eConnectome: A MATLAB Toolbox for Mapping and Imaging of Brain Functional Connectivity

Abstract

We have developed a MATLAB-based toolbox, eConnectome (electrophysiological connectome), for mapping and imaging functional connectivity at both the scalp and cortical levels from the electroencephalogram (EEG), as well as from the electrocorticogram (ECoG). Graphical user interfaces were designed for interactive and intuitive use of the toolbox. Major functions of eConnectome include EEG/ECoG preprocessing, scalp spatial mapping, cortical source estimation, connectivity analysis, and visualization. Granger causality measures such as Directed Transfer Function and adaptive Directed Transfer Function were implemented to estimate the directional interactions of brain functional networks, over the scalp and cortical sensor spaces. Cortical current density inverse imaging was implemented using a generic realistic geometry brain-head model from scalp EEGs. Granger causality could be further estimated over the cortical source domain from the inversely reconstructed cortical source signals as derived from the scalp EEG. Users may implement other connectivity estimators in the framework of eConnectome for various applications. The toolbox package is open-source and freely available at http://econnectome.umn.edu under the GNU general public license for noncommercial and academic uses.

1. Introduction

Brain activity is distributed in the three-dimensional space and evolves in time. The brain networks are formed and characterized by organized neuronal oscillations that span several orders of magnitudes in frequency. The spatio-temporal distribution of brain activity and the network behavior provide important physiological and psychological information and it is of significance to image brain functional connectivity for understanding the brain functions and dysfunctions (Ioannides, 2007).

Electrophysiological signals including the electroencephalogram (EEG) and electrocorticogram (ECoG) have been widely used to reveal dynamic activity and functional connectivity of the brain due to their excellent temporal resolution on the order of milliseconds. Recent methodological developments have been made for mapping the brain activity in high spatial resolution while maintaining the millisecond temporal information (He and Lian, 2005; He and Liu, 2008). However, images of brain regions activated at every instant alone do not convey sufficient information with respect to how these regions communicate with each other. The concept of brain functional connectivity thus now plays an important role in neuroscience as a way to understand the organized behavior of brain regions beyond mapping and localization of their activities (Varela et al., 2001).

Several connectivity analysis techniques have been developed to meet this need. One of the most commonly utilized connectivity tools in fMRI data, Structural Equation Modeling (SEM), has been widely used to identify the directional interactions between ROIs identified from the fMRI paradigms (Tomarken et al., 2005). In SEM, a priori information or calculated assumptions regarding the network structure must be made prior to these calculations. Another widely used approach is Granger causality (Granger, 1969), which is a data-driven approach to assess the connectivity among different brain regions. Different from the model-based connectivity analysis (e.g. SEM), the Granger causality analysis can be used to determine the directional causal interaction among electrophysiological signals. Particularly, the measure of directed transfer function (DTF) has been developed to describe the causality among an arbitrary number of signals while the traditional Granger causality was limited in a bivariate manner (Kaminski et al., 2001; Babiloni et al., 2005; Astolfi et al., 2007). The Granger causality analysis has been successfully applied to data ranging from local field potentials (Wang et al., 2007) to intracranial recordings (Franaszczuk et al., 1994; Brovelli et al., 2004; Wilke et al., 2009, 2010) and to noninvasive recordings (Babailoni et al. 2005; Ding et al., 2007). In addition, partial directed coherence (PDC) has also been proposed to assess the Granger causality (Baccala and Sameshima, 2001). Investigations on electrocortical data from patients undergoing pre-surgical observations have shown successful identification of ictal sources that were highly correlated with the clinically identified foci (Wilke et al., 2010). In the meanwhile, applications to the noninvasive EEG/MEG recordings were desirable but the far-field nature of these noninvasive recordings complicates the estimation of causal interactions with the head volume conductor effect. This challenge was addressed by an innovative approach of combining electrophysiological source imaging with the Granger causality analysis, which has demonstrated promising applications for noninvasively delineating the brain network connectivity under normal (Astolfi et al., 2004; Babiloni et al., 2005) and pathologic conditions (Ding et al., 2007).

In the present study, we have developed a MATLAB toolbox, the eConnectome (Electrophysiological Connectome) software, which implemented the above discussed techniques for mapping and imaging brain functional connectivity from the EEG and ECoG recordings (He et al., 2010). The eConnectome is an open-source MATLAB software package with graphical user interfaces. As part of the efforts of the Human Connectome project, which shall be aimed at mapping and imaging structural and functional neural circuits and networks of human brain, the development of eConnetome was intended to facilitate the investigation of functional brain connectivity. It provides an interactive platform for analysis of electrophysiological signals, including EEG/ECoG preprocessing, scalp spatial mapping, source imaging, functional connectivity analysis and visualization. Particularly, the implemented connectivity measures include the DTF and adaptive DTF (Wilke et al., 2008) algorithms, which may be used to map functional connectivity. An EEG-based cortical source imaging module was also implemented, which enables the estimation of cortical source imaging and the subsequent connectivity analysis of cortical sources. Statistic evaluation of the connectivity was conducted using the surrogate approaches. Visualization of the EEG/ECoG images and connectivity patterns can be achieved at both the scalp and cortical surfaces. The remainder of this paper describes the principles of the algorithms implemented and presents representative results from simulations and real data applications.

2. Methods

2.1 Overview of the use of the toolbox

The eConnectome toolbox is developed in MATLAB (Mathworks, Inc.) with graphical user interfaces as an open source package. It is integrated by the modules of preprocessing, source imaging, and connectivity analysis, which can be called individually or coordinately for EEG/ECoG processing, as illustrated in Fig. 1. While the focus of the toolbox lies on the mapping and imaging of functional connectivity, a set of preprocessing tools were easily available to handle the raw electrophysiological signals in the time and frequency domains. Three-dimensional visualization of the brain activity images and connectivity patterns was implemented at both the sensor and source levels based on the standard Montreal Neurological Institute (MNI) brain (Collins et al, 1994) or a user-defined anatomy.

Fig. 1.

The framework of the eConnectome toolbox. A graphical user interface can be started by calling ‘econnectome’ function in the command window of MATLAB. The EEG and ECoG modules can then be called individually. EEG/ECoG preprocessing, source imaging, and connectivity analysis using DTF and ADTF were implemented in the current version of the toolbox. Graphical representation of EEG/ECoG waveforms, scalp or cortical potential distributions, scalp or cortical connectivity patterns can be visualized.

The graphical user interfaces of the eConnectome allow users to analyze EEG/ECoG data interactively and intuitively without MATLAB programming experience. Several primary graphical user interfaces are illustrated in Fig. 2. The MATLAB-based interface also allows users to run modules in command line or write customized modules with available functions and interfaces. A uniform structure ‘ECOM’ was designed to store EEG/ECoG data including acquisition information (e.g. sampling rate), electrodes locations, time series and event information (e.g. onset time). Intermediate data such as preprocessed EEG/ECoG data, estimated cortical sources and connectivity measures can be exported for later analysis and review.

Fig. 2.

The main user interfaces in the eConnectome toolbox. (a) Scalp and cortical source imaging of a typical event-related potential (VEP data, see section 3.1). Functions of scalp potential mapping and source imaging can be activated by interactive selection of a time point. (b) Estimation of connectivity based on DTF/ADTF (ictal ECoG data, see section 3.3.1). The time interval and frequency band can be set interactively. The optimal order for the autoregressive model can be determined according to the curves plotted based on the Final Prediction Error (FPE) criterion (Akaike, 1971) and Schwarz Bayesian Criterion (SBC) (Schwarz, 1978). (c) Connectivity visualization (interictal ECoG data, see section 3.3.2). Stationary or time-varying information flows among multiple channels can be illustrated using graphics (upper left) and image (upper right). A set of options (bottom) is provided to control the visualization properties of the connectivity patterns.

The first beta version of the eConnectome was released on March 12, 2010, and the first full version (V.1.0) of the eConnectome was released on August 19, 2010. There have been more than 500 downloads from the eConnectome website (http://econnectome.umn.edu/) and from the online directory of the Neuroimaging Informatics Tools and Resources Clearinghouse (NITRC) at the National Institute of Health (NIH). The MVAAR (Multivariate Adaptive Autoregressive) modeling tool in the TSA (Time Series Analysis) package (Schlögl, 1996-2002) is required for the ADTF function and is included in the eConnectome toolbox. Two additional packages, the Regularization Tools (Hansen, 2007) and the ARfit package (Schneider and Neumaier, 2001), need to be downloaded and included for the source imaging and DTF functions, respectively.

2.2 Preprocessing of EEG/ECoG data

Multi-channel EEG or ECoG recordings can be loaded into the software for preprocessing in the time domain including artifact rejection, baseline correction, temporal filtering and electrodes co-registration. The EEG and ECoG data can then be used to construct and visualize potential and spectrum maps over a generic realistic geometry of scalp and cortex, respectively. Time-frequency representation of each electrode in a trial can be calculated using the Complex Morlet's wavelet (Qin et al., 2004; Qin & He, 2005) and visualized. Paradigm-related analysis was available in the toolbox for extracting the event-related potentials (ERP). The non-phase-locking type of analysis was also implemented to calculate the event-related synchronization / desynchronization (ERD/ERS, Pfurtscheller et al., 1998). The ERD/ERS was defined as the percentage change of power in the event period relative to the reference period within the frequency band of interest (Yuan et al., 2008). The power of event or reference periods was averaged across trials before calculating ERD/ERS.

2.3 Directed Transfer Function

The Directed Transfer Function (DTF) is a frequency-domain estimator of causal interaction based on the multivariate autoregressive (MVAR) modeling. As such, it is necessary that this method be applied to quasi-stationary datasets (Kaminski & Blinowska, 1991). To calculate the DTF measures, signals Y(t) from multiple channels are firstly modeled as the following MVAR process:

$$\sum _{k=0}^p\mathrm{\Lambda }\left(k\right)\mathbf{\text{Y}}\left(t-k\right)=\mathbf{\text{E}}\left(t\right),\text{with}\mathrm{\Lambda }\left(0\right)=\mathbf{\text{I}}$$ (1)

where E(t) is a vector of a multivariate zero-mean uncorrelated white noise process, Λ (1), Λ (2),…, and Λ (p) are the N×N matrices of model coefficients and the model order p can be determined using the Final Prediction Error (FPE) criterion (Akaike, 1971) and Schwarz Bayesian Criterion (SBC) (Schwarz, 1978). In order to investigate the spectral properties of the examined process, the above equation are transformed to the frequency domain:

$$\mathrm{\Lambda }\left(f\right)\mathbf{\text{Y}}\left(f\right)=\mathbf{\text{E}}\left(f\right),\text{where}\mathrm{\Lambda }\left(f\right)=\sum _{k=0}^p{\mathrm{\Lambda }}_k{e}^{-j2\pi f\mathrm{\Delta }tk}$$ (2)

This equation are then rewritten as (3)

$$\mathbf{\text{Y}}\left(f\right)={\mathrm{\Lambda }}^{-1}\left(f\right)\mathbf{\text{E}}\left(f\right)=\mathbf{\text{H}}\left(f\right)\mathbf{\text{E}}\left(f\right)$$ (3)

where H(f) is the inverse of the frequency-transformed coefficient matrix, Λ (f), and is defined as the transfer matrix of the system. From the transfer matrix, the DTF measures, γ²_ij(f) (Kaminski and Blinowska, 1991), is defined by the elements of the transfer matrix in the spectrum domain which describes the directional causality from channel j to channel i:

$${\gamma }_{ij}^2\left(f\right)=\frac{{\left|H_{ij}\left(f\right)\right|}^2}{\sum _{m=1}^k{\left|H_{im}\left(f\right)\right|}^2}$$ (4)

where k is the number of channels, which may be the number of sensors in the sensor domain, or the number of regions of interest in the source domain. Note that the DTF measures are simply a function of frequency, which can be selected according to the frequency range of interest.

The ARfit package (Schneider and Neumaier, 2001) is used in the DTF computation function for the estimation of multivariate autoregressive models.

2.4 Adaptive Directed Transfer Function

While the DTF measure is suitable for the quasi-stationary signals, the adaptive DTF (ADTF), a time-varying multivariate method, has been developed for the estimation of rapidly changing connectivity relationships between cortical areas of the human brain (Wilke et al., 2008). Similarly with DTF estimation, it is based on the modeling of the adaptive MVAR (AMVAR) process. The multiple-channel signals are described as follows:

$$\mathbf{\text{X}}\left(t\right)=\sum _{i=1}^p\mathrm{\Lambda }\left(i,t\right)\mathbf{\text{X}}\left(t-i\right)+\mathbf{\text{E}}\left(t\right)$$ (5)

where X(t) is the data vector over time, Λ (i, t), are the matrices of time-varying model coefficients, E(t) is multivariate independent white noise and p is the model order. The time-varying coefficient matrices of the AMVAR were resolved by using the Kalman filter algorithm (Arnold et al., 1998). With the time-varying model coefficients, the transfer function H(f, t) can thus be obtained from the time-varying transfer matrix. The adaptive DTF values were then defined as a function of both time and frequency as follows:

$${\gamma }_{ij}^2\left(f,t\right)=\frac{{\left|H_{ij}\left(f,t\right)\right|}^2}{\sum _{m=1}^k{\left|H_{im}\left(f,t\right)\right|}^2}$$ (6)

As the causality measure is obtainable at each time instant, the ADTF allows the observation of rapidly changing influences between the cortical areas and is suitable for analysis of short duration signals such as interictal activities (Wilke et al., 2009), and event-related potentials.

The MVAAR (Multivariate Adaptive Autoregressive) modeling tool in the TSA (Time Series Analysis) package (Schlögl, 1996-2002) is used in the ADTF computation function.

2.5 Electrophysiological Source Imaging

Although the DTF and ADTF measures can be directly applied to the multi-channel signals recorded from EEG or ECoG sensors, the estimation of causal interactions from the EEG data can be complicated by the volume conductor effect whereas it is less an issue for the near-field ECoG recordings. Our solution to reduce the volume conduction is thus by reconstructing the source signals in the brain that underlie the sensor signals. The cortical current density (CCD) source model (Dale and Sereno, 1993) was used to solve the inverse problem from the scalp EEG to cortical source distribution using minimum norm estimate (MNE) or lead field weighted minimum norm (WMN) algorithm with the aid of the boundary element method (He et al., 1987; Hämäläinen and Sarvas, 1989). A high-resolution cortical surface consisting of 41136 triangles was segmented and reconstructed for visualization from the MRI images of the Montreal Neurological Institute (MNI) brain using the Curry software (NeuroScan, North Carolina, USA). A down-sampled cortical surface with 7850 dipoles formed the calculated source space. The dipoles were constrained to the gray matter with their orientations perpendicular to the local cortical surface. A scalp surface, a skull surface and a brain surface were segmented and reconstructed from the MNI brain. The scalp surface consisting of 2054 triangles formed the sensor space. Such generic realistic head model has been suggested to provide improved accuracy in source analysis (Darvas et al., 2006; Valdés-Hernández et al., 2009). A high-resolution lead field matrix (2054×7850) was pre-computed relating all the scalp triangles to the sources. A specific lead field matrix for a user's electrode montage can thus be constructed as a subset of the pre-computed lead field matrix to solve the inverse problem. The electrode system includes 10-5 system or user defined electrode montages. The solution of the inverse problem yielded estimates of continuous time courses for cortical sources. Twenty-six predefined cortical regions of interest (ROI) according to Brodmann Areas (such as area 5, 6, etc.) are available and user-defined ROIs can be created interactively. The ROI source can then be computed by averaging estimated cortical sources in the ROI. With the ROI sources, the cortical ROI functional connectivity can be computed using the DTF or ADTF method in selected frequency components among selected ROIs. The solution of MNE or WMN can be derived using Tikhonov regularization in the Regularization Toolbox (Hansen, 2007).

2.6 Statistic Assessment of Connectivity

The above DTF/ADTF functions yield arbitrary values representing the functional connectivity, which, however, are still subject to statistical assessments of their significance. Since the DTF/ADTF measures have a highly nonlinear relation to the time series from which they are derived, it is difficult to apply traditional parametric statistical methods. Instead, a nonparametric method based on surrogate data is used to assess the significance of the estimated connectivity measures (Theiler et al., 1992; Palus and Hoyer, 1998; Ding et al., 2007). In this method, the original time series were transformed to the Fourier space, in which the phases are randomly shuffled without changing the magnitude. The surrogate data in the Fourier space are then transformed back to the time domain. This process of phase shuffling preserves the spectral structure of the time series, which is suited for DTF and ADTF analysis as both are measures of frequency-specific causal interactions. After shuffling, the connectivity estimation is applied to the surrogate data. The shuffling and connectivity estimation procedures are repeated by a certain number of times (e.g. 1000), yielding a distribution of the DTF (or ADTF) values under the null hypothesis that no connectivity exists. Based on this empirical distribution, the critical value of significance can be set at a desired level, e.g. p < 0.05 (Ding et al., 2007). The statistical assessment procedure is only implemented for connectivity estimation.

2.7 Visualization of Functional Connectivity

The directional connectivity patterns are represented by arrows pointing from one signal channel (“the source”) toward another (“the target”), either at the EEG/ECoG sensor level or the cortical source level. The arrow's color and size are used to code the strength of the functional connectivity estimated between the source and the target. The connectivity patterns in terms of the total inflow for each target channel or each ROI (defined as the normalized sum of the statistically significant connections from all the other EEG/ECoG channels or source ROIs toward the target channel or ROI) is represented by a color-coded sphere centered on the target channel or ROI, whose color and size are linearly related to the total inflow (Babiloni et al., 2005). The same conventions are used to represent the total outflow from an EEG/ECoG channel or a source ROI. At the sensor or source level, the connectivity patterns can be visualized overlaying on the scalp or cortex surface where signals originated, which allows a combined presentation of spatiotemporal information and its embedded connectivity. Connectivity patterns at the EEG sensor level can also be visualized overlaying on a spherical head model, where the standard 10-5 electrode system (Oostenveld and Praamstra, 2001) is used.

3. Results

3.1 ERP Analysis

Fig. 3(a) shows a segment of continuous EEG data in a visual task. The subject was instructed to stay motionless while passively viewing a flashing check board (Fig. 3(b), upper left panel) at the lower right quadrant (marker ‘S2’) of the screen. ERP evoked by the stimuli (Fig. 3(b), lower left panel) shows an early peak at 76 ms predominantly from the left posterior electrodes (Fig. 3(b), upper right panel). Source imaging results further localized the early visual response to V1 area in the left hemisphere (Fig. 3(b), lower right panel), which is in line with the retinotopic organization of human primary visual cortex.

Fig. 3.

(a) A segment of visual evoked EEG recordings. Marker S2 represents stimulus onsets. (b) Scalp potential mapping (upper right) and source imaging (lower right) at an early peak of the averaged VEP (lower left). (c) Scalp ERS/ERD mapping of mu rhythm during a right-hand movement task.

3.2 ERD/ERS Analysis

While ERP represents the phase-locking feature of brain activity, the non-phase-locking oscillations can also be analyzed using eConnectome. Fig. 3(c) shows the ERD and ERS of mu rhythm during a right hand movement task. A blocking (ERD) of mu rhythm over the contralateral scalp and an enhancement (ERS) of mu rhythm over the ipsilateral scalp can be observed.

3.2 ECoG Potential Mapping

ECoG recordings are widely used to aid in the presurgical localization of epileptogenic brain in patients suffering from medically intractable epilepsy. Fig. 4(a) shows a period of quasi-stationary ECoG waveforms recorded during a seizure of a patient. The EcoG potential map at an early spike around the seizure onset (Fig. 4(b)) indicates a focus of seizure activity from temporal lobe electrodes, which overlaps but is not well consistent with the epileptogenic zones resected in the surgery (Fig. 4(c)). Because of the rapid speed at which seizures propagate throughout the cortex, it is challenging to determine the origin of seizure onset solely from the ECoG waveforms and cortical potential distribution.

Fig. 4.

(a) A segment of ictal ECoG waveforms. (b) Cortical potential mapping of the ictal ECoG at an early latency (see (a)) after the seizure onset. (c) The seizure-onset zones (SOZs) determined by the epileptologist are shown in red highlight. (d) In the ictal ECoG data, the electrodes with significant outflows calculated using DTF are localized in the vicinity of SOZs (see (c)) identified by epitologists. (e) A segment of interictal ECoG spike waveforms. (f) Total outflows of the channels at the interictal spike peak (see (e)) based on the ADTF method. The identified source focus is in concordance with the SOZ (see (c)) determined by epitologist.

3.3 Granger Causality Analysis

3.3.1 Localize causal sources from ictal ECoG using DTF

Because of the ambiguity of cortical potential mapping, the seizure data were analyzed using the DTF method. From the ictal ECoG data presented in Fig. 4(a), we calculated the connectivity (p < 0.01) and visualized the total outflow from each ECoG channel (Fig. 4(d)). A temporal lobe focus and a frontal focus were identified as causal sources (red and yellow nodes in Fig. 4(d)). A good correlation can be observed between the spatial locations of the causal source activity and the seizure onset zone (SOZ) identified by experienced clinical epileptologist. The patient underwent a right temporal lobectomy and resection of the frontal focus, and experienced a 70% reduction in seizure frequency following the surgery.

3.3.2 Localize causal sources from interictal ECoG using ADTF

ADTF further improves the connectivity analysis by taking the rapid changing of connectivity relationships into consideration. An interictal spike (Fig. 4(e)) recorded in the same patient was analyzed using the ADTF method (p < 0.05). The greatest amount of information outflow is located in the posterior ECoG grids (Fig. 4(f)), which is consistent with the right temporal epileptogenic region identified by clinical epitologists. However, no causal source was found adjacent to the right frontal focus. This can be explained by the fact that irritative zones identified from interictal spikes may not be necessarily consistent with epileptogenic zone identified from seizures. In fact, visual inspection of the original ECoG data also found that the majority of the spiking activity was observed in the posterior ECoG grid with little to no activity observed in the vicinity to the frontal focus.

3.3.3 Localize cortical causal source from scalp EEG

Causal connectivity can also be estimated from source imaging results. We simulated two cortical dipole sources. Their waveforms were generated so that source 1 is the primary driver and source 2 is the sink. Continuous EEG (Fig. 5(a)) was generated by solving an EEG forward problem, and 10% Gaussian white noise was added. Cortical source distribution (Fig. 5(c)) was derived by solving an inverse problem at the peak of the waveform (Fig. 5(b)). Two regions were shown with significant source activity and thus were selected as source ROIs. Source waveforms at the two ROIs (Fig. 5(c)) were estimated, and the DTF analysis (Fig. 5(d)) showed directional information flow from source 1 to source 2 (p<0.05), which is consistent with the simulation setting.

Fig. 5.

From simulated EEG signals (see (a)), two source regions were localized by solving the cortical current source imaging problem (see (b), (c)). Using the estimated time courses of the two ROIs (see (c)), DTF analysis identified directional information flow from source 1 to source 2 (see (d)), which is consistent with the simulation setting.

4. Discussion

Mapping functional connectivity of human brain represents a grand challenge to neuroscience and neuroimaging research. We have developed the eConnectome, a MATLAB toolbox for mapping and imaging brain functional connectivity from electrophysiological measurements. There are many related free and open-source software packages for analysis of electrophysiological data. EEGLAB (Delorme and Makeig, 2004) is an interactive MATLAB toolbox for processing continuous and event-related electrophysiological data. FieldTrip (http://fieldtrip.fcdonders.nl/) is a MATLAB software toolbox for MEG and EEG analysis. NUTMEG (Dalal et al., 2004) is an MEG/EEG analysis toolbox for reconstructing and visualizing the spatiotemporal dynamics of brain sources. Brainstorm (http://neuroimage.usc.edu/brainstorm/) is a MATLAB software dedicated to MEG and EEG data visualization, processing and cortical source estimation. Compared to existing software packages, a unique feature of the eConnectome toolbox is that it provides a flexible and easy-to-use platform to image brain functional connectivity using EEG or ECoG data and to visualize functional connectivity patterns over the realistic geometry scalp or cortical surface. The toolbox is aimed at addressing where, when and how neuronal assemblies are activated and coordinated and allows users to obtain integrated connectivity visualization results.

DTF is a method to extract directional connectivity from multivariate time series data, and considers the multivariate time series as a stationary process. Previous studies from our group and others have demonstrated its applications to study causal sources in normal brain functions (Babiloni et al., 2005; Astolfi et al., 2007) or abnormal brain disorders (e.g., epilepsy) (Ding et al., 2007; Wilke et al., 2010). However, while real electrophysiological recordings may be approximated to be stepwise stationary, it is still difficult to decide the terms of stationarity. We therefore integrated the ADTF (Wilke et al., 2008) module in eConnectome that extracts time-varying directional connectivity from multi-channel EEG, ECoG or source ROI time series data without a priori information on the terms of stationarity. As we have shown previously (Wilke et al., 2008, 2009) and in the present results, ADTF holds the promise to reveal dynamic brain connectivity.

While DTF has been shown to be able to reliably recover the connectivity patterns under a wide range of signal-to-noise ratios and recording lengths (Astolfi et al., 2005, 2007), it is noteworthy that the formulation of DTF makes it possible in certain conditions to derive an incorrect estimation of the paths between cortical areas. One of the shortcomings of the DTF method is the potential inclusion of the indirect pathways. For example, supposing A->B and B->C (with no direct interaction between A and C), DTF similar to pair measures may indicate A->C. With PDC, this potential limitation is presumably reduced by the exclusion of indirect pathway information in the connectivity calculation. Another estimation method, direct DTF (dDTF), has also been proposed to deal with such indirect pathway by combining the DTF with PDC. However, a recent study (Astolfi et al., 2007) found in simulation data that the DTF had the lowest error variance in the calculation of the direct pathways (i.e. A->B and B->C) compared to the PDC and dDTF. Furthermore, when all the three connectivity measures, DTF/dDTF/PDC, were applied to experimental data of the Stroop protocol, there was no significant difference in the estimation of the causality drivers and sinks of the cortical sources using the three methods.

An important issue in connectivity analysis is to estimate the true connectivity patterns among brain regions of interest. The volume conduction effect introduces difficulty as electrophysiological signals (e.g. EEG and MEG) are recorded as mass response from large areas of activated neurons. The phase scrambling is a procedure used to assess the statistical significance of an arbitrary connectivity value, which is calculated based on the AR modeling. By using the scrambling process, the calculated original connectivity value will be compared to a population of bootstrapped values under a null hypothesis of no effective connectivity being present, i.e. the scrambled data. However, the significance level determined by the phase scrambling is not necessarily related to the volume conduction effect. The scrambling may not be able to fundamentally resolve such apparent connectivity induced by volume conduction, which are likely the same for other assessment methods based on the scalp measurements. In the eConnectome software we have used the approach of first estimating cortical source signals and then assessing the connectivity patterns in the source domain. Such deconvoluted inverse solution is expected to have less mixing as compared with scalp EEG signals. Furthermore, we have adapted the concept of ROI to image the functional connectivity among cortical regions. Such ROI approach shall further reduce the effect of mix of signals, as less mixing would be anticipated when signals are derived from locations, which are not adjacent to each other.

The present toolbox is designed for both multi-trial event-related and single-trial electrophysiological data sets. ERP analysis can be performed on the multi-trial event-related EEG or ECoG recordings to get the phase-locked average of data for source imaging or functional connectivity analysis. A single-trial epoch of interest in a continuous EEG or ECoG data can also be extracted for connectivity analysis, e.g., interictal spikes (Wilke et al., 2008, 2009). When analyzing stimulus triggered activity which usually has short duration, it is difficult to use DTF measure to estimate the Granger causality. The adaptive DTF may be used to tackle such task, or more sophisticated analysis may be needed (Wang et al., 2008).

There are yet some limitations for the current toolbox package. Currently only a few EEG/ECoG file formats are supported, including ASCII file format and MATLAB .mat file format. More file formats compatible with various electrophysiological recording devices is planned to be integrated in the future releases of the toolbox. Only two cortical source imaging methods (MNE and WMN) are currently implemented and more optional source imaging methods are planned to be implemented in eConnectome. Some functions such as dynamic source imaging and statistical significance testing are time-consuming due to the intensive computation and limited execution speed of MATLAB. C-language compiled modules can be used to replace these parts, and the software can be more computationally efficient. For connectivity analysis only DTF and ADTF are implemented. Future implementation of PDC would be desirable. In addition to EEG and ECoG, MEG is another major electrophysiological metric that can capture transient neural activities in milliseconds. Currently only EEG and ECoG are supported in eConnectome and we plan to add a MEG functional connectivity module in the future. Furthermore, multimodal functional neuroimaging has been pursued by integration of EEG/MEG with fMRI (Im et al., 2006, 2007; He and Liu, 2008; Liu and He, 2008; Yang et al., 2010). It will also be highly desirable to add the function of integration of EEG/MEG with fMRI in the future.

While we have attempted to include as much as possible the connectivity mapping in the present version of eConnectome software, by no means we are suggesting the implemented DTF/ADTF are the only desirable algorithms for use for all the neuroscience problems. Rather, this work reports our efforts in developing an open-source and mouse-driven software, which can be used for source localization and functional connectivity mapping from EEG/ECoG data. While the friendly user interface of eConnectome provides user of little MATLAB experience with access of the functions by mouse clicking, it also allows flexible usage of customized codes in the MATLAB environment jointly with the provided functions. Users may opt to simply use the DTF/ADTF functions in the software for their research. Or they could execute other alternative connectivity estimation algorithms under the MATLAB-based interface to fit into their research needs. As such, the eConnectome provides a software platform to significantly facilitate the research of functional brain connectivity, and much remains to be investigated on what would be the optimal way to mapping such connectivity.

The eConnectome toolbox can be freely downloaded from http://econnectome.umn.edu under the GNU general public license (http://www.gnu.org/licenses/gpl.txt) for non-commercial and academic uses. A set of simulated and realistic EEG and ECoG sample data are included in the download package, including a simulated 62-channel EEG data, an averaged 62-channel Visual Evoked Potential EEG data, a simulated 9-channel ECoG data for testing DTF, a simulated 4-channel ECoG data for testing ADTF, a realistic 64-channel seizure ECoG data, and a multi-trial VEP data. A manual describing the details of how to use the toolbox and a tutorial presenting examples with the sample data are included as well on the eConnectome website. An email account econnect@umn.edu welcomes user feedbacks for improving the toolbox.

Highlights.

1. Open source software for connectivity mapping from EEG and ECoG;

2. Open source software for mapping connectivity over source domain from EEG;

3. Comprehensive software package with graphic interface to process and visualize brain activity and connectivity from electrophysiological recordings.