Filippo Carducci

Estimation of the cortical functional connectivity with the multimodal integration of high-resolution EEG and fMRI data by directed transfer function

Nowadays, several types of brain imaging device are available to provide images of the functional activity of the cerebral cortex based on hemodynamic, metabolic, or electromagnetic measurements. However, static images of brain regions activated during particular tasks do not convey the information of how these regions communicate with each other. In this study, advanced methods for the estimation of cortical connectivity from combined high-resolution electroencephalography (EEG) and functional magnetic resonance imaging (fMRI) data are presented. These methods include a subjects multicompartment head model (scalp, skull, dura mater, cortex) constructed from individual magnetic resonance images, multidipole source model, and regularized linear inverse source estimates of cortical current density. Determination of the priors in the resolution of the linear inverse problem was performed with the use of information from the hemodynamic responses of the cortical areas as revealed by block-designed (strength of activated voxels) fMRI. We estimate functional cortical connectivity by computing the directed transfer function (DTF) on the estimated cortical current density waveforms in regions of interest (ROIs) on the modeled cortical mantle. The proposed method was able to unveil the direction of the information flow between the cortical regions of interest, as it is directional in nature. Furthermore, this method allows to detect changes in the time course of information flow between cortical regions in different frequency bands. The reliability of these techniques was further demonstrated by elaboration of high-resolution EEG and fMRI signals collected during visually triggered finger movements in four healthy subjects. Connectivity patterns estimated for this task reveal an involvement of right parietal and bilateral premotor and prefrontal cortical areas. This cortical region involvement resembles that revealed in previous studies where visually triggered finger movements were analyzed with the use of separate EEG or fMRI measurements.

Human Movement-Related Potentials vs Desynchronization of EEG Alpha Rhythm: A High-Resolution EEG Study

Movement-related potentials (MRPs) and event-related desynchronization (ERD) of alpha rhythm were investigated with an advanced high-resolution electroencephalographic technology (128 channels, surface Laplacian estimate, realistic head modeling). The working hypothesis was that MRPs and alpha ERD reflect different aspects of sensorimotor cortical processes. Both MRPs and alpha ERD modeled the responses of primary sensorimotor (M1-S1), supplementary motor (SMA), and posterior parietal (PP, area 5) areas during the preparation and execution of unilateral finger movements. Maximum responses were modeled in the contralateral M1-S1 during both preparation and execution of the movement. The SMA and PP responses were modeled mainly from the MRPs and alpha ERD, respectively. The modeled ipsilateral M1-S1 responses were larger and stronger in the alpha ERD than MRPs. These results may suggest that alpha ERD reflects changes in the background oscillatory activity in wide cortical sensorimotor areas, whereas MRPs represent mainly increased, task-specific responses of SMA and contralateral M1-S1.

Multimodal integration of high-resolution EEG and functional magnetic resonance imaging data: A simulation study

Previous simulation studies have stressed the importance of the use of fMRI priors in the estimation of cortical current density. However, no systematic variations of signal-to-noise ratio (SNR) and number of electrodes were explicitly taken into account in the estimation process. In this simulation study we considered the utility of including information as estimated from fMRI. This was done by using as the dependent variable both the correlation coefficient and the relative error between the imposed and the estimated waveforms at the level of cortical region of interests (ROI). A realistic head and cortical surface model was used. Factors used in the simulations were the different values of SNR of the scalp-generated data, the different inverse operators used to estimated the cortical source activity, the strengths of the fMRI priors in the fMRI-based inverse operators, and the number of scalp electrodes used in the analysis. Analysis of variance results suggested that all the considered factors significantly afflict the correlation and the relative error between the estimated and the simulated cortical activity. For the ROIs analyzed with simulated fMRI hot spots, it was observed that the best estimation of cortical source currents was performed with the inverse operators that used fMRI information. When the ROIs analyzed do not present fMRI hot spots, both standard (i.e., minimum norm) and fMRI-based inverse operators returned statistically equivalent correlation and relative error values.

High resolution EEG: A new model-dependent spatial deblurring method using a realistically-shaped MR-constructed subject's head model

This paper presents a new model-dependent method for the spatial deblurring of scalp-recorded EEG potentials based on boundary-element and cortical imaging techniques. This model-dependent spatial deblurring (MDSD) method used MR images for the reconstruction of the subjects head model, and a layer of 364 radially-oriented equivalent current dipoles as a source model. The validation of the MDSD method was performed on simulated potential distributions generated from equivalent dipoles oriented radially, obliquely, and tangentially to the head surface. Furthermore, this method was used to localize neocortical sources of human movement-related and somatosensory-evoked potentials. It was shown that the new MDSD method improved markedly the spatial resolution of the simulated surface potentials and scalp-recorded event-related potentials. The spatial information content of the scalp-recorded EEG potentials increased progressively by increasing the spatial sampling from 28 to 128 channels. These results indicate that the new method could be satisfactorily used for high resolution EEG studies.

Performances of surface Laplacian estimators: A study of simulated and real scalp potential distributions

SummaryThis paper presents a study of the performance of various local and spherical spline methods currently in use for the surface Laplacian (SL) estimate of scalp potential distributions. The SL was estimated from simulated instantaneous event-related scalp potentials generated over a three-shell spherical head model. Laplacian estimators used planar and spherical scalp models. Noise of increasing magnitude and spatial frequency was added to the potential distributions in order to simulate noise presumed to contaminate scalp-recorded event-related potentials. A comparison of noise effects on various Laplacian estimates was made for increasing number of “electrode” positions in variants of the 10–20 system. Furthermore, to evaluate the error due to the use of unrealistic scalp models, the matching between SL estimates of human scalp-recorded movement-related potentials computed on spherical and realistically-shaped MRI-constructed models of the scalp was examined. With all methods the error of the SL estimate increased proportionally with the magnitude and spatial frequency of noise. Increased number of “electrodes” up to 256 significantly reduced the error (p<0.05). In general, the best SL estimates were computed by second and third order splines including λ correction, the performances of the second order spline being better with more than 64 “electrodes”. Compared with spline Lapladans, the best local methods provided nearly equal estimates with low spatial sampling (19 and 28 “electrodes”), as well as high spatial frequency noise. The error of the SL estimate due to unrealistic scalp model was significant, and it augmented with increased spatial sampling from 64 to 128 electrodes.

Assessing cortical functional connectivity by linear inverse estimation and directed transfer function: simulations and application to real data

OBJECTIVE To test a technique called Directed Transfer Function (DTF) for the estimation of human cortical connectivity, by means of simulation study and human study, using high resolution EEG recordings related to finger movements. METHODS The method of the Directed Transfer Function (DTF) is a frequency-domain approach, based on a multivariate autoregressive modeling of time series and on the concept of Granger causality. Since the spreading of the potential from the cortex to the sensors makes it difficult to infer the relation between the spatial patterns on the sensor space and those on the cortical sites, we propose the use of the DTF method on cortical signals estimated from high resolution EEG recordings, which exhibit a higher spatial resolution than conventional cerebral electromagnetic measures. The simulation study was followed by an analysis of variance (ANOVA) of the results obtained for different levels of Signal to Noise Ratio (SNR) and temporal length, as they have been systematically imposed on simulated signals. The whole methodology was then applied to high resolution EEG data recorded during a visually paced finger movement. RESULTS The statistical analysis performed returns that during simulations, DTF is able to estimate correctly the imposed connectivity patterns under reasonable operative conditions, i.e. when data exhibit a SNR of at least 3 and a length of at least 75 s of non-consecutive recordings at 64 Hz of sampling rate, equivalent, more generally, to 4800 data samples. CONCLUSIONS Functional connectivity patterns of cortical activity can be effectively estimated under general conditions met in any practical EEG recordings, by combining high resolution EEG techniques, linear inverse estimation and the DTF method. SIGNIFICANCE The estimation of cortical connectivity can be performed not only with hemodynamic measurements, by using functional MRI recordings, but also with modern EEG recordings treated with advanced computational techniques.

Linear inverse source estimate of combined EEG and MEG data related to voluntary movements

A method for the modeling of human movement‐related cortical activity from combined electroencephalography (EEG) and magnetoencephalography (MEG) data is proposed. This method includes a subjects multi‐compartment head model (scalp, skull, dura mater, cortex) constructed from magnetic resonance images, multi‐dipole source model, and a regularized linear inverse source estimate based on boundary element mathematics. Linear inverse source estimates of cortical activity were regularized by taking into account the covariance of background EG and MEG sensor noise. EEG (121 sensors) and MEG (43 sensors) data were recorded in separate sessions whereas normal subjects executed voluntary right one‐digit movements. Linear inverse source solution of EEG, MEG, and EEG‐MEG data were quantitatively evaluated by using three performance indexes. The first two indexes (Dipole Localization Error [DLE] and Spatial Dispersion [SDis]) were used to compute the localization power for the source solutions obtained. Such indexes were based on the information provided by the column of the resolution matrix (i.e., impulse response). Ideal DLE values tend to zero (the source current was correctly retrieved by the procedure). In contrast, high DLE values suggest severe mislocalization in the source reconstruction. A high value of SDis at a source space point mean that such a source will be retrieved by a large area with the linear inverse source estimation. The remaining performance index assessed the quality of the source solution based on the information provided by the rows of the resolution matrix R, i.e., resolution kernels. The i‐th resolution kernels of the matrix R describe how the estimation of the i‐th source is distorted by the concomitant activity of all other sources. A statistically significant lower dipole localization error was observed and lower spatial dispersion in source solutions produced by combined EEG‐MEG data than from EEG and MEG data considered separately (P < 0.05). These effects were not due to an increased number of sensors in the combined EEG‐MEG solutions. They result from the independence of source information conveyed by the multimodal measurements. From a physiological point of view, the linear inverse source solution of EEG‐MEG data suggested a contralaterally preponderant bilateral activation of primary sensorimotor cortex from the preparation to the execution of the movement. This activation was associated with that of the supplementary motor area. The activation of bilateral primary sensorimotor cortical areas was greater during the processing of afferent information related to the ongoing movement than in the preparation for the motor act. In conclusion, the linear inverse source estimate of combined MEG and EEG data improves the estimate of movement‐related cortical activity. Hum. Brain Mapping 14:197–209, 2001.

High-resolution electro-encephalogram: source estimates of Laplacian-transformed somatosensory-evoked potentials using a realistic subject head model constructed from magnetic resonance images

A novel high-resolution electro-encephalographic (EEG) procedure is proposed, including high spatial sampling (128 channels), a realistic magnetic resonance-constructed subject head model, a multi-dipole cortical source model and regularised weighted minimum-norm linear inverse source estimation (WMN). As an innovation, EEG potentials (two healthy subjects; median-nerve, short-latency somatosensory-evoked potentials (SEPs)) are preliminarily Laplacian-transformed (LT) to remove brain electrical activity generated by subcortical sources (i.e. not represented in the source model). LT-WMN estimates are mathematically evaluated by figures of merit (WMN estimates as a reference). Results show higher dipole identifiability (0.69;0.88), lower dipole localisation error (0.6 mm; 7.8mm) and lower spatial dispersion (8.6 mm; 24mm) in LT-WMN than in WMN estimates (Bonferroni corrected p<0.001). These estimates are presented on the subject modelled cortical surface to highlight the increased spatial information content in LT-WMN compared with WMN estimates. The proposed high-resolution EEG technique is useful for the study of somatosensory functions in basic research and clinical applications.

IMPROVED REALISTIC LAPLACIAN ESTIMATE OF HIGHLY-SAMPLED EEG POTENTIALS BY REGULARIZATION TECHNIQUES

In this study we investigated the effects of lambda correction, generalized cross-validation (GCV), and Tikhonov regularization techniques on the realistic Laplacian (RL) estimate of highly-sampled (128 channels) simulated and actual EEG potential distributions. The simulated EEG potential distributions were mathematically generated over a 3-shell spherical head model (analytic potential distributions). Noise was added to the analytic potential distributions to mimic EEG noise. The magnitude of the noise was 20, 40 and 80% that of the analytic potential distributions. Performance of the regularization techniques was evaluated by computing the root mean square error (RMSE) between regularized RL estimates and analytic surface Laplacian solutions. The actual EEG data were human movement-related and short-latency somatosensory-evoked potentials. The RL of these potentials was estimated over a realistically-shaped, magnetic resonance-constructed model of the subjects scalp surface. The RL estimate of the simulated potential distributions was improved with all the regularization techniques. However, the lambda correction and Tikhonov regularization techniques provided more precise Laplacian solutions than the GCV computation (P < 0.05); they also improved better than the GCV computation the spatial detail of the movement-related and short-latency somatosensory-evoked potential distributions. For both simulated and actual EEG potential distributions the Tikhonov and lambda correction techniques provided nearly equal Laplacian solutions, but the former offered the advantage that no preliminary simulation was required to regularize the RL estimate of the actual EEG data.

Resting state cortical electroencephalographic rhythms are related to gray matter volume in subjects with mild cognitive impairment and Alzheimer's disease

Cortical gray matter volume and resting state cortical electroencephalographic rhythms are typically abnormal in subjects with amnesic mild cognitive impairment (MCI) and Alzheimers disease (AD). Here we tested the hypothesis that in amnesic MCI and AD subjects, abnormalities of EEG rhythms are a functional reflection of cortical atrophy across the disease. Eyes‐closed resting state EEG data were recorded in 57 healthy elderly (Nold), 102 amnesic MCI, and 108 AD patients. Cortical gray matter volume was indexed by magnetic resonance imaging recorded in the MCI and AD subjects according to Alzheimers disease neuroimaging initiative project (http://www.adni‐info.org/). EEG rhythms of interest were delta (2–4 Hz), theta (4–8 Hz), alpha1 (8–10.5 Hz), alpha2 (10.5–13 Hz), beta1 (13–20 Hz), beta2 (20–30 Hz), and gamma (30–40 Hz). These rhythms were indexed by LORETA. Compared with the Nold, the MCI showed a decrease in amplitude of alpha 1 sources. With respect to the Nold and MCI, the AD showed an amplitude increase of delta sources, along with a strong amplitude reduction of alpha 1 sources. In the MCI and AD subjects as a whole group, the lower the cortical gray matter volume, the higher the delta sources, the lower the alpha 1 sources. The better the score to cognitive tests the higher the gray matter volume, the lower the pathological delta sources, and the higher the alpha sources. These results suggest that in amnesic MCI and AD subjects, abnormalities of resting state cortical EEG rhythms are not epiphenomena but are strictly related to neurodegeneration (atrophy of cortical gray matter) and cognition. Hum Brain Mapp, 2013.