functional and causal connectivity in the brain based on

22nd Annual Meeting of the Organization for Human Brain Mapping

Geneva, June 28, 2016

Fernando Lopes da SilvaSwammerdam Institute for Life Sciences, Amsterdam;

Dept Bio-Engineering, Instituto Superior Técnico, Lisbon

Functional and causal connectivity in the brain based on EEG/MEG signals

OUTLINE:Functional and causal connectivity in the brain

based on EEG/MEG signals

1. Measures of FUNCTIONAL Connectivity: general methodologies.

2. Measures of CAUSAL Connectivity: the concept of Transfer function, phase and time delays.

3. Granger Causality; basics: Autoregressive modeling and the Arrow of Time; Directed Transfer Function (DTF); direct DTF; Partial Directed Coherence (PDC). Mutual Information and Transfer Entropy.

4. From Autoregressive models to Neural Mass Models. Testing specific hypotheses.






4. From Autoregressive models to Neural Mass Models. Testing specific hypotheses

General Methodologies

Which method to chose and why?

To estimate functional connectivity, and functional connectivity of brain signals with special focus on LFPs, ECoG, EEG / MEG

Estimates of brain Functional Connectivity based on EEG / MEG signals

1. Regression methods:- Pearson correlation coefficient (R2);- Coherence function:- Non-linear correlation coefficient (h2);

2. Phase synchronization methods:- Hilbert phase entropy (HE);- Hilbert mean phase coherence (HR);- Wavelet phase entropy (WE);- Wavelet mean phase coherence (WR)

3. Generalized synchronization methods:- two similarity indices (S, N) and asynchronization likelihood;

Functional connectivity is estimated simply by measuring statistical dependencies between neurophysiological signals.

Wendling et al JNM 2009) used a simple model to compare the performance of these methods on the basis of a large variety of EEG-like signals

Q – measure of the estimated connectivity between 2 signals (0 -1) ;

C – coupling parameter to generate the 2 signals.

What is the comparative performance of the most common measures used to estimate functional connectivity?

Some General points to take in consideration:

1.Some methods are poorly sensitive to the coupling parameter;2.In general, methods performed better in broad band than in narrow band signals;3.There is no ideal method. It is recommended to compare results obtained using different methods to get more reliable insight in the connectivity. 4.Regression methods showed sensitivity in all tested models with relative good performance, with the exception of Hénon nonlinear attractor (M4 - 2 identical systems).

Lopes da Silva, Event-related neural activities: what about phase? Progr. Brain Res 159, 2006

The analytical procedure (Hilbert Transform) consists in computing from the cross-power spectrum, the corrected phase function, from the slope of which, ∆φ/∆f, the time delay ∆t can be estimated.

Structures of the Limbic cortex: PPC and Hippocampal formation (Entorhinal cortex, EC) in cat.

Effective connectivity is essentially linked to the notion of what Granger called the arrow of time, i.e, the time delay ∆t between signals A and B.

EXAMPLE #1

PPC ECa

Δt = Δφ / Δf In this experimental case 9.4±3ms, for the gamma frequency band (28 - 42 Hz), what corresponds to a propagation velocity of 1.6±0.5ms-1.

Recordings in monkey, in V1 and V4 (areas with overlapping RFs).Coherence LFPs of V1 & V4. applying Fourier anlaysis.Phase spectrum showing the best fit slopes for the alpha [V4 V1]and gamma [V1 V4]frequency band, and corresponding time delays:[V4 V1] 9 ms & [V1 V4] 3 ms.

Granger causality between V1 & V4 and between V4 & V1. Van Kerkoerle et al PNAS 2014 (Fig 7)

Different time delays are associated with different EEG (ECoG) frequency bands. These time delays are the arrows of time according to Granger’s nomenclature.

Timo van Kerkoerle et al (PNAS, 2014) found (in awake monkeys) that γ-waves start in cortical input layer IV, whereas α-waves start in recipient layers I, II, and V. Is this associated with corresponding time-lags between lower and higher visual areas, and can this be assigned to cortico-cortical feedforward and feedback pathways?

EXAMPLE

#2

Quotation from:

C.W.J. Granger: TESTING FOR CAUSALITY, A personal viewpoint. J. of Economic Dynamics and Control 2 (1980) 329 -352.

“The definition of causation essentially says that Xn+jwill consist of a part that can be explained by some proper information set, plus an unexplained part. If Yn-j can be used to partly forecast the unexplained part of Xn+j, then Y is said to be a prima facie cause of X”.

The beauty of Granger’s approach is its simplicity and its pragmatism

Estimates of brain Causal Connectivity based on EEG / MEG signals

What are the essential features of Granger approach?

K i k t l H B i M i 2008

Auditory perception stage Response preparation Verbal response

Short-time direct Directed Transfer Function [SdDtf] Applied to ElectroCorticograms

are the elements of the transfer function H: l-th input; k-th output;

represents partial coherence;

Event-Related Causality in the frequency range 82-100 Hz; arrows indicate flow direction; width indicates the value of ERC integral.

E9- Auditory Association CortexE3/E4 – Mouth/Tongue Motor Cortex

E4/E5/E11 Aud Ass Cx – “Wernicke’sE2 E7 Broca’s area - Aud Ass Cx

E2/E1 – “Broca’s” E4 Mouth motor CortexAlso activation feedback pathways: E4 E2

An example of time-varying Partial Directed Coherence applied to signals corresponding to Epileptiform Spikes at the level of the sources using linear inverse source solutions. Application of PDC normalized with respect to incoming connections

Epilepsia 2015

Circle diameter correspond to the summed outflow related to the Epileptiform Spike for LTLE and RTLE groups of patients

Another method, related to Mutual Information, is the computation of the Transfer Entropy (TE), that is becoming popular. Transfer Entropy (TE) can be defined as follows:

The mutual information (I) between the past of the source (Xt-u ) and the current value of the target process (Yt ) is conditional on the past state of the target (Yt-1);

I is given by I (Yt; Xt-u | Yt-1),

and the interaction conduction delay: Δt = arg maxu (TE (X Y, u))

- Roux, Wibral, Singer, Aru, Uhlhaas. The phase of Thalamic Alpha activity modulates cortical Gamma-band activity: evidence from resting-state MEG recordings. J Neuroscience 2013.

- See also Lobier, Siebenhühner, S Palva nd MJ Palva, Phase transfer entropy: a novel phase-based measure for directed connectivity in networks coupled by oscillatory interactions. Neuroimage 2014.

Note:Barnett et al (2009) showed that for Gaussian variables Granger causality and TE are entirely equivalent.Physical Review Letters; 2009)

X is the source; Y is the target.

Based on MEG and spatial filtering techniques Roux et al (2013) show phase amplitude coupling of γ-band activity in posterior medial parietal Cortex modulated by the phase of thalamic α (resting state, eyes-closed). Using Transfer Entropy conductions delays from Thalamus and Cortex were estimated. PLV showed the phase coupling between Thalamus – Cortex.

Thalamo-Cortical delay, estimated using TE: 15.8 ± 2.4 ms

Based on MEG and spatial filtering techniques (n-45)

Addressing causality in neural circuitsThe dependency of cortical alpha rhythms on thalamic (pulvinar) nuclei by means of the computation of Partial Coherence what constitutes a “theoretical deafferentation” in

thalamo-cortical neural circuits

Cohrence between Z (8) vs Y (15)

Partialization on X (27)

(Lopes da Silva et al 1980)

Cortex

Partial Coherence

13 ±4 ms

17.6±2ms

A demonstration of the effect of Granger’s Missing Variable.

Showing time-delays between Thalamic Nuclei and Occipital Cortex computed from phase spectra.

Thalamo-Cortical delay, estimated using Transfer Entropy : 15.8 ± 2.4 ms

Dynamics of Neural Mass Models

In order to analyze the complexity of many neurophysiological processes such as the dynamics of EEG/MEG signals one requires elaborated models.

The groundwork for DCMs lies in the creation of Neural Mass Models in the 70’s.

A family of such elaborated models is constituted by the so-called Dynamic Causal Models (DCMs) introduced by Karl Friston and collaborators. Here I focus simply on Neural Mass Models (NMM).


The Wilson-Cowan model is a model of interactingpopulations of neurons (excitatory and inhibitory) based onthe mean-field approach.

It consists of a set of differential equations that describe the meanlevel of the activity of neuronal populations as function of time.

The Wilson–Cowan modelKybernetik 1972, 1973

Interesting reading: Destexhe and Sejnowski: The Wilson-Cowan model, 36 years later, Biol Cybern, 2009; 101(1):1-2.

Intermezzo 1:A short historical perspective :

the very beginning

INTERMEZZO 2: Mean-field Neural Mass Models

• Population models : Wilson & Cowan (1972, 1973), Lopes da Silva (1974), Freeman (1975), Jansen (1993) Jansen and Rit (1995), Valdes-Sosa et al (1999), Wendling (2000), Suffczynski(2001), David and Friston (2003), Robinson et al (2005),Stephan et al (2006), Valdez-Sosa et al (2009) and others

Main features:

- Two populations: excitatory (E) andinhibitory (I).

- Relevant variable: mean firing-rate orpulse density (P(t), E(t)).

- Synaptic inputs sum linearly into thesoma (mean-field approximation).

- Sigmoid functions (fE, fI) relating pulsedensity (P) to membrane potential(wave W)

-- Connectivity parameters (c1, c2)

Early contribution:

Lopes da Silva, F.H., Hoeks, A., Smits, H., Zetterberg, L.H., Model of brain rhythmic activity. The alpha-rhythm of the thalamus. Kybernetik 1974. 15, 27–37.

Neural Mass Models (NMM)

One example to illustrate the power of NMMs in testing hypotheses about how causal connectivity can account for two neurophysiological phenomena.

The mechanism underlying the phenomenon of focal Event-Related Desynchronization (ERD) / surround Event-Related Synchronization (ERS) of Mu-Rhythm dynamics:the event is a voluntary movement in human.

Neural Mass Models

One example to illustrate the power of DCM in testing hypotheses about how causal connectivity can account for two neurophysiological phenomena. DCM relies on specific assumptions of the underlying neuronal populations.

The mechanism underlying the phenomenon of focal Event-Related Desynchronization (ERD) / surround Event-Related Synchronization (ERS) of Mu-Rhythm dynamics: The event is a voluntary movement in human.

This is a Neurophysiological/ Biophysical model of neuronal dynamics that is used to understand a puzzling EEG/MEG phenomenon.

Neural Mass Models Focal ERD / Surround ERS

(Pfurtscheller and Lopes da Silva, 1999)

Event-related desynchronization(ERD) of α (μ) , and Event-related Synchonization(ERS) of β – and γ – activities at the same recording site but at different times.

Pfurtscheller, Lopes da Silva. Clin Neurophysiol. 1999 Nov;110(11):1842-57.


Adapted from Pfurtscheller

Parallel finding in EEG and fMRI (BOLD) domains

Neural Mass Models

The question is how can be explained that the α (μ) rhythm power can increase in one cortical area and decreases in the neighboring area, in response to the same behavioral event ?

Hypothesis: Since there are no connections between the two areas at the level of the cortex, the hypothesis is that the interaction between both systems might take place at the level where the two systems can interact: the Thalamic Reticular Nucleus.

Thalamocortical reentry network

© SEIN, 2003Medical Physics Department

Extracellular activity of a RE neuron (yellow) and cortical field potential (green) recorded in the GAERS during a spike and wave discharge

pyramidal cell

GABAergic interneuron

thalamic reticular (RE) neuron

thalamocortical (TC) neuron

ThalamicReticularNuc leus

Thalamo-corticalRelayNuc leus

Exc itation Inhib ition

Parallel cortico-thalamic reentrant modules interact by reciprocal inhibitory interactions at the level of the Reticular Nucleus of the Thalamus

Module 1

Module 2

Suffczynski P, Kalitzin S, Pfurtscheller G, Lopes da Silva FH. Int J Psychophysiol. 2001 Dec;43(1):25-40.

Attention alerting signal - Modulating Ch burst

Depolarization

Hyperpolarization

Decrease surround inhibition

Alpha Oscillatory Loop Gain

Alpha Oscillatory Loop Gain

# 1

# 2

ERD

ERS

X

X

Neural Mass Models

Modulating(cholinergic) input to the target module:

ERD in target module;

ERS in neighboringmodule.

Some points to think over with respect to Functional and Effective connectivity using brain signals:

1. Give priority to studies of Effective connectivity over Functional connectivity ones.

2. Pay special attention to estimates of the “arrow of time”.

3. There is no lack of Methods to estimate Causal and Effective connectivity; but from a practical point of view there is a lack of unbiased analyses of the performance of the different methods applied to the same and well defined sets of data (stimulate collaborative projects between different centers).

4. In addition it is necessary to design comprehensive validating studies combining different approaches, not only regarding methodology but also at the experimental level, i.e. to combine human studies using scalp EEG/MEG recordings with ECoG/intra-cranial recordings.

5. To strengthen the interplay between experiments and computational modeling, in particular by developing more realistic Neural Mass Models.

functional and causal connectivity in the brain based on

Documents