© 2010 Federation of European Psychophysiology Societies L. Astolfi et al.:Journal Time-Varying of Psychophysiology Co rticalC onn 2010; ectivity Hogrefe Vol. 24(2):83–90 Estimation Publishing
Article
Time-Varying Cortical Connectivity Estimation from Noninvasive, High-Resolution EEG Recordings Laura Astolfi1,2,3, Febo Cincotti1,3, Donatella Mattia1, Fabrizio De Vico Fallani1,3, Giovanni Vecchiato1,3, Serenella Salinari2, Gianni Vecchiato1,3, Herbert Witte4, and Fabio Babiloni1,3 1
IRCCS “Fondazione Santa Lucia,” Rome, Italy, 2Department of Computer Science and Systems of the University of Rome “La Sapienza,” Italy, 3Department of Physiology and Pharmacology of the University of Rome “La Sapienza,” Italy, 4Institute of Medical Statistics, Computer Sciences, and Documentation, Schiller University of Jena, Germany Abstract. Objective: In this paper, we propose a body of techniques for the estimation of rapidly changing connectivity relationships between EEG signals estimated in cortical areas, based on the use of adaptive multivariate autoregressive modeling (AMVAR) for the estimation of a time-varying partial directed coherence (PDC). This approach allows the observation of rapidly changing influences between the cortical areas during the execution of a task, and does not require the stationarity of the signals. Methods: High resolution EEG data were recorded from a group of spinal cord injured (SCI) patients during the attempt to move a paralyzed limb. These data were compared with the time-varying connectivity patterns estimated in a control group during the real execution of the movement. Connectivity was estimated with the use of realistic head modeling and the linear inverse estimation of the cortical activity in a series of regions of interest by using time-varying PDC. Results: The SCI population involved a different cortical network than those generated by the healthy subjects during the task performance. Such a network differs for the involvement of the parietal cortices, which increases in strength near to the movement imagination onset for the SCI when compared to the normal population. Conclusions: The application of time-varying PDC allows tracking the evolution of the connectivity between cortical areas in the analyzed populations during the proposed tasks. Such details about the temporal evolution of the connectivity patterns estimated cannot be obtained with the application of the standard estimators of connectivity. Keywords: time varying cortical connectivity, PDC, RLS, linear inverse procedure, spinal cord injury
Introduction The estimation of brain connectivity allows describing the functional links established between different cortical areas during the execution of a particular experimental task and is an important step toward understanding the functional organization of the brain (Horwitz, 2003; Urbano et al., 1998). The importance of using noninvasive methods for the measurement of brain activity has focused more and more attention on techniques such as electroencephalography (EEG), magnetoencephalography (MEG), and functional resonance imaging (fMRI). While the fMRI measurements allow for a very high spatial resolution (on the order of millimeters) but of a poor temporal resolution (order of seconds), EEG and MEG show a very high temporal resolution (on the order of milliseconds) with a poor spatial resolution (order of centimeters) (Astolfi et al., 2005; BabiHogrefe Publishing
loni et al., 2000, 2004, Gross, Timmermann, Kujala, Salmelin, & Schnitzler, 2003; Oliveri et al., 2003; Urbano, Babiloni, Onorati, & Babiloni, 1996). To overcome the limitations of conventional EEG and MEG, a body of techniques has been developed in the last 15 years to improve the spatial resolution of the EEG, under the name of highresolution EEG (Babiloni et al., 2000). These include the use of a large spatial sample of the EEG on the scalp, a multicompartment head model (scalp, skull, dura mater, cortex) constructed from individual MRI from each subject, a distributed source model, and regularized linear inverse source estimates of cortical current density (linear inverse problem [LIP]). The result is a reconstruction of the electrical activity at the cortical level with a spatial resolution that is greatly improved with respect to the conventional EEG. There is also an increasing interest in the use of mathematical algorithms for estimating the flow of information Journal of Psychophysiology 2010; Vol. 24(2):83–90 DOI: 10.1027/0269-8803/a000017
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between different scalp or cortical areas in humans (Baccalà & Sameshima, 2001; David, Cosmelli, & Friston, 2004). Recent studies have stressed the limits of conventional pairwise methods with respect to the multivariate spectral measures based on the autoregressive modeling of multichannel EEG, in order to compute efficient connectivity estimates (Kus, Kaminski, & Blinowska, 2004). Among the multivariate methods, the partial directed coherence (PDC; Baccalà & Sameshima, 2001) is an estimator characterizing, at the same time, direction and spectral properties of the interaction between brain signals, and requires only one multivariate autoregression model (MVAR) model to be estimated from all the time series. However, the classical estimation of this method requires the stationarity of the signals; moreover, with the estimation of a unique MVAR model on an entire time interval, transient pathways of information transfer remain hidden. This limitation could bias the physiologic interpretation of the results obtained with the connectivity technique employed. To overcome this limitation, different algorithms for the estimation of MVAR with time-dependent coefficients were recently developed. Ding, Bressler, Yang, and Liang (2000) used a short-time windows technique, which requires the stationarity of the signal within short-time windows. Moeller, Shack, Arnold, and Witte (2001) proposed an application of the extension of the recursive least squares (RLS) algorithm with a forgetting factor to MVAR estimation. This estimation procedure allows for the simultaneous fit of one mean MVAR model to a set of single trials, each one representing a measurement of the same task. In contrast to short-window techniques, the multitrial RLS algorithm does not require the stationarity of the signals, and involves the information of the actual past of the signal, whose influence decreases exponentially with the time distance to the actual samples. The advantages of this estimation technique are an effective computation algorithm and a high adaptation capability. It was demonstrated by Moeller et al. that the adaptation capability of the estimation (measured by its adaptation speed and variance) does not depend on the model dimension. Simulations on the efficacy of time-variant Granger causality based on adaptive MVAR (AMVAR) computed by RLS algorithm were also provided (Hesse, Möller, Arnold, & Schack, 2003). In this paper we propose the use of the adaptive multivariate approach applied to high-resolution EEG techniques. The performances of some multivariate linear signal processing techniques have been recently investigated (Winterhalder et al., 2005). The quality of the time-varying PDC estimates have been validated by a previous simulation study (Astolfi et al., 2008), which showed the performances and suggested appropriate choices for the parameters to be set in such a method. Here, we describe the time-varying cortical connectivity patterns estimated in a group of spinal cord injury (SCI) patients and a group of controls during the attempt (or the execution) of a combined foot and lips movement. Such time-varying cortical connectivity patterns were estimated Journal of Psychophysiology 2010; Vol. 24(2):83–90
in regions of interest (ROIs) by using the time-varying PDC estimator previously developed (Astolfi et al., 2008). The experimental hypothesis is that the time-varying approach could shed light on the occurrence of similar or different rapidly shifting cortical networks in the two populations during the analyzed task. In particular, we would like to know if the attempts to move the affected limbs by SCIs could arose cerebral activations of either several “premotor” and more executive motor areas in such population. Such cerebral activity will be described in terms of the cortical network estimated with the PDC both in normal subjects and in SCI patients. In fact, the expected task-related differences in the estimated cortical functional networks might address some aspects of the cortical reorganizational processes that occur in the SCI population when compared to the normal one.
Materials and Methods Time-Varying Multivariate Connectivity Estimation PDC (Baccalà & Sameshima, 2001) is a method to determine the directed influences between any given pair of signals in a multivariate data set. The approach is based on an MVAR simultaneously modeling the whole set of signals. PDC is based on the concept of Granger causality (Granger, 1969), according to which an observed time series x(n) can be said to cause another series y(n) if the prediction error for y(n) at the present time is reduced by the knowledge of x(n)’s past measurements. In this study, we used an adaptive formulation of PDC (Astolfi et al., 2008), based on an AMVAR model. The time-dependent parameter matrices were estimated by means of the RLS algorithm with a forgetting factor. The RLS algorithm represents a particular variant of the Kalman filter. This recursive estimator for the AMVAR-parameter is characterized by a more universal practicability, since it requires less computational effort, and it is possible to extend this approach to the presence of multiple realizations of the same process. The extension to multiple trials was introduced by Moeller et al. (2001). The fitting procedure of the autoregressive (AR) parameters exploits the RLS technique with the use of a forgetting factor. It is based on the minimization of the sum of exponentially weighted prediction errors of the process past. Thereby, the weighting depends on an adaptation constant 0 ≤ c < 1 that controls the compromise between adaptation speed and the quality of the estimation. Values close to zero result in a slower adaptation with more stable estimations and vice versa. Effects of different weightings were shown in a simulation study (Astolfi et al., 2008). A comprehensive description of this algorithm may be found in (Hesse et al., 2003; Moeller et al., 2001). Hogrefe Publishing
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Experimental Design and EEG Recordings We examined five subjects with SCI (four males, one female, mean age 22.4 ± 2.8 years) and five healthy control subjects (CTRL; four males, one female, mean age 24.1 ± 1.5). Informed consent was obtained from each subject after explanation of the study, which was approved by the local institutional ethics committee. The SCIs were all of traumatic etiology and located at the cervical level. All patients had a stabilized lesion (mean distance from trauma 18.4 months, SD 6 months). Neurological status was assessed according to the American Spinal Injury Association (ASIA) standards. Lesion was complete in four patients (ASIA-A: complete motor and sensory loss below the lesion level) and incomplete in the remaining one. None of the SCI patients had suffered from a head or brain lesion associated with the trauma leading to the injury. The task consisted of repetitive self-generated attempted (SCI subjects) or overt (control subjects) executions of a right foot dorsal flexion at the ankle. To capture the EEG activity related to the attempted motor execution, SCI subjects were instructed to end the task by a brisk lip pursing (intact movements, FL’) whose electromyogram (EMG) functioned as a trigger for the subsequent EEG trial segmentation. As a control condition, in the healthy control group the data were collected from controls during foot movements simultaneously executed with lip pursing, (FL). Each task was repeated every 6–7 s in a self-paced manner. Scalp potentials were collected with a 96-channel EEG system (BrainAmp, Brainproducts GmbH, Germany). EEG data sampling frequency was 200 Hz and no hardware filtering was applied except for the internal antialiasing filter of the device. Three different frequency bands were considered in this study; alpha (8–12 Hz), beta1 (12–22 Hz), and beta2 (22–30 Hz). These bands were selected since it is known from the literature that EEG spectrum rapidly change in these bands before a movement occurs. Bipolar EMG was recorded with surface electrodes in order to detect the onset of foot and lip movements. One hundred single EEG trials were recorded for each subject. The EEG signals for each task condition were averaged separately and time-locked to onsets of EMG. Structural MRIs of the subject’s head, necessary for the realistic head modeling of each subject, were taken with a Siemens 1.5T Vision Magnetom MR system (Germany). The analysis period for the potentials time-locked to the movement execution was set from 1500 ms before to zero time (EMG trigger).
Estimation of the Cortical Activity The cortical signals were estimated from high resolution EEG recordings, by using realistic head models and a cortical reconstruction with an average of 5000 dipoles uniformly disposed along such cortical surface. The estimation Hogrefe Publishing
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of the cortical activity was obtained by the application of the linear inverse procedure as described in Babiloni, Babiloni et al., 2003. Cortical activity was then estimated in ROIs generated by the segmentation of the Brodmann areas on the accurate cortical model used. The average cortical signals obtained in each ROI were then subjected to the MVAR modeling in order to compute the PDC. The cortical ROIs employed in the study were drawn on the computer-based cortical reconstruction of the individual head models of the 10 subjects. Twelve ROIs, thought to be involved in the preparation and execution of simple self-generated movements, were defined on the cortical model, specifically: the supplementary motor area proper (SMAp) left and right; the caudal cingulate motor area (CMAc) from the left and right hemispheres; the primary motor foot (M1-foot) representational area and the primary motor lip (M1-lip) representational area, both from the left and right hemisphere; the superior parietal cortex, SP, and the premotor dorsal cortex, PMd, both in the left and right hemispheres. For each time point of the gathered ERP data, an estimate of the signed magnitude of the dipolar moment for each one of the 5000 cortical dipoles was obtained as described in (Babiloni, Babiloni et al., 2003). The instantaneous average of the dipole’s signed magnitude belonging to a particular ROI generates the representative time-value of the cortical activity in that given ROI. These waveforms can then be subjected to the estimation of connectivity patterns between ROIs by time-varying PDC.
Statistical Evaluation of Connectivity Measurements: The Estimation of the Null Distribution of Cortical Connectivity As PDC functions have a highly nonlinear relation to the time-series data from which they are derived, the distribution of their estimators is not well established, although a recent attempt has been made in this direction (Sato et al., 2009). This makes tests of significance difficult to perform. A possible solution to this problem was proposed (Kaminski, Ding, Truccolo, & Bressler, 2001) and consists of the use of a surrogate data technique (Theiler, Eubank, Longtin, Galdrikian, & Farmer, 1992), in which one generates an empirical distribution for a given estimator when interactions between signals are removed. Significance tests based on this empirical distribution can then be performed. Specifically, one randomly and independently shuffles the time-series data from each ROI to create a surrogate data set. A bivariate autoregressive model is then fit to the shuffled data and the PDC functions are computed from such a model. Carrying out this process many times, each time performed on an independently shuffled data set, it is possible to construct an empirical distribution for the PDC functions. Since the shuffling procedure destroys all the temporal structure in the data, Journal of Psychophysiology 2010; Vol. 24(2):83–90
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Figure 1. Time-varying connectivity patterns in the beta2 band [22–30 Hz], extracted at –500, –250, and 0 ms before the lips movement onset, for a representative subject of each group: first row, SCI patients; second row, control subjects. Reconstruction of the head and cortex of the subjects obtained from sequential MRIs. The different regions of interest selected are depicted in different colors and described by the labels. The color and size of the arrows code for the interaction strength (see color bars on the right).
this empirical distribution gives the variability for the PDC functions for the null hypothesis case. Using this distribution, one can then assess the significance of the causal measures evaluated from the actual data. Without having an explicit formulation for the shape of this distribution, one can, thus, compute an empirical threshold for a given significance level. A limit of this method results from the fact that it destroys interdependency among time series, as well as the temporal structure within a time series. In fact, in the above-mentioned procedure, samples from all the frequencies are combined into a single distribution, which is independent of frequency and gives a single threshold for all the PDC values. In order to randomize the sequential order while preserving the correlation structure, we adopted a variation of this method. The surrogate data set was created by shuffling the trials within each series, without shuffling single samples within a trial. In this way, we preserved the spectral properties of the time series, thus, being able to obtain a distribution for each frequency value and a consequent threshold dependent on frequency. The shuffling procedure was performed for a sufficient number of times to reach the statistical significance level set to 0.001%. Only the estimated PDC connections that were statistically significant (at p < .001, Bonferroni corrected for multiple comparisons), after the comparison with the surrogate distribution of the PDC values on the same ROIs obtained with this Montecarlo-like procedure (Astolfi et al., 2007), were considered for the analysis. This procedure allowed us to consider only the particular functional links not resulting from chance and different, in a consistent way, from the background EEG. Journal of Psychophysiology 2010; Vol. 24(2):83–90
Results By means of the linear inverse procedure, the estimation of the current density waveforms in the ROIs employed was performed for the 10 subjects. Time-frequency distribution of the instantaneous PDC was obtained for all the subjects from the set of cortical waveforms estimated in the 12 ROIs considered. The adaptation constant c was set to 0.02, according to the indications from a previous simulation study for the amount of data available (Astolfi et al., 2008). The optimum MVAR model order was 16 or 17 for the different subjects, as obtained by the Akaike information criterion (AIC). High values of connectivity could be noted, in particular, in the alpha [8–12 Hz] and beta2 [22–30 Hz] frequency bands, and involved mainly the PMd areas from the left and right hemispheres, the M1F left and right, the SMAp left and right, and the CMAc left and right. Figure 1 shows the time-varying connectivity patterns in the beta2 band, extracted at –500, –250, and 0 ms before the lips movement onset, provided for a representative subject of the SCI group and for a representative subject for the control group. Results are presented on the realistic reconstruction of the head and cortex of each subject, obtained from sequential MRIs. The different ROIs selected are depicted in different colors and described by labels. The connectivity links are represented by arrows, pointing from one cortical area (“the source”) toward another one (“the target”). The color and size of the arrows code for the interaction strength, with the minimum strength coded in black and the maximum in light yellow. Only statistically Hogrefe Publishing
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Figure 2. Time-courses of connectivity strength involving the parietal cortices, same representative subject of Figure 1, in the beta2 frequency band [22–30 Hz]. Time is expressed in ms from the EMG onset (0 time). Black shows the threshold of significance adopted.
Figure 3. Time-courses of connectivity strength between selected regions of interest, obtained for the 5 SCI patients (upper row, in red the average and the bar represents the standard deviation) and from the 5 control subjects (lower row, in blue, same conventions used), in the beta2 frequency band [22–30 Hz]. The thick line is the mean value of the time-varying connectivity strengths obtained across subjects of each group. The error bars describe the variance in each group. Time is expressed in ms from the EMG onset (0 time). The waveforms were normalized to allow comparison despite different power spectra. significant links are reported, with respect to a significance threshold computed as described in Astolfi et al. (2008). A common functional pattern involving the cingulate motor areas as a principal source of information directed toward the motor areas of the foot and the lips, as well as the premotor cortices, can be noted both in the SCI subject and in the control. The time evolution of the links revealed by time-varying PDC allows uncovering a different behavior in the two subjects, which would have been invisible to conventional estimators. In particular, the connection between the CMAc of the left hemisphere and the MIL of the same hemisphere is stable for the control subjects while its strength increases significantly in the period preceding the movement for the SCI subject. The connection from the Hogrefe Publishing
SMAp_R and the MIF_R, which is weak and appears only in the last 250 ms before the movement attempt for the SCI subject, shows, on the contrary, a different behavior for the control subject, increasing its strength during the movement preparation. Also the connection directed from the CMA of the left hemisphere and the MIF of the same hemisphere shows an opposite behavior for the two subjects. In fact, for the SCI (first row) it decreases in time and is absent at the EMG trigger (third figure of the first row). On the contrary, for the control subject this connection increases its strength during the movement preparation. The most interesting difference in the cortical network supporting the task is probably the one involving the parietal cortices in the SCI subject, which changes dramatically over time, by Journal of Psychophysiology 2010; Vol. 24(2):83–90
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assuming more importance near to the EMG onset with respect to the half second before. This involvement of the parietal areas in the task is completely absent in the control population. A detail of the time evolution of such pattern involving the parietal cortices for the SCI subject is shown in Figure 2. Such waveforms can be obtained by averaging the time-frequency distribution of connectivity given by time-varying PDC in the frequency band of interest (beta2), and describe how the connectivity link directed from one cortical area to another evolves in time. In order to compare results from different subjects in each group and between the two groups, we focused on the connectivity time course of the five SCI patients and the five healthy controls. We normalized the waveforms to allow comparison despite different power spectra across subjects, and then we reported mean value and variance of such waveforms in each group (SCI and controls). To avoid spurious results, only results statistically significant for at least three out of five subjects from each group were used and reported. Figure 3 shows the mean time courses of interaction strength between selected ROIs from each group of subjects analyzed. The first column refers to the SCI patients group; the second column refers to the control group. The thick line is the mean value of the time-varying connectivity strengths obtained across subjects of each group. The error bars describe the variance in each group. Time is expressed in ms from the EMG onset (0 time). The ROIs presented are the Brodmann area 6 of the right hemisphere (PMd_R), the primary motor area for the lips of the right hemisphere (M1L_R), and the SMAp left and right. For these functional connections, it is possible to recognize a common trend for the two groups of subjects. In particular, we noted a decrease of the connectivity strength from the premotor dorsal cortex of the right hemisphere (PMd_R) toward the primary motor area of the lips (M1L) during the 500 ms preceding the lips EMG onset in both groups of subjects. In addition, an increase of connectivity strengths was also observed during the period of time from 250 ms to the EMG onset between the SMAp and the M1L.
Discussion Methodological Considerations Previously performed simulation studies suggested that a maximum number of ROIs could be analyzed with the Granger-causality methods in the frequency domains (Astolfi et al., 2005, 2007). This limitation introduces a bias in the generality of the results obtained here, since a decision had to be made on the selection of the ROIs to be included in the analysis, in this particular case, the primary motor and premotor areas were selected. This limitation is a result of the nature of the MVAR processes and can be removed Journal of Psychophysiology 2010; Vol. 24(2):83–90
by using bivariate measures of Granger causality. However, such bivariate measures have the tendency to introduce spurious causal relations between signals (Astolfi et al., 2007). Other methodologies for the estimation of functional connectivity do not have these limitations, such as coherence or cross-covariance estimation. However, the information returned by cross-covariance or coherence cannot be discussed in terms of causal relations between signals, but rather in terms of the temporal correlation of the data that do not imply causality (Horwitz, 2003).
Experimental Considerations The application of the time varying cortical connectivity estimation techniques to the EEG data recorded from normal and SCI patients returned information about their cortical networks. In particular, the cortical network estimated in the control subjects highlights a substantially stable topology in the last 500 ms before the EMG onset, as observed by the second row of Figure 1, with small changes in the strength of the cortical connectivity between the primary and the supplementary motor cortices. Taken together, this evidence suggest a stable pattern of connectivity between the primary and premotor areas of the control subjects in the last 500 ms before the movement execution. This pattern was, in part, replicated in the SCI group, for the involvement of the motor and premotor cortices in the 500 ms before the EMG onset (first row of Figure 1) but the analysis of time-varying connections showed differences in the evolution of these links during movement preparation, in particular in the flows from the premotor to the primary motor areas. The time-varying PDC also showed similarities in the time courses between some areas in the two groups. The first row of Figure 3 shows the substantial agreement of the strength evolution over time for the premotor, and primary and supplementary motor areas for the SCI patients. The similarity to the time evolution of the cortical connectivity strength in the control population (second row of Fig. 3) is evident. The experimental evidence of the present study is in accordance with a previous study (De Vico Fallani et al., 2007) that also shows some functional links in the SCI group changing in time with respect to the control subjects. Moreover, that network differs for the involvement of the parietal cortices. A precise increment of the cortical connectivity between right and successively left superior parietal areas is observed in the group of SCI when compared to the control group. Such connectivity increases with time and is generated by both parietal cortices around the EMG onset, while almost absent at about half a second before. One possible interpretation relies on the fact that the attempt to move a paralyzed limb for the SCI patients needed more cortical resources than in the control population, because of the need to restore the sensation and the relative position of the lost limb within the body structure. In fact, it is already known that the imagination of the spatial relaHogrefe Publishing
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tionships between the limbs and the body structure are usually performed by the parietal cortices (Daprati & Sirigu, 2006; Fogassi & Luppino, 2005). In the case of the control group, this lack of connectivity between such cortical areas probably subtends an increase of the functional independence in the organization of the movement generated by the motor cortices, because the rather simple movements of the right foot may not be sufficient to elicit significant functional links from and to this area in normals (Babiloni, Carducci et al., 2003).
Conclusions In this paper we presented a methodology that allows tracking the evolution of the network of cortical connectivity from EEG recordings in populations of SCI and normal subjects. By using this tool we were able to enlarge the results already obtained by using a stationary approach for the estimation of cortical connectivity in a similar population of SCI patients (Mattia et al., 2009) when compared to controls. In particular, with the application of the methodology presented here, we inferred the precise time-course of the strengths of the estimated cortical network active during the task in both populations. Such results cannot be obtained with the conventional stationary analysis of connectivity.
Acknowledgments This study was performed with the support of the Programma Neuroscienze of the Compagnia di San Paolo of the European Union through the COST program NEUROMATH (BM0601), by the European IST Program FET Project FP6–003758, and by the German Research Foundation (DFG Priority Program SPP 1114, LE 2025/1–3, and BMBF “Bernstein Group Jena”).
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Fabio Babiloni Dept. Physiology and Pharmacology University of Rome Sapienza P.le A. Moro 5 00185 Rome Italy Tel. +39 32 8769-7914 Fax +39 06 2332-6835 E-mail
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