Rosalyn Moran Virginia Tech Carilion Research Institute Dynamic Causal Modelling for Cross Spectral Densities

Outline DCM & Spectral Data Features (the Basics) DCM for CSD vs DCM for SSR DCM for CSD Example

Outline DCM & Spectral Data Features (the Basics) DCM for CSD vs DCM for SSR DCM for CSD Example

Dynamic Causal Modelling: Generic Framework simple neuronal model Slow time scale fMRI complicated neuronal model Fast time scale EEG/MEG Neural state equation: Hemodynamic forward model: neural activity BOLD Time Domain Data Electromagnetic forward model: neural activity EEG MEG LFP Time Domain ERP Data Phase Domain Data Time Frequency Data Steady State Frequency Data Cross Spectral Densities (Frequency Domain)

Dynamic Causal Modelling: Generic Framework simple neuronal model Slow time scale fMRI complicated neuronal model Fast time scale EEG/MEG Neural state equation: Electromagnetic forward model: neural activity EEG MEG LFP CSDs Hemodynamic forward model: neural activity BOLD Time Domain Data Frequency (Hz) Power (mV 2 ) “theta”

Dynamic Causal Modelling: Framework Generative Model Bayesian Inversion Empirical Data Model Structure/ Model Parameters

Inference on models Dynamic Causal Modelling: Framework Bayesian Inversion Bayes’ rules: Model 1 Model 2 Model 1 Free Energy: max Inference on parameters Model comparison via Bayes factor: accounts for both accuracy and complexity of the model allows for inference about structure (generalisability) of the model

Inference on models Inference on parameters Dynamic Causal Modelling: Framework Bayesian Inversion Model comparison via Bayes factor: Bayes’ rules: accounts for both accuracy and complexity of the model allows for inference about structure (generalisability) of the model Model 1 Model 2 Model 1 Free Energy: max

Dynamic Causal Modelling: Neural Mass Model neuronal (source) model State equations Extrinsic Connections spiny stellate cells inhibitory interneurons Pyramidal Cells Intrinsic Connections Internal Parameters EEG/MEG/LFP signal EEG/MEG/LFP signal Properties of tens of thousands of neurons approximated by their average response

Dynamic equations mimic physiology and produce electrophysiological responses A Neural Mass Model (6) layer cortical regions) State equations: A dynamical systems description of anatomy and physiology Extrinsic Connections spiny stellate cells Supragranular Pyramidal Cells + inhibitory interneurons Deep Pyramidal Cells + inhibitory interneurons Intrinsic Connections Internal Parameters Eg. Time constants of Sodium ion channels GABAa receptors AMPA receptors Neurotransmitters: Glu/GABA

Dynamics mimicked at AMPA and GABA receptors AP generation zone synapses Cortico-cortical connection GABAa receptors AMPA receptors Neurotransmitters: Glu/GABA AP generation zone Intrinsic Connection Cortico-cortical connection Granular Layer: Excitatory Cells Supragranular Layer: Inhibitory Cells Infragranular Layer: Pyramidal Cells

Parameters quantify contributions at AMPA and GABA receptors synapses Cortico-cortical connection GABAa receptors AMPA receptors Neurotransmitters: Glu/GABA AP generation zone Intrinsic Connection Granular Layer: Excitatory Cells Supragranular Layer: Inhibitory Cells Infragranular Layer: Pyramidal Cells

Extrinsic forward connections Extrinsic backward connections Intrinsic connections Extrinsic lateral connections spiny stellate cells inhibitory interneurons pyramidal cells State equations in a 6 layer cortical model

Time Differential Equations State Space Characterisation Transfer Function Frequency Domain Linearise mV State equations to Spectra Moran, Kiebel, Stephan, Reilly, Daunizeau, Friston (2007) A neural mass model of spectral responses in electrophysiology. NeuroImage

Predicted response (Pyramidal Cell Depolarization) Given an empirical recording: estimate parameters of the model 4  3  2  ))((xxuaxsH x xx eeee     Excitatory spiny cells in granular layers 3  1  2  5  AMPA receptor density GABAa receptor density Glutamate release AMPA time constant GABA release Bayesian Inversion Increased activity at GABA receptors in supragranular layers Superficial layers Granular layers Deep layers GABAa TC Moran, Stephan, Seidenbecher, Pape, Dolan, Friston (2009) Dynamic Causal Model of Steady State Responses. NeuroImage Friston, Bastos, Litvak, Stephan, Fries, Moran (2012) DCM for complex data: cross-spectra, coherence and phase-delays. NeuroImage

Neuromodulators: Acetylcholine/Dopamine f Mg   Superficial layers Granular layers Deep layers Sodium Channel Chloride Channel Potassium Channel Depolarization dependent Calcium Channel NMDA mediated switch Neurotransmitters: Glu/GABA A conductance model offers more biological plausibility Moran, Stephan, Dolan, Friston (2011) Consistent Spectral Predictors for Dynamic Causal Models of Steady State Responses. NeuroImage

Roadmap Specify model Extract Data Features Maximise the model evidence (~-F) Test models or MAP parameters Find your experimental data

Prediction Summary: DCM for Steady State Responses Cortical Macrocolumns and free parameters dx/dt = Ax + B | H 1 (ω). H 1 * (ω) | | H 1 (ω). H 2 * (ω) | | H 2 (ω). H 2 * (ω) | Generative Model

Cortical Macrocolumns and free parameters dx/dt = Ax + B | H 1 (ω). H 1 * (ω) | | H 1 (ω). H 2 * (ω) | | H 2 (ω). H 2 * (ω) | Model Inversion Summary: DCM for Steady State Responses

Outline DCM & Spectral Data Features (the Basics) DCM for CSD vs DCM for SSR DCM for CSD Example

Time to Frequency Domain Linearise around a stable fixed point or LC DCM for SSR DCM for CSD

Prediction DCM for Cross Spectral Densities Cortical Macrocolumns and free parameters dx/dt = Ax + B H 1 (ω). H 2 * (ω) Generative Model Spectra and Phase lag Coherence Cross Correlations H 1 (ω). H 1 * (ω) H 2 (ω). H 2 * (ω)

Cortical Macrocolumns and free parameters dx/dt = Ax + B Model Inversion using full complex signal Spectra and Phase lag Coherence Cross Correlations H 1 (ω). H 2 * (ω) H 2 (ω). H 2 * (ω) H 1 (ω). H 1 * (ω) DCM for Cross Spectral Densities Prediction

Accommodating Imaginary Numbers F E: M: Real and imaginary errors Real and imaginary derivatives wrt fx, G

1.Interface Additions 2.New CSD routines, similar to SSR 3.SPM_NLSI_GN accommodates imag numbers, slopes, curvatures 4.A host of new results features, in channel and source space! Roadmap Specify model Extract Data Features Maximise the model evidence (~-F) Test models or MAP parameters Find your experimental data And also report phase lags coherence & delays In channel or source space

PFC Hipp Conditional Estimates: Spectral Power Abs(H 1 (ω). H 1 * (ω)) Abs(H 1 (ω). H 2 *(ω)) Abs(H 2 (ω). H 1 * (ω)) Abs(H 2 (ω). H 2 *(ω)) Power

PFC Hipp Conditional Estimates: Coherence |(H 1 (ω).H 2 * (ω))| 2 ______________________ {(H 1 (ω).H 1 *(ω)) + (H 2 (ω).H 2 *(ω))}

PFC Hipp F -1 (H 1 (ω).H 1 * (ω)) F -1 (H 1 (ω).H 2 * (ω)) F -1 (H 2 (ω).H 1 * (ω)) F -1 (H 2 (ω).H 2 * (ω)) mode 1 to 1 lag (ms) mode 2 to 1 lag (ms) Auto-covariance (in channel-space) Lag (ms) auto-covariance mode 2 to 2 lag (ms) trial 1 channel 1 channel 2 Conditional Estimates: Covariance

PFC Hipp arg(H 1 (ω).H 2 * (ω)) ____________ ω Conditional Estimates: Delays

Outline DCM & Spectral Data Features (the Basics) DCM for CSD vs DCM for SSR DCM for CSD Examples

Pharmacological Manipulation of Glutamate and GABA -4 levels of anaesthesia: each successively decreasing glutamate and increasing GABA (Larsen et al Brain Research 1994; Lingamaneni et al Anesthesiology 2001; Caraiscos et al J Neurosci 2004 ; de Sousa et al Anesthesiology 2000 ) -LFP recordings from primary auditory cortex (A1) & posterior auditory field (PAF) -White noise stimulus & Silence mV A2 LFP mV mV mV A1 1.4 % Isoflurane 1.8 % Isoflurane 2.4 % Isoflurane 2.8 % Isoflurane

Summary DCM for CSD: Suitable for long time series with trial-specific spectral features eg pronounced beta Fits complex spectral data features Offers similar connectivity estimates to DCM for ERPs With estimates of frequency specific delays and coherence Can be used with all biophysical, Neural Mass Models (CMC, LFP etc.)

Thank You The FIL Methods Group Karl Friston Dimitris Pinotsis Marco Leite Vladimir Litvak Jean Daunizeau Stephan Kiebel Will Penny Klaas Stephan Andre Bastos Pascal Fries Acknowledgments