= Tutorial 28: Connectivity =
'''[TUTORIAL UNDER DEVELOPMENT: NOT READY FOR PUBLIC USE] '''

''Authors: Hossein Shahabi, Mansoureh Fahimi, Francois Tadel, Esther Florin, Sergul Aydore, Syed Ashrafulla, Elizabeth Bock, Sylvain Baillet''

== Introduction ==
During the past few years, the research focus in brain imaging moved from localizing functional regions to understanding how different regions interact together. It is now widely accepted that some of the brain functions are not supported by isolated regions but rather by a dense network of nodes interacting in various ways.

Brain networks (connectivity) is a recently developed field of neuroscience which investigates interactions among regions of this vital organ. These networks can be identified using a wide range of connectivity measures applied on neurophysiological signals, either in time or frequency domain. The knowledge provides a comprehensive view of brain functions and mechanisms.

This module of Brainstorm tries to facilitate the computation of brain networks and the representation of their corresponding graphs. Figure 1 illustrates a general framework to analyze brain networks. Preprocessing and source localization tasks for neural data are thoroughly described in previous sections of this tutorial. The connectivity module is designed to carry out remained steps, including the computation of connectivity measures, and statistical analysis and visualizations of networks.

{{attachment:FlowChartGeneral.png||height="230",width="850"}}

== General terms/considerations for a connectivity analysis ==
'''Sensors vs sources: '''The connectivity analysis can be performed either on sensor data (like EEG, MEG time series) or reconstructed sources.

'''Nature of the signals: '''

'''Point-based connectivity vs. full network: '''Most of connectivity functions provide you the option to either compute the connectivity between one point (channel) and the rest of the network (1 x N) or the entire network (N x N). While the later calculate the graph thoroughly, the first options enjoy a faster computation and it is more useful when you are interested in the connectivity of an ROI with the other regions of the brain.

'''Temporal resolution: '''Connectivity networks can be computed in two ways; static and dynamic. In Table1 metrics are classified based on this feature. Dynamic networks can present the time-varying property of the brain. In contrast, the static graphs illustrate a general … which is also helpful in many conditions. The user needs to decide which type of network is more informative for their study.

'''Time-frequency transformation: '''

--(Consider how to choose window (length and overlap) depends on frequency bands )--

'''Output data structure:'''

__'' Consequently, computed connectivity matrices in this toolbox can have up to four dimensions; channels x channels x frequency bands x time. ''__

== Simulated data (AR model) ==
In order to compare different connectivity measures, we use simulated data with known ground truth. Three channels are

{{attachment:TransferMatrix_AR3.png||height="400",width="550"}}




== Coherence (FFT-based) ==
 * Put the Simulated data in the Process1 tab.
 * Click on [Run] to open the Pipeline editor.
 * Run the process: '''Connectivity > Coherence NxN ''' <<BR>><<BR>>

{{attachment:StatCoherence_Process_ms.PNG||height="400",width="350"}}

 * Set the options as follows:
  * '''Time window''': Select the entire signal.
  * '''Estimator options''': leave the box unchecked so the means will be subtracted before computing the correlation.
  * '''Output configuration''': Select one file per input.

In general, after running the connectivity processes, you can find a multi-dimensional matrix of connectivity in the database. Right click on file and select '''Connectivity > Correlation NxN'''

== Granger Causality ==
Granger Causality (GC) is a method of functional connectivity, adapted by Clive Granger in the 1960s, but later refined by John Geweke in the form that is used today. Granger Causality is originally formulated in economics but has caught the attention of the neuroscience community in recent years. Before this, neuroscience traditionally relied on stimulation or lesioning a part of the nervous system to study its effect on another part. However, Granger Causality made it possible to estimate the statistical influence without requiring direct intervention (ref: wiener-granger causality a well-established methodology).

== Coherence and envelope (Hilbert/Morlet) ==
This process

{{attachment:FlowChartHCorr.png||height="170",width="850"}}

 * '''Input Options:''' The time range of the input signal can be specified here. Also, bad channels and the evoked response of trials can be discarded, if appropriate.
 * '''Time-frequency transformation method:''' The method for this transformation (Hilbert transform or Morlet Wavelet) should be selected. Additionally, this analysis needs further inputs, e.g. frequency ranges, number of bins, and Morlet parameters, which can be defined by an external panel as depicted in Figure 4 (By clicking on “Edit”). A complete description regarding time-frequency transformation can be found here. In the context of connectivity study, we must analyze complex output values of these functions, so two other options (power and magnitude) are disabled on the bottom of this panel.
 * '''Signal splitting:''' This process has the capability of splitting the input data into several blocks for performing time-frequency transformation, and then merging them to build a single file. This feature helps to save a huge amount of memory and, in the same time, avoid breaking a long-time recording to short-time signals, which makes inconsistency in dynamic network representation of a spontaneous data. The maximum number of blocks which can be specified is 20.
 * '''Connectivity measure:''' Here, three major and widely used coherence based measures of brain connectivity can be computed. Next, desired parameters for windowing, i.e. window length and overlap, should be determined. Please note that these values are usually defined based on the nature of data, the purpose of the study, and the selected connectivity measure.
 * '''Parallel processing:''' This feature, which is only applicable for envelope correlation, employs the parallel processing toolbox in Matlab to fasten the computational procedure. As described in the advanced section of this tutorial, envelope correlation utilizes a pairwise orthogonalization approach to attenuate the cross-talk between signals. This process requires heavy computation, especially for a large number of channels, however, using Parallel Processing Toolbox, the software distributes calculations on several threats of CPU. The maximum number of pools varies on each computer and it is dependent on the CPU.
 * '''Output configuration:''' Generally, the above calculation results in a 4-D matrix, where dimensions represent channels (1st and 2nd dimensions), time points (3rd dimension), and frequency (4th dimension). In the case that we analyze event-related data, we have also several files (trials). However, due to poor signal to noise ratio of a single trial, an individual realization of connectivity matrices for each of them is not in our interests. Consequently, we need to average connectivity matrices among all trials of a specific event. The second option of this part performs this averaging.

== Simulated data (phase synchrony) ==
== Correlation ==
The correlation is the basic approach to show the dependence or association among two random variables or MEG/EEG signals. While this method has been widely used in electrophysiology, it should not be considered as the best technique for finding the connectivity matrices. The correlation by its nature fails to alleviate the problem of volume conduction and cannot explain the association in different frequency bands. However, it still can provide valuable information in case we deal with a few narrow-banded signals.

 * Put the Simulated data in the Process1 tab.
 * Click on [Run] to open the Pipeline editor.
 * Run the process: '''Connectivity > Correlation NxN ''' <<BR>>

{{attachment:StatCorrelation_Process.PNG||height="350",width="350"}}

 * Set the options as follows:
  * '''Time window''': Select the entire signal.
  * '''Estimator options''': leave the box unchecked so the means will be subtracted before computing the correlation.
  * '''Output configuration''': Select one file per input.

== Phase locking value ==
== Method selection and comparision ==
--(a)--

== Additional documentation ==
==== References ====
==== Articles ====
 * '''Phase transfer entropy''': Lobier M, Siebenhühner F, Palva S, Palva JM [[http://www.sciencedirect.com/science/article/pii/S1053811913009191|Phase transfer entropy: A novel phase-based measure for directed connectivity in networks coupled by oscillatory interactions]], NeuroImage 2014, 85:853-872

==== Forum discussions ====
 * Forum: Connectivity matrix storage:[[http://neuroimage.usc.edu/forums/showthread.php?1796-How-the-Corr-matix-is-saved|http://neuroimage.usc.edu/forums/showthread.php?1796]]

 * Forum: Comparing coherence values: http://neuroimage.usc.edu/forums/showthread.php?1556

 * Forum: Reading NxN PLV matrix: http://neuroimage.usc.edu/forums/t/pte-how-is-the-connectivity-matrix-stored/4618/2

 * Forum: Scout function and connectivity: http://neuroimage.usc.edu/forums/showthread.php?2843

 * Forum: Unconstrained sources and connectivity: http://neuroimage.usc.edu/forums/t/problem-with-surfaces-vs-volumes/3261

 * Forum: Digonal values: http://neuroimage.usc.edu/forums/t/choosing-scout-function-before-or-after/2454/2

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