# Analysis of sensor- and source-level connectivity

## Introduction

## Background

## Procedure

This tutorial consists of three parts:

- Simulated data with directed connections. In this part we are going to simulate some data and use these data to compute various connectivity metrics. As a generative model of the data we will use a multivariate autoregressive model and we will use
**ft_connectivitysimulation**for this. Subsequently, we will estimate the multivariate autoregressive model and the spectral transfer function, and the cross-spectral density matrix using the functions**ft_mvaranalysis**and**ft_freqanalysis**. In the next step we will compute and inspect various measures of connectivity with**ft_connectivityanalysis**and**ft_connectivityplot**. - Simulated data with common pick-up and different noise levels. In this part we are going to simulate some data consisting of an instantaneous mixture of 3 'sources', creating a situation of common pick up. We will explore the effect of this common pick up on the consequent estimates of connectivity, and we will investigate the effect of different mixings on these estimates.
- Connectivity between MEG virtual channel and EMG. In this part we are going to reconstruct MEG virtual channel data and estimate connectivity between this virtual channel and EMG. The data used for this part are the same as in the Analysis of corticomuscular coherence tutorial.

## Simulated data with directed connections

## Simulated data with common pick-up and different noise levels

## Connectivity between MEG virtual channel and EMG

The previous two examples were using simulated data, either with a clear directed connectivity structure, or with a trivial pick-up of a common source in two channels. We will now continue with connectivity analysis on real MEG data. The dataset is the same as the one used in the Analysis of corticomuscular coherence tutorial.

In short, the dataset consists of combined MEG and EMG recordings while the subject lifted his right hand. The coherence tutorial introduction contains a more elaborate description of the experiment and the dataset and a detailed analysis can be found in the corresponding paper ^{1)}. Due to the long distance between the EMG and the MEG, there is no volume conduction and hence no common pick-up. Hence this dataset lends itself well for connectivity analysis. But rather than doing an analysis between the EMG and one of the MEG channels (as in the original study), we will extract the cortical activity using a beamformer virtual channel.

### Compute the spatial filter for the region of interest

We start with determining the motor cortex as the region of interest. At the end of the coherence tutorial it is demonstrated how to make a 3-D reconstruction of the cortico-muscolar coherence (CMC) using the DICS algorithm. That source reconstruction serves as starting point for this analysis.

You can download the result from the DICS reconstruction from the FieldTrip ftp server (source.mat)

We will first determine the position on which the cortico-muscular coherence is the largest.

load source [maxval, maxindx] = max(source.avg.coh); maxpos = source.pos(maxindx,:) maxpos = 4 -3 12

The cortical position is expressed in individual subject head-coordinates and in centimeter. Relative to the center of the head (in between the ears) the position is 4 cm towards the nose, -3 towards the left side (i.e., 3 cm towards the right!) and 12 cm towards the vertex.

The **ft_sourceanalysis** methods are usually applied to the whole brain using a regular 3-D grid or using a triangulated cortical sheet. You can also just specify the location of a single or multiple points of interest with *cfg.grid.pos* and the LCMV beamformer will simply be performed at the location of interest.

The LCMV beamformer spatial filter for the location of interest will pass the activity at that location with unit-gain, while optimally suppressing all other noise and other source contributions to the MEG data. The LCMV implementation in FieldTrip requires the data covariance matrix to be computed with **ft_timelockanalysis**.

Rather than doing all the preprocessing again, you can download the preprocessed data from the FieldTrip ftp server (data.mat)

load data %% compute the beamformer filter cfg = []; cfg.covariance = 'yes'; cfg.channel = 'MEG'; cfg.vartrllength = 2; cfg.covariancewindow = 'all'; timelock = ft_timelockanalysis(cfg, data); cfg = []; cfg.method = 'lcmv'; cfg.hdmfile = 'SubjectCMC.hdm'; cfg.grid.pos = maxpos; cfg.keepfilter = 'yes'; source = ft_sourceanalysis(cfg, timelock);

The source reconstruction contains the estimated power and the source-level time-series of the averaged ERF, but here we are not interested in those. The *cfg.keepfilter* option results in the spatial filter being kept in the output source structure. This filter can be used to reconstruct the single-trial time series as a virtual channel by multiplying it with the original MEG data.

### Extract the virtual channel time-series

%% construct the 3-D virtual channel at the location of interest beamformer = source.avg.filter{1}; chansel = ft_channelselection('MEG', data.label); % find the names chansel = match_str(data.label, chansel); % find the indices sourcedata = []; sourcedata.label = {'x', 'y', 'z'}; sourcedata.time = data.time; for i=1:length(data.trial) sourcedata.trial{i} = beamformer * data.trial{i}(chansel,:); end

If you would know that the subsequent analysis would be limited to a specific frequency range in the data (e.g. everything above 30 Hz), you could first apply a filter using **ft_preprocessing** (e.g. *cfg.hpfilter=yes* and *cfg.hpfreq=30*) prior to computing the covariance and the spatial filter.

The *sourcedata* structure resembles the raw-data output of **ft_preprocessing** and consequently can be used in any follow-up function. You can for example visualize the single-trial virtual channel time-series using **ft_databrowser**:

cfg = []; cfg.viewmode = 'vertical'; % you can also specify 'butterfly' ft_databrowser(cfg, sourcedata);

Notice that the reconstruction contains three channels, for the x-, the y- and the z-component of the equivalent cu rrent dipole source at the location of interest.

### Project along the strongest dipole direction

The interpretation of connectivity is facilitated if we can compute it between two plain channels rather than between one channel versus a triplet of channels. Therefore we will project the time-series along the dipole direction that explains most variance. This projection is equivalent to determining the largest (temporal) eigenvector and can be computationally performed using the singular value decomposition (svd).

%% construct a single virtual channel in the maximum power orientation timeseries = cat(2, sourcedata.trial{:}); [u, s, v] = svd(timeseries, 'econ'); % whos u s v % Name Size Bytes Class Attributes % % s 3x3 72 double % u 3x3 72 double % v 196800x3 4723200 double

Matrix u contains the spatial decomposition, matrix v the temporal and on the diagonal of matrix s you can find the eigenvalues. See “help svd” for more details.

We now recompute the virtual channel time-series, but now only for the dipole direction that has the most power.

% this is equal to the first column of matrix V, apart from the scaling with s(1,1) timeseriesmaxproj = u(:,1)' * timeseries;

virtualchanneldata = []; virtualchanneldata.label = {'cortex'}; virtualchanneldata.time = data.time; for i=1:length(data.trial) virtualchanneldata.trial{i} = u(:,1)' * beamformer * data.trial{i}(chansel,:); end

#### Exercise 8

*cfg.lcmv.fixedori='yes'*option.

Recompute the spatial filter for the optimal source orientation and using that spatial filter (a 1×151 vector) recompute the time-series.

Investigate and describe the difference between the two time-series. What is the difference between the two dipole orientations?

Note that one orientation is represented in the SVD matrix “u” and the other is in the source.avg.ori field.

### Combine the virtual channel with the EMG

The raw data structure containing one (virtual) channel can be combined with the two EMG channels from the original preprocessed data.

%% select the two EMG channels cfg = []; cfg.channel = 'EMG'; emgdata = ft_selectdata(cfg, data); %% combine the virtual channel with the two EMG channels cfg = []; combineddata = ft_appenddata(cfg, virtualchanneldata, emgdata); save combineddata combineddata

### Compute the connectivity

The resulting combined data structure has three channels: the activity from the cortex, the left EMG and the right EMG. We can now continue with regular channel-level connectivity analysis.

%% compute the spectral decomposition cfg = []; cfg.output = 'fourier'; cfg.method = 'mtmfft'; cfg.foilim = [5 100]; cfg.tapsmofrq = 5; cfg.keeptrials = 'yes'; cfg.channel = {'cortex' 'EMGlft' 'EMGrgt'}; freq = ft_freqanalysis(cfg, combineddata); cfg = []; cfg.method = 'coh'; coherence = ft_connectivityanalysis(cfg, freq);

This computes the spectral decomposition and the coherence spectrum between all channel pairs, which can be plotted with

cfg = []; cfg.zlim = [0 0.2]; figure ft_connectivityplot(cfg, coherence); title('coherence')

To look in more detail into the numerical representation of the coherence results, you can use

figure plot(coherence.freq, squeeze(coherence.cohspctrm(1,2,:))) title(sprintf('connectivity between %s and %s', coherence.label{1}, coherence.label{2})); xlabel('freq (Hz)') ylabel('coherence')

The spectrum reveals coherence peaks at 10 and 20 Hz (remember that the initial DICS localizer was done at beta). Furthermore, there is a broader plateau of coherence in the gamma range from 40-50 Hz.

#### Exercise 9

#### Exercise 10

#### Exercise 11

## Summary and further reading

This tutorial demonstrates how to compute connectivity measures between two time series. If you want to learn how to make a distributed representation of connectivity throughout the whole brain, you may want to continue with the corticomuscular coherence tutorial.

FAQs:

2011/06/08 09:49 | Jan-Mathijs Schoffelen | |

2009/02/17 15:15 | Robert Oostenveld |

Example scripts:

2009/05/20 14:57 | ||

2016/06/24 09:59 | Robert Oostenveld | |

2009/03/31 14:21 |

This tutorial was last tested by Jörn with version r9460 (April 30 2014) of FieldTrip using MATLAB 2010b on a 64-bit Linux platform.

^{1)}