introduction to various connectivity...

Introduction to Various Connectivity Analyses

Chapter 25John JB Allen

Connectivity

Any analysis for which more than one signal is considered at a time.

two signals from two different electrodestwo signals from the same electrode multiple signals from multiple electrodes.

Includes measures based on phase and on powerIncludes linear and nonlinear methodsAll approaches share the common goal of identifying brain connectivity

Bivariate Connectivity

The brain ain’t that simple, but …Bivariate versions are easier to implement, interpret, and test with established statistical procedures.Plus .. bivariate connections are the most relevant types of connections for many cognitive functions.

Bivariate Connectivity

Can inflate or misrepresent estimates if network structure is actually multivariate

But such inflation can affect all conditions equally, so if comparing conditions may be less problematic

Bivariate Connectivity Concepts

Phase lag not considered, provided it is constant

connectivity between a electrodes that are 0 ms, 10 ms, or 100 ms lagged from each other can be equally strongly synchronized

Nonzero phase lag in connectivity does not necessarily imply a causal or directed relationship


Lag or lead?

Teaser: Granger prediction (chapter 28) and the phase-slope-index (chapter 26) provide better evidence for directed connectivity compared to connectivity measures based on phase angle distributions (chapter 26) or power correlations (chapter 27)

If claims about directionality or causality are important for your experiment and for interpreting

your results, use directional methods such as Granger prediction and try to buttress your interpretation of

causality or directionality with theory, known anatomical directional connectivity, previous relevant research, and, if possible, causal interference methods such as transcranial magnetic or electrical stimulation.


Results differ…phase-based and power-based measures of connectivity tend to reveal different patterns of results

Not surprising necessarily..Phase reflects timing of activity within a neural population Power reflects number of neurons or spatial extent of the neural population


Phase vs Power approachesPhase-based most often usedPhase-based may be preferred for hypotheses concerning instantaneous connectivity Power-based analyses are more robust to temporal offsets and jitters

Bivariate Connectivity ConceptsFunctional connectivity

linear or nonlinear covariation between fluctuations in activity recorded from distinct neural networks

Effective connectivity a causal influence of activity in one neural network over activity in another neural network

Functional vs effective connectivity Analogous to correlation vs causation

Bivariate Connectivity ConceptsThe problem of volume conduction

What approach to Connectivity?Good news: No single correct methodMay wish to model your approach after similar published papers

What approach to Connectivity?Phase-based approaches

Rely on distribution of phase angle differences

What approach to Connectivity?Phase-based approaches

Rely on distribution of phase angle differencesAdvantages

Widely used!Computationally fastGenerally insensitive to lag

DisadvantagesRely on precise temporal relationships; are thus susceptible to temporal jitter or uncertaintyPhase-based measures do not provide compelling evidence for directionality

What approach to Connectivity?Power-based approaches

Correlate time-frequency power between two electrodes across time or over trials.May be between activity in the same or different frequencies May be at same or different time points

AdvantagesFlexibleMost similar to fMRI connectivity analyses (slow time-series covariation)Relatively insensitive to temporal jitter

Granger Prediction!AKA Granger Causality

Teaser: See Chapter 28 (Ezra’s big day!)

AdvantagesCan dissociate directional connectivity

A → B versus B → A connectivityCan ignore simultaneous connectivity (less susceptible to volume conduction)

DisadvantagesSensitive to violations of stationarityComputationally time-consuming to performDoubles the number of results because each pair of electrodes contains two connectivity values

Twice the number of statistical comparisons that need to be controlled for

Mutual InformationDetects shared information between two variables

Teaser: See Chapter 29 (Lauritz’s big day!)

AdvantagesCan detect many kinds of relationships

Includes linear and nonlinear interactions that a correlation would fail to identify

Has a long tradition of use and development in engineering and information technologySeveral extensions for using mutual information and entropy to estimate system complexity or signal transmission integrity

Mutual InformationDetects shared information between two variables

Teaser: See Chapter 29 (Lauritz’s big day!)

DisadvantagesNo information about whether a relationship is

linear or nonlinearpositive or negative

Sensitive to the number of histogram binsComputationally intensiveNo clear neurophysiological interpretation

Cross-Frequency CouplingIdentifies a statistical relationship between activities in two different frequency bands

Teaser: See Chapter 30 (Uri’s big day!)

AdvantagesCan infer local or long-range connectivityFindings can be linked across species and to computational modelsIdentify task-related high-frequency power, which is more difficult with EEG in trial-averaging-based analyses

Cross-Frequency Coupling

Jirsa & Müller (2013), Frontiers in Computational Neuroscience

Cross-Frequency Coupling

Adriano et al. (2008), PNAS

Cross-Frequency CouplingIdentifies a statistical relationship between activities in two different frequency bands

Teaser: See Chapter 30 (Uri’s big day!)

DisadvantageHuge search space

freqs × freqs × trodes × trodes × conditions × timeTime consuming, multiple statistical comparisons

Of course … this is also the advantage!

Graph TheoryMathematical framework characterizing networks represented as graphs

Graphs contain nodes (electrodes) and vertices (connectivity strengths)

Teaser: See Chapter 31 (Goffredina’s big day!)

Social networks and drinking (Framingham Heart Study)

Rosenquist et al. (2010) Annals of Internal Medicine

Graph TheoryMathematical framework characterizing networks represented as graphs

Graphs contain nodes (electrodes) and vertices (connectivity strengths)

Teaser: See Chapter 31 (Goffredina’s big day!)

http://home.kpn.nl/stam7883/brainwave.html

Graph TheoryAdvantages

Useful and often easy-to-interpret characterizations of multivariate networksSame analyses can be applied to very different kinds of data, and high-level summary variables can be directly compared across these data (EEG connectivity, fMRI connectivity, diffusion MRI connectivity, etc)

DisadvantageOften used in exploratory data-mining analyses that lack a theoretical frameworkConcerns of replicability and interpretability

Problem of volume conduction…

http://hanzismatter.blogspot.com/2006/03/interviews-and-comics.html

Problem of volume conduction…

Sources generate large fields that propagate to more than one electrode (B)Fields spread laterally (C)Will inflate connectivity metrics (but not represent true connectivity)

Is my finding due to volume conduction?Zero or π phase lag (π if on opposite sides of dipole)

But it it can reflect true zero-phase-lag brain connectivity too

Very strong connectivity at neighboring electrodes and a decrease of connectivity strength with interelectrode distancePositive correlations In the frequency and time-frequency domains (can only cause positive r’s)Positive correlations between connectivity and power in same frequency band

If volume conduction is at play, changes in power should correlate with changes in connectivity

“If your connectivity results are consistent with these four predictions, you should be concerned that those connectivity results are artifacts of volume conduction. On the other hand, if your results fail to conform to these predictions, it is unlikely that your connectivity results are due to volume conduction.”

If … you just might be a redneck!You think "loading the dishwasher" means getting your wife drunk.You ever cut your grass and found a car.You own a home that is mobile and 5 cars that aren't.You think the stock market has a fence around it.

Ten ways to deal with volume conduction

Ten ways to deal with volume conduction#1: Apply a spatial filter priorto computing connectivity

Surface Laplacian is a goodfor electrode-level analysisDistributed adaptive source solutions such as beamforming are good spatial filters for source-space analyses

#2: Examine only negative correlations in the frequency or time-frequency domains

Cannot be due to volume conductionIs everything negative?!!!

Ten ways to deal with volume conduction#3: Test for temporally lagged connectivity rather than simultaneous connectivity

Volume-conducted spurious connectivity is instantaneousBUT…. Autocorrelation will potentially pose problems

Safer if comparing conditions, and over many trials

Bandpass filtered random noise

Ten ways to deal with volume conduction#4: Test for condition differences in connectivity rather than single-condition effects

Some biases introduced by connectivity analyses will affect all conditions equally

#5: Test for a cross-frequency correlation IS 6-Hz activity in one electrode correlated with 20-Hz activity in another electrode. If the 6-Hz and 20-Hz power activities are not correlated within each electrode, the correlation across electrodes cannot be due to volume conductionCorrelations across frequency bands should be interpreted cautiously if activity at those two frequency bands is correlated within one or both electrodes individually

Ten ways to deal with volume conduction#6: Test for a statistical or qualitative dissociation between connectivity and power

Look for no relationship or inverse relationship, as volume conduction produces positive correlationCan look for trial-by-trial dissociations (e.g., connectivity predicts RT, power does not)

#7: Test whether phase lag of connectivity between electrodes is sig. different from zero or π#8: For phase-based connectivity, you can use measures that are insensitive to volume conduction:

imaginary coherencephase-lag indexweighted phase-lag indexphase-slope-index

Ten ways to deal with volume conduction#9: For power-based connectivity, you can compute partial correlations between two electrodes holding constant a third electrode

Third electrode: a neighbor of one of the electrodesCan remove shared activity to volume conduction

#10: For power-based connectivity you can modify pairs of time series before calculating connectivity such that the coherent real parts (which include volume conduction effects) are removed, thereby removing any potentially volume-conducted signals

Hipp, J. F., D. J. Hawellek, M. Corbetta, M. Siegel, and A. K. Engel. 2012. Large-Scale Cortical CorrelationStructure of Spontaneous Oscillatory Activity. Nature Neuroscience 15 (6):884–890.

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