Biological Cybernetics.

[66]  J. E. Skinner,et al.  Chaos and physiology: deterministic chaos in excitable cell assemblies. , 1994, Physiological reviews.

[67]  Richard M. Leahy,et al.  Electromagnetic brain mapping , 2001, IEEE Signal Process. Mag..

[68]  Karl J. Friston,et al.  DCM for complex-valued data: Cross-spectra, coherence and phase-delays , 2012, NeuroImage.

[69]  Michael A. Buice,et al.  Systematic Fluctuation Expansion for Neural Network Activity Equations , 2009, Neural Computation.

[70]  Karl J. Friston,et al.  Dynamic causal modelling of induced responses , 2008, NeuroImage.

[71]  Karl J. Friston,et al.  Basal ganglia–cortical interactions in Parkinsonian patients , 2013, NeuroImage.

[72]  Juan C. Jiménez,et al.  Nonlinear EEG analysis based on a neural mass model , 1999, Biological Cybernetics.

[73]  Duane Q. Nykamp,et al.  A Population Density Approach That Facilitates Large-Scale Modeling of Neural Networks: Extension to Slow Inhibitory Synapses , 2001, Neural Computation.

[74]  D. Alistair Steyn-Ross,et al.  Complementarity of Spike- and Rate-Based Dynamics of Neural Systems , 2012, PLoS Comput. Biol..

[75]  Louis Lemieux,et al.  Networks involved in seizure initiation , 2012, Neurology.

[76]  Gereon R Fink,et al.  Network connectivity and individual responses to brain stimulation in the human motor system. , 2014, Cerebral cortex.

[77]  Karl J. Friston,et al.  Population dynamics: Variance and the sigmoid activation function , 2008, NeuroImage.

[78]  P. Nunez The brain wave equation: a model for the EEG , 1974 .

[79]  Murtaza Z Mogri,et al.  Optical Deconstruction of Parkinsonian Neural Circuitry , 2009, Science.

[80]  Roy D. Patterson,et al.  Predictive Coding and Pitch Processing in the Auditory Cortex , 2011, Journal of Cognitive Neuroscience.

[81]  Marta I. Garrido,et al.  Dynamic Causal Modelling of epileptic seizure propagation pathways: A combined EEG–fMRI study , 2012, NeuroImage.

[82]  Hideo Hasegawa Dynamical mean-field theory of noisy spiking neuron ensembles: application to the Hodgkin-Huxley model. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[83]  Karl J. Friston,et al.  Evaluation of different measures of functional connectivity using a neural mass model , 2004, NeuroImage.

[84]  Karl J. Friston,et al.  Dysconnectivity in the Frontoparietal Attention Network in Schizophrenia , 2013, Front. Psychiatry.

[85]  Ryan Chamberlain,et al.  Simultaneous fMRI and local field potential measurements during epileptic seizures in medetomidine‐sedated rats using raser pulse sequence , 2010, Magnetic resonance in medicine.

[86]  Karl J. Friston,et al.  On conductance-based neural field models , 2013, Front. Comput. Neurosci..

[87]  Eugene M. Izhikevich,et al.  Which model to use for cortical spiking neurons? , 2004, IEEE Transactions on Neural Networks.

[88]  D A Steyn-Ross,et al.  Toward a theory of the general-anesthetic-induced phase transition of the cerebral cortex. I. A thermodynamics analogy. , 2001, Physical review. E, Statistical, nonlinear, and soft matter physics.

[89]  Donald O. Walter,et al.  Mass action in the nervous system , 1975 .

[90]  L. Lemieux,et al.  Combined EEG-fMRI and tractography to visualise propagation of epileptic activity , 2007, Journal of Neurology, Neurosurgery, and Psychiatry.

[91]  H C Tuckwell,et al.  Noisy spiking neurons and networks: useful approximations for firing probabilities and global behavior. , 1998, Bio Systems.

[92]  F. H. Lopes da Silva,et al.  Model of brain rhythmic activity , 1974, Kybernetik.

[93]  Thomas Boraud,et al.  Dynamic changes in the cortex-basal ganglia network after dopamine depletion in the rat. , 2008, Journal of neurophysiology.

[94]  Karl J. Friston,et al.  Nonlinear coupling between occipital and motor cortex during motor imagery: A dynamic causal modeling study , 2013, NeuroImage.

[95]  Karl J. Friston,et al.  Comparing dynamic causal models , 2004, NeuroImage.

[96]  Peter Brown,et al.  Effects of dopamine depletion on information flow between the subthalamic nucleus and external globus pallidus. , 2011, Journal of neurophysiology.

[97]  T. Robbins,et al.  Risk-Sensitive Decision-Making in Patients with Posterior Parietal and Ventromedial Prefrontal Cortex Injury , 2013, Cerebral cortex.

[98]  H. Bergman,et al.  Reversal of experimental parkinsonism by lesions of the subthalamic nucleus. , 1990, Science.

[99]  S. Amari Dynamics of pattern formation in lateral-inhibition type neural fields , 1977, Biological Cybernetics.

[100]  D. J. Felleman,et al.  Distributed hierarchical processing in the primate cerebral cortex. , 1991, Cerebral cortex.

[101]  Karl J. Friston,et al.  The functional anatomy of attention: a DCM study , 2013, Front. Hum. Neurosci..

[102]  Karl J. Friston,et al.  A dynamic causal model study of neuronal population dynamics , 2010, NeuroImage.

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

[104]  Karl J. Friston,et al.  Bayesian estimation of synaptic physiology from the spectral responses of neural masses , 2008, NeuroImage.

[105]  Karl J. Friston,et al.  Dynamic causal modeling , 2010, Scholarpedia.

[106]  H. Haken,et al.  Field Theory of Electromagnetic Brain Activity. , 1996, Physical review letters.

[107]  A. Hutt,et al.  Effects of the anesthetic agent propofol on neural populations , 2010, Cognitive Neurodynamics.

[108]  Karl J. Friston,et al.  A theory of cortical responses , 2005, Philosophical Transactions of the Royal Society B: Biological Sciences.

[109]  Karl J. Friston,et al.  Deconstructing the Architecture of Dorsal and Ventral Attention Systems with Dynamic Causal Modeling , 2012, The Journal of Neuroscience.

[110]  T. Elbert,et al.  Modeling extended sources of event‐related potentials using anatomical and physiological constraints , 1999, Human brain mapping.

[111]  Karl J. Friston,et al.  Bayesian model selection for group studies , 2009, NeuroImage.

[112]  C. Price,et al.  Perturbation of the left inferior frontal gyrus triggers adaptive plasticity in the right homologous area during speech production , 2013, Proceedings of the National Academy of Sciences.

[113]  Louis Lemieux,et al.  Causality within the Epileptic Network: An EEG-fMRI Study Validated by Intracranial EEG , 2013, Front. Neurol..

[114]  Hitoshi Kita,et al.  Subthalamo‐pallidal interactions underlying parkinsonian neuronal oscillations in the primate basal ganglia , 2011, The European journal of neuroscience.

[115]  Karl J. Friston,et al.  The Dynamic Brain: From Spiking Neurons to Neural Masses and Cortical Fields , 2008, PLoS Comput. Biol..

[116]  Hamid Soltanian-Zadeh,et al.  Connectivity analysis of novelty process in habitual short sleepers , 2012, NeuroImage.

[117]  Karl J. Friston,et al.  Modulation of excitatory synaptic coupling facilitates synchronization and complex dynamics in a biophysical model of neuronal dynamics , 2003 .

[118]  D. Liley,et al.  Drug-induced modification of the system properties associated with spontaneous human electroencephalographic activity. , 2003, Physical review. E, Statistical, nonlinear, and soft matter physics.

[119]  Peter Brown,et al.  Effects of low-frequency stimulation of the subthalamic nucleus on movement in Parkinson's disease , 2007, Experimental Neurology.

[120]  D. Liley,et al.  Understanding the Transition to Seizure by Modeling the Epileptiform Activity of General Anesthetic Agents , 2005, Journal of clinical neurophysiology : official publication of the American Electroencephalographic Society.

[121]  M. Kutas,et al.  Electrophysiology of cognitive processing. , 1983, Annual review of psychology.

[122]  D. Durstewitz,et al.  The Dual-State Theory of Prefrontal Cortex Dopamine Function with Relevance to Catechol-O-Methyltransferase Genotypes and Schizophrenia , 2008, Biological Psychiatry.

[123]  P. Goldman-Rakic Regional and cellular fractionation of working memory. , 1996, Proceedings of the National Academy of Sciences of the United States of America.

[124]  Karl J. Friston,et al.  Dynamic causal modeling with neural fields , 2012, NeuroImage.

[125]  Karl J. Friston,et al.  Bayesian Estimation of Dynamical Systems: An Application to fMRI , 2002, NeuroImage.

[126]  J. Hindmarsh,et al.  The assembly of ionic currents in a thalamic neuron I. The three-dimensional model , 1989, Proceedings of the Royal Society of London. B. Biological Sciences.

[127]  Lawrence Sirovich,et al.  Dynamics of neuronal populations: eigenfunction theory; some solvable cases , 2003, Network.

[128]  C. Gonzalez-Islas,et al.  Dopamine Enhances EPSCs in Layer II–III Pyramidal Neurons in Rat Prefrontal Cortex , 2003, The Journal of Neuroscience.

[129]  H. C. Tuckwell,et al.  A dynamical system for the approximate moments of nonlinear stochastic models of spiking neurons and networks , 2000 .

[130]  P. A. Robinson,et al.  Spike, rate, field, and hybrid methods for treating neuronal dynamics and interactions , 2012, Journal of Neuroscience Methods.

[131]  B H Jansen,et al.  Evoked potential enhancement using a neurophysiologically-based model. , 2001, Methods of information in medicine.

[132]  Karl J. Friston,et al.  Broadband Cortical Desynchronization Underlies the Human Psychedelic State , 2013, The Journal of Neuroscience.

[133]  Peter Brown,et al.  Intra-operative recordings of local field potentials can help localize the subthalamic nucleus in Parkinson's disease surgery , 2006, Experimental Neurology.

[134]  Lyle J. Graham,et al.  Population model of hippocampal pyramidal neurons, linking a refractory density approach to conductance-based neurons. , 2007, Physical review. E, Statistical, nonlinear, and soft matter physics.

[135]  Karl J. Friston The free-energy principle: a unified brain theory? , 2010, Nature Reviews Neuroscience.

[136]  Y. Smith,et al.  Microcircuitry of the direct and indirect pathways of the basal ganglia. , 1998, Neuroscience.

[137]  Bruce W. Knight,et al.  Dynamics of Encoding in Neuron Populations: Some General Mathematical Features , 2000, Neural Computation.

[138]  Raymond J. Dolan,et al.  Alterations in Brain Connectivity Underlying Beta Oscillations in Parkinsonism , 2011, PLoS Comput. Biol..

[139]  P. Brown,et al.  New insights into the relationship between dopamine, beta oscillations and motor function , 2011, Trends in Neurosciences.

[140]  Hartwig R. Siebner,et al.  Levodopa reinstates connectivity from prefrontal to premotor cortex during externally paced movement in Parkinson's disease , 2014, NeuroImage.

[141]  R. Traub,et al.  Fast Oscillations in Cortical Circuits , 1999 .

[142]  Karl J. Friston,et al.  Dynamic Causal Models and Physiological Inference: A Validation Study Using Isoflurane Anaesthesia in Rodents , 2011, PloS one.

[143]  Karl J. Friston,et al.  Large-scale neural models and dynamic causal modelling , 2006, NeuroImage.

[144]  Karl J. Friston,et al.  A neural mass model for MEG/EEG: coupling and neuronal dynamics , 2003, NeuroImage.

[145]  S. Amari Homogeneous nets of neuron-like elements , 1975, Biological Cybernetics.

[146]  P. Brown,et al.  Stimulation of the subthalamic region at 20Hz slows the development of grip force in Parkinson's disease , 2011, Experimental Neurology.

[147]  Felix Blankenburg,et al.  Subjective Rating of Weak Tactile Stimuli Is Parametrically Encoded in Event-Related Potentials , 2013, The Journal of Neuroscience.

[148]  W. Penny,et al.  The right hemisphere supports but does not replace left hemisphere auditory function in patients with persisting aphasia. , 2013, Brain : a journal of neurology.