Rosalyn Moran Virginia Tech Carilion Research Institute Bradley Department of Electrical & Computer Engineering Department of Psychiatry and Behavioral Medicine, VTC School of Medicine Dynamic Causal Modelling For Cross-Spectral Densities

Data Features in DCM for CSD Generative Models in the time domain Generative Models in the frequency domain DCM Inversion procedure Example 1: L-Dopa Modulations of theta spectra using DCM for CSD Example 2: Propofol Modulations of Delta and Gamma spectra using DCM for CSD Outline

Data Features in DCM for CSD Generative Models in the time domain Generative Models in the frequency domain DCM Inversion procedure Example 1: L-Dopa Modulations of theta spectra using DCM for CSD Example 2: Propofol Modulations of Delta and Gamma spectra using DCM for CSD Outline

Dynamic Causal Modelling: Generic Framework simple neuronal model (slow time scale) fMRI detailed neuronal model (synaptic time scales) EEG/MEG Neural state equation: Hemodynamic forward model: neural activity BOLD Time Domain Data Resting State Data Electromagnetic forward model: neural activity EEG MEG LFP Time Domain ERP Data Phase Domain Data Time Frequency Data Spectral Data

Dynamic Causal Modelling: Generic Framework simple neuronal model (slow time scale) fMRI detailed neuronal model (synaptic time scales) EEG/MEG Neural state equation: Hemodynamic forward model: neural activity BOLD Time Domain Data Resting State Data Electromagnetic forward model: neural activity EEG MEG LFP Time Domain ERP Data Phase Domain Data Time Frequency Data Spectral Data Frequency (Hz) Power (mV 2 ) “theta”

DCM for Steady State Responses Under linearity and stationarity assumptions, the model’s biophysical parameters (e.g. post-synaptic receptor density and time constants) prescribe the cross-spectral density of responses measured directly (e.g. local field potentials) or indirectly through some lead-field (e.g. electroencephalographic and magnetoencephalographic data).

Steady State Statistically: A “Wide Sense Stationary” signal has 1 st and 2 nd moments that do not vary with respect to time Dynamically: A system in steady state has settled to some equilibrium after a transient Data Feature: Quasi-stationary signals that underlie Spectral Densities in the Frequency Domain

Dynamic Causal Modelling: Framework Generative Model Bayesian Inversion Empirical Data Model Structure/ Model Parameters Explanandum Competing Hypotheses (Models) Optimization under model constraints

Spectral Densities Frequency (Hz) Power (uV 2 ) Frequency (Hz) Power (uV 2 ) Spectral Density in Source 1 Spectral Density in Source 2

Spectral Densities Frequency (Hz) Power (uV 2 ) Frequency (Hz) Power (uV 2 ) Frequency (Hz) Power (uV 2 ) Cross-Spectral Density between Sources 1 & 2 Spectral Density in Source 1 Spectral Density in Source 2

Cross Spectral Density: The Data EEG - MEG – LFP Time Series Cross Spectral Density A few LFP channels or EEG/MEG spatial modes

Autoregressive Model used to extract spectral representations from data Imaginary Numbers Retained Averaged over trial types Real and Imaginary Data features Cross Spectral Density: The Data Default order 8 AR coefficients prescribe the spectral densities

Outline Data Features in DCM for CSD Generative Models in the time domain Generative Models in the frequency domain DCM Inversion procedure Example 1: L-Dopa Modulations of theta spectra using DCM for CSD Example 2: Propofol Modulations of Delta and Gamma spectra using DCM for CSD

A selection of intrinsic architectures in SPM A suite of neuronal population models including neural masses, fields and conductance-based models…expressed in terms of sets of differential equations

Neural Mass Models in DCM neuronal (source) model State equations Extrinsic Connections Granular Layer Supragranular Layer Infragranular Layer Intrinsic Connections Internal Parameters EEG/MEG/LFP signal EEG/MEG/LFP signal Properties of tens of thousands of neurons approximated by their average response

Conductance-Based Neural Mass Models in DCM Current in Conductance Potential Difference Noise Term: Since properties of tens of thousands of neurons approximated by their average response Two governing equations: V = IR ……….. Ohms Law I = C dV/dt ……. for a capacitor

Current in Conductance Potential Difference Noise Term: Since properties of tens of thousands of neurons approximated by their average response Time constant: κ Afferent Spikes : Strength of connection x σ Channels already open: g Conductance-Based Neural Mass Models in DCM Two governing equations: V = IR ……….. Ohms Law I = C dV/dt ……. for a capacitor

Current in Conductance Potential Difference Noise Term: Since properties of tens of thousands of neurons approximated by their average response Time constant : κ Channels already open: g σ μ - V Afferent Spikes : Strength of connection x σ Conductance-Based Neural Mass Models in DCM Two governing equations: V = IR ……….. Ohms Law I = C dV/dt ……. for a capacitor

Intrinsic Afferents Extrinsic Afferents Conductance-Based Neural Mass Models in DCM

Different Neurotransmitters and Receptors? Different Cell Types in 3/6 Layers? Conductance-Based Neural Mass Models in DCM

Spiny stellate cells Pyramidal cells Inhibitory interneuron Current Conductance Reversal Pot – Potential Diff Afferent Firing No. open channels Time Constant Conductance Unit noise Firing Variance Exogenous input Excitatory spiny cells in granular layers Excitatory pyramidal cells in extragranular layers Inhibitory cells in extragranular layers Measured response Conductance-Based Neural Mass Models in DCM

Spiny stellate cells Pyramidal cells Inhibitory interneuron Maximum Post Synaptic Potential Parameterised Sigmoid Inverse Time Constant Synaptic Kernel H Intrinsic connectivity Convolution-Based Neural Mass Models in DCM Extrinsic Forward Input Extrinsic Backward Input

Spiny stellate cells Pyramidal cells Inhibitory interneuron 5  Exogenous input Excitatory spiny cells being granular layers Excitatory pyramidal cells in extragranular layers Inhibitory cells in extragranular layers Measured response Maximum Post Synaptic Potential Parameterised Sigmoid Inverse Time Constant Synaptic Kernel H Intrinsic connectivity Convolution-Based Neural Mass Models in DCM Extrinsic Forward Input Extrinsic Backward Input

Spiny stellate Pyramidal cells Inhibitory interneuron Extrinsic Output Extrinsic Forward Input Extrinsic Backward Input GABA Receptors AMPA Receptors NMDA Receptors 4 population Canonical Micro-Circuit (CMC) Spiny stellate Superficial pyramidal Inhibitory interneuron Deep pyramidal 4-subpopulation Canonical Microcircuit Backward Extrinsic Output Forward Extrinsic Output Extrinsic Forward Input Extrinsic Backward Input Temporal Derivatives

Outline Data Features in DCM for CSD Generative Models in the time domain Generative Models in the frequency domain DCM Inversion procedure Example 1: L-Dopa Modulations of theta spectra using DCM for CSD Example 2: Propofol Modulations of Delta and Gamma spectra using DCM for CSD

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 u: spectral innovations White and colored noise

State Space Characterisation Generative Model of Spectra Moran, Kiebel, Stephan, Reilly, Daunizeau, Friston (2007) A neural mass model of spectral responses in electrophysiology. NeuroImage Populated According to the neural mass model equations The Output State (Pyramidal Cells) The Input State (Stellate Cells)

State Space Characterisation Modulation Transfer Function An analytic mixture of state space parameters Output Spectrum (Y) = Modulation Transfer Function x Spectrum of Innovations Generative Model of Spectra

Frequency NMDA connectivty Posterior Cingulate Cortex Frequency Log Power Posterior Cingulate Cortex Frequency NMDA connectivty Anterior Cingulate Cortex Frequency Log Power Anterior Cingulate Cortex Generative Model of Spectra

Observer Model in the Frequency Domain Frequency (Hz) Power (mV 2 ) Spectrum channel/mode 1 Spectrum mode 2 Cross-spectrum modes 1& 2 + White Noise in Electrodes

Interconnected Neural mass models Lead Field Sensor Level Spectral Responses Summary: Neural Mass Models in DCM

Outline Data Features in DCM for CSD Generative Models in the time domain Generative Models in the frequency domain DCM Inversion procedure Example 1: L-Dopa Modulations of theta spectra using DCM for CSD Example 2: Propofol Modulations of Delta and Gamma spectra using DCM for CSD

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

Inference on models Dynamic Causal Modelling: Inversion & Inference 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: Inversion & Inference 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 A Neural Mass Model

Inversion in the real & complex domain Frequency (Hz ) real prediction and response: E-Step: Frequency (Hz) imaginary prediction and response: E-Step: parameter conditional [minus prior] expectation

Outline Data Features in DCM for CSD Generative Models in the time domain Generative Models in the frequency domain DCM Inversion procedure Example 1: L-Dopa Modulations of theta spectra using DCM for CSD Example 2: Propofol Modulations of Delta and Gamma spectra using DCM for CSD

Dopaminergic modulation in Humans Aim: Infer plausible synaptic effects of dopamine in humans via non-invasive imaging Approach: Double blind cross-over (within subject) design, with participants on placebo or levodopa Use MEG to measure effects of increased dopaminergic transmission Study a simple paradigm with “known” dopaminergic effects (from the animal literature): working memory maintenance Apply DCM to one region (a region with sustained activity throughout maintenance prefrontal) Moran, Symmonds, Stephan, Friston, Dolan (2011) An In Vivo Assay of Synaptic Function Mediating Human Cognition, Current Biology

Animal unit recordings have shown selective persistent activity of dorsolateral prefrontal neurons during the delay period of a delayed- response visuospatial WM task (Goldman-Rakic et al, 1996) The neuronal basis for sustained activity in prefrontal neurons involves recurrent excitation among pyramidal neurons and is modulated by dopamine (Gao, Krimer, Goldman- Rakic, 2001) Dose dependant inverted U Working Memory

Dopamine in Working Memory DA terminals converge on pyramidal cells and inhibitory interneurons in PFC (Sesack et al, 1998) DA modulation occurs through several pre and post synaptic mechanisms (Seamans & Yang, 2004) - Increase in NMDA mediated responses in pyramidal cells – postsynaptic D1 mechanism - Decrease in AMPA EPSPs in pyramidal cells – presynaptic D1 mechanism - Increase in spontaneous IPSP Amplitude and Frequency in GABAergic interneurons - Decrease in extrinsic input current Gao et al, 2001 Wang et al, 1999 Seamans et al, 2001

Memory Probe Image Target Image.. 4 sec. 300 ms.. 2 sec. 300 ms Memory e.g. match e.g. no match WM Paradigm in MEG on and off levodopa Maintenance Period Load titrated to 70% accuracy (predrug)

Behavioural Results Memory Probe Image Target Image match Placebo L-Dopa Titration * % Accuracy

Activity at sensors during maintenance Localised main effect and interaction in right prefrontal cortex Significant effects of memory in different frequency bands (channels over time) Sustained effect throughout maintenance in delta - theta - alpha bands Broad Band Low Frequency Activity P APA P A Time (s) 0 4 sensors Sustained Activity during memory maintenance: Sensor Space

DCM Architecture AMPA receptors NMDA receptors GABAa receptors Receptor Types Pyramidal Cell (Population 3) Inhibitory Interneurons (Population 2) Spiny Stellates (Population 1) Cell Populations γ : The strengths of presynaptic inputs to and postsynaptic conductances of transmitter-receptor pairs i.e. a coupling measure that absorbs a number of biophysical processes, e.g.: Receptor Density Transmitter Reuptake

Synaptic Hypotheses Membrane Potential (mV) pyrami dal cells spiny stellate cells inhibitory interneurons pyramidal cells Extrinsic Cortical Input (u) L-Dopa relative to Placebo, Memory – No Memory Trials 1. Decrease in AMPA coupling (decreased γ 1,3 ) 2. Increased sensitivity by NMDA receptors (increased α) 3. Increase in GABA coupling (increased γ 3,2 ) 4. Decreased exogenous input (decreased u)

Parameter Estimates L-Dopa : Memory – No Memory: Interaction of Parameter and Task on L-Dopa ( p = 0.009) L-Dopa : Memory – No Memory MAP Parameter estimates γ 1,3 α γ 3,2 u u x * * L-Dopa relative to Placebo, Memory – No Memory Trials 1. Decrease in AMPA coupling (decreased γ 1,3 ) 2. Increased sensitivity by NMDA receptors (increased α) 3. Increase in GABA coupling (increased γ 3,2 ) 4. Decreased exogenous input (decreased u) Moran, Symmonds, Stephan, Friston, Dolan (2011) An In Vivo Assay of Synaptic Function Mediating Human Cognition, Current Biology

Individual Behaviour L-Dopa : Memory – No Memory MAP Parameter estimates γ 1,3 α γ 3,2 u x * * Decrease in AMPA coupling (decreased γ 1,3 ) Increased sensitivity by NMDA receptors (increased α) Performance Increase AMPA connectivity γ 1, R = p < 0.05 Performance Increase NMDA Nonlinearity α R = 0.59 p < 0.05 Moran, Symmonds, Stephan, Friston, Dolan (2011) An In Vivo Assay of Synaptic Function Mediating Human Cognition, Current Biology

Outline Data Features in DCM for CSD Generative Models in the time domain Generative Models in the frequency domain DCM Inversion procedure Example 1: L-Dopa Modulations of theta spectra using DCM for CSD Example 2: Propofol Modulations of Delta and Gamma spectra using DCM for CSD

Connectivity changes underlying spectral EEG changes during propofol-induced loss of consciousness. Wake Mild Sedation: Responsive to command Deep Sedation: Loss of Consciousness Boly, Moran, Murphy, Boveroux, Bruno, Noirhomme, Ledoux, Bonhomme, Brichant, Tononi, Laureys, Friston, J Neuroscience, 2012

Propofol-induced loss of consciousness Wake Mild Sedation: Responsive to command Deep Sedation: Loss of Consciousness Anterior Cingulate /mPFC Precuneus /Posterior Cingulate

Wake Mild Sedation: Responsive to command Deep Sedation: Loss of Consciousness Increased gamma power in Propofol vs Wake Increased low frequency power when consiousness is lost Murphy et al Propofol-induced loss of consciousness Anterior Cingulate /mPFC Precuneus /Posterior Cingulate

Bayesian Model Selection Wake Mild Sedation Deep Sedation Propofol-induced loss of consciousness ACC PCC ACC PCC ACC PCC Thalamus Thalami

Wake Mild Sedation Deep Sedation Propofol-induced loss of consciousness ACC PCC ACC PCC ACC PCC Thalamus Thalami

Wake Propofol-induced loss of consciousness Parameters of Winning Model ACC PCC Thalamus

Wake Mild Sedation :Increase in thalamic excitability Propofol-induced loss of consciousness ACC PCC Thalamus ACC PCC Thalamus

Wake Mild Sedation :Increase in thalamic excitability Propofol-induced loss of consciousness ACC PCC Thalamus ACC PCC Thalamus Loss of Consciousness :Breakdown in Cortical Backward Connections ACC PCC Thalamus

Propofol-induced loss of consciousness Loss of Consciousness :Breakdown in Cortical Backward Connections ACC PCC Thalamus Boly, Moran, Murphy, Boveroux, Bruno, Noirhomme, Ledoux, Bonhomme, Brichant, Tononi, Laureys, Friston, J Neuroscience, 2012

Summary DCM is a generic framework for asking mechanistic questions of neuroimaging data Neural mass models parameterise intrinsic and extrinsic ensemble connections and synaptic measures DCM for SSR is a compact characterisation of multi- channel LFP or EEG data in the Frequency Domain Bayesian inversion provides parameter estimates and allows model comparison for competing hypothesised architectures Empirical results suggest valid physiological predictions

Thank You FIL Methods Group