A bioelectric inverse imaging technique based on surface Laplacians

Accounting for linear transformations of EEG and MEG data in source analysis

Analyses of electro- and magnetoencephalography (EEG, MEG) data often involve a linear modification of signals at the sensor level. Examples include re-referencing of the EEG, computation of synthetic gradiometer in MEG, or the removal of artifactual independent components to clean EEG and MEG data. A question of practical relevance is, if such modifications must be accounted for by adapting the physical forward model (leadfield) before subsequent source analysis. Here, we show that two scenarios need to be differentiated. In the first scenario, which corresponds to re-referencing the EEG and synthetic gradiometer computation in MEG, the leadfield must be adapted before source analysis. In the second scenario, which corresponds to removing artifactual components to 'clean' the data, the leadfield must not be changed. We demonstrate and discuss the consequences of wrongly modifying the leadfield in the latter case for an example. Future EEG and MEG studies employing source analyses should carefully consider whether and, if so, how the leadfield must be modified as explicated here.

Usefulness of ventricular endocardial electric reconstruction from body surface potential maps to noninvasively localize ventricular ectopic activity in patients

As radio frequency (RF) catheter ablation becomes increasingly prevalent in the management of ventricular arrhythmia in patients, an accurate and rapid determination of the arrhythmogenic site is of important clinical interest. The aim of this study was to test the hypothesis that the inversely reconstructed ventricular endocardial current density distribution from body surface potential maps (BSPMs) can localize the regions critical for maintenance of a ventricular ectopic activity. Patients with isolated and monomorphic premature ventricular contractions (PVCs) were investigated by noninvasive BSPMs and subsequent invasive catheter mapping and ablation. Equivalent current density (CD) reconstruction (CDR) during symptomatic PVCs was obtained on the endocardial ventricular surface in six patients (four men, two women, years 23-77), and the origin of the spontaneous ectopic activity was localized at the location of the maximum CD value. Compared with the last (successful) ablation site (LAS), the mean and standard deviation of localization error of the CDR approach were 13.8 and 1.3 mm, respectively. In comparison, the distance between the LASs and the estimated locations of an equivalent single moving dipole in the heart was 25.5 ± 5.5 mm. The obtained CD distribution of activated sources extending from the catheter ablation site also showed a high consistency with the invasively recorded electroanatomical maps. The noninvasively reconstructed endocardial CD distribution is suitable to predict a region of interest containing or close to arrhythmia source, which may have the potential to guide RF catheter ablation.

Noninvasive mapping of transmural potentials during activation in swine hearts from body surface electrocardiograms

The three-dimensional cardiac electrical imaging (3DCEI) technique was previously developed to estimate the initiation site(s) of cardiac activation and activation sequence from the noninvasively measured body surface potential maps (BSPMs). The aim of this study was to develop and evaluate the capability of 3DCEI in mapping the transmural distribution of extracellular potentials and localizing initiation sites of ventricular activation in an in vivo animal model. A control swine model (n = 10) was employed in this study. The heart-torso volume conductor model and the excitable heart model were constructed based on each animal's preoperative MR images and a priori known physiological knowledge. Body surface potential mapping and intracavitary noncontact mapping (NCM) were simultaneously conducted during acute ventricular pacing. The 3DCEI analysis was then applied on the recorded BSPMs. The estimated initiation sites were compared to the precise pacing sites; as a subset of the mapped transmural potentials by 3DCEI, the electrograms on the left ventricular endocardium were compared to the corresponding output of the NCM system. Over the 16 LV and 48 RV pacing studies, the averaged localization error was 6.1±2.3 mm, and the averaged correlation coefficient between the estimated endocardial electrograms by 3DCEI and from the NCM system was 0.62±0.09. The results demonstrate that the 3DCEI approach can well localize the sites of initiation of ectopic beats and can obtain physiologically reasonable transmural potentials in an in vivo setting during focal ectopic beats. This study suggests the feasibility of tomographic mapping of 3D ventricular electrograms from the body surface recordings.

The role of the pain-evoked negative difference potential in dual-task response conflict

The possible role of the generators of the sural nerve pain-evoked negative difference potential (NDP), the anterior cingulate cortex and supplementary somatosensory area, in monitoring response conflict was investigated in 19 healthy adults. Each trial consisted of a visual arrow stimulus and a painful electrical stimulus applied to the sural nerve. The subjects determined whether their left or right sural nerve had been stimulated and whether the arrow was pointing to the left or to the right. The sural nerve pain detection task reaction times and response errors were greater in the incongruent condition, where the arrow pointed to the side opposite of that receiving the sural nerve pain, than in the congruent condition, where the arrow pointed to the same side as that receiving the sural nerve pain. Response conflict was greatest, therefore, in the incongruent condition. There were no differences in NDP amplitude across the congruent and incongruent conditions. These results argue against the hypothesis that the NDP generators are involved in monitoring response conflict.

Localization of endocardial ectopic activity by means of noninvasive endocardial surface current density reconstruction

Localization of the source of cardiac ectopic activity has direct clinical benefits for determining the location of the corresponding ectopic focus. In this study, a recently developed current-density (CD)-based localization approach was experimentally evaluated in noninvasively localizing the origin of the cardiac ectopic activity from body-surface potential maps (BSPMs) in a well-controlled experimental setting. The cardiac ectopic activities were induced in four well-controlled intact pigs by single-site pacing at various sites within the left ventricle (LV). In each pacing study, the origin of the induced ectopic activity was localized by reconstructing the CD distribution on the endocardial surface of the LV from the measured BSPMs and compared with the estimated single moving dipole (SMD) solution and precise pacing site (PS). Over the 60 analyzed beats corresponding to ten pacing sites (six for each), the mean and standard deviation of the distance between the locations of maximum CD value and the corresponding PSs were 16.9 mm and 4.6 mm, respectively. In comparison, the averaged distance between the SMD locations and the corresponding PSs was slightly larger (18.4 ± 3.4 mm). The obtained CD distribution of activated sources extending from the stimulus site also showed high consistency with the endocardial potential maps estimated by a minimally invasive endocardial mapping system. The present experimental results suggest that the CD method is able to locate the approximate site of the origin of a cardiac ectopic activity, and that the distribution of the CD can portray the propagation of early activation of an ectopic beat.

Three-Dimensional Cardiac Electrical Imaging From Intracavity Recordings

A novel approach is proposed to image 3-D cardiac electrical activity from intracavity electrical recordings with the aid of a catheter. The feasibility and performance were evaluated by computer simulation studies, where a 3-D cellular-automaton heart model and a finite-element thorax volume conductor model were utilized. The finite-element method (FEM) was used to simulate the intracavity recordings induced by a single-site and dual-site pacing protocol. The 3-D ventricular activation sequences as well as the locations of the initial activation sites were inversely estimated by minimizing the dissimilarity between the intracavity potential "measurements" and the model-generated intracavity potentials. Under single-site pacing, the relative error (RE) between the true and estimated activation sequences was 0.03 +/- 0.01 and the localization error (LE) (of the initiation site) was 1.88 +/- 0.92 mm, as averaged over 12 pacing trials when considering 25 microV additive measurement noise using 64 catheter electrodes. Under dual-site pacing, the RE was 0.04 +/- 0.01 over 12 pacing trials and the LE over 24 initial pacing sites was 2.28 +/- 1.15 mm, when considering 25 microV additive measurement noise using 64 catheter electrodes. The proposed 3-D cardiac electrical imaging approach using intracavity electrical recordings was also tested under various simulated conditions and robust inverse solutions obtained. The present promising simulation results suggest the feasibility of obtaining 3-D information of cardiac electrical activity from intracavity recordings. The application of this inverse method has the potential of enhancing electrocardiographic mapping by catheters in electrophysiology laboratories, aiding cardiac resynchronization therapy, and other clinical applications.

Tripolar Laplacian electrocardiogram and moment of activation isochronal mapping

The electrocardiogram (ECG) provides useful global temporal assessment of the cardiac activity, but has limited spatial capabilities. The Laplacian electrocardiogram (LECG), an improvement over the ECG, provides high spatiotemporal distributed information about cardiac electrical activation. We designed and developed LECG tripolar concentric ring electrode active sensors based on the finite element algorithm 'nine-point method' (NPM). The active sensors were used in an array of 6 by 12 (72) locations to record bipolar and tripolar LECG from the body surface over the anterolateral chest. Compared to bipolar LECG, tripolar LECG showed significantly higher spatial selectivity which may be helpful in inferring information about cardiac activations detected on the body surface. In this study the moment of activation (MOA), an indicator of a depolarization wave passing below the active sensors, was used to surmise possible timing information of the cardiac electrical activation below the active sensors' recording sites. The MOA on the body surface was used to generate isochronal maps that may some day be used by clinicians in diagnosing arrhythmias and assessing the efficacy of therapies.

The feasibility study of the laplacian electrode for EEG

The surface Laplacian can give more localized information of the brain. A concentric bipolar electrode (consisting of a central disc and an outer annulus) can measure the surface Laplacian of the body surface electrical potential distribution. In this article we will study the feasibility of the Laplacian electrode for EEG from the problems of SNR, selection of the electrode parameter. And a new kind of active Laplacian electrode will be introduced to detect the visual evoked potential.

Noninvasive reconstruction of three-dimensional ventricular activation sequence from the inverse solution of distributed equivalent current density

We propose a new electrocardiographic (ECG) inverse approach for imaging the three-dimensional (3-D) ventricular activation sequence based on the modeling and estimation of the equivalent current density throughout the entire volume of the ventricular myocardium. The spatio-temporal coherence of the ventricular excitation process has been utilized to derive the activation time from the estimated time course of the equivalent current density. In the present study, we explored four different linear inverse algorithms (the minimum norm and weighted minimum norm estimates in combination with two regularization schemes: the instant-by-instant regularization and the isotropy method) to estimate the current density at each time instant during the ventricular depolarization. The activation time at any given location within the ventricular myocardium was determined as the time point with the occurrence of the maximum local current density estimate. Computer simulations were performed to evaluate this approach using single- and dual-site pacing protocols in a physiologically realistic cellular automaton heart model. The performance and stability of the proposed approach was evaluated with respect to the various levels of measurement noise (0, 5, 10, 20, 40, and 60 microV), the various numbers of ECG electrodes and the modeling errors on the torso geometry and heart position. The simulation results demonstrate that: 1) the single-site paced 3-D activation sequence can be well reconstructed from 200-channel body surface potential maps with additive Gaussian white noise of 20 microV (correlation coefficient = 0.90, relative error = 0.19, and localization error = 5.49 mm); 2) a higher imaging accuracy can be obtained when the activation is initiated from the left/right ventricle (LV/RV) compared to from the septum; 3) the isotropy method gives rise to a better performance than the conventional instant-by-instant regularization; 4) a decreased imaging accuracy results from a larger noise level, a fewer number of electrodes, or the volume conductor modeling errors; however, a reasonable imaging accuracy can still be obtained with a 60 microV noise level, 64 electrodes, or mild errors on both the torso geometry and heart position, respectively; 5) the dual-site paced 3-D activation sequence can be imaged when the two sites are paced either simultaneously or with a time delay of 20 ms; 6) two pacing sites can be resolved and localized in the imaged 3-D activation sequence when they are located at the contralateral sides of ventricles or at the ventricular lateral wall and the apex, respectively.

Three-dimensional myocardial activation imaging in a rabbit model

This study evaluated a recently developed three-dimensional (3-D) electrocardiographic imaging (3DECI) approach in a closed-chest rabbit model. First, the performance and sensitivity of parameters of 3DECI were evaluated using a geometrically realistic rabbit heart-torso model. Second, a 3-D intracardiac mapping procedure was evaluated based on the heart-torso rabbit model. Third, comparisons were made among the forward-simulated ventricular activation sequence, the activation sequence derived by the intracardiac mapping, and the 3DECI inverse solution. Finally, the present procedures were tested in vivo in a rabbit, in which the relative error between the measured and imaged activation sequence was 0.20 and the localization error was 5.1 mm. The present simulation and experimental results suggest the merits of the 3DECI imaging approach, and the validity of intracardiac mapping as a tool to evaluate the 3DECI.

Localization of the site of origin of reentrant arrhythmia from body surface potential maps: a model study

We have developed a model-based imaging approach to estimate the site of origin of reentrant arrhythmia from body surface potential maps (BSPMs), with the aid of a cardiac arrhythmia model. The reentry was successfully simulated and maintained in the cardiac model, and the simulated ECG waveforms over the body surface corresponding to a maintained reentry have evident characteristics of ventricular tachycardia. The performance of the inverse imaging approach was evaluated by computer simulations. The present simulation results show that an averaged localization error of about 1.5 mm, when 5% Gaussian white noise was added to the BSPMs, was detected. The effects of the heart-torso geometry uncertainty on the localization were also initially assessed and the simulation results suggest that no significant influence was observed when 10% torso geometry uncertainty or 10 mm heart position shifting was considered. The present simulation study suggests the feasibility of localizing the site of origin of reentrant arrhythmia from non-invasive BSPMs, with the aid of a cardiac arrhythmia model.

Classifying EEG-based motor imagery tasks by means of time–frequency synthesized spatial patterns

OBJECTIVE

To develop a single trial motor imagery (MI) classification strategy for the brain-computer interface (BCI) applications by using time-frequency synthesis approach to accommodate the individual difference, and using the spatial patterns derived from electroencephalogram (EEG) rhythmic components as the feature description.

METHODS

The EEGs are decomposed into a series of frequency bands, and the instantaneous power is represented by the envelop of oscillatory activity, which forms the spatial patterns for a given electrode montage at a time-frequency grid. Time-frequency weights determined by training process are used to synthesize the contributions from the time-frequency domains.

RESULTS

The present method was tested in nine human subjects performing left or right hand movement imagery tasks. The overall classification accuracies for nine human subjects were about 80% in the 10-fold cross-validation, without rejecting any trials from the dataset. The loci of MI activity were shown in the spatial topography of differential-mode patterns over the sensorimotor area.

CONCLUSIONS

The present method does not contain a priori subject-dependent parameters, and is computationally efficient. The testing results are promising considering the fact that no trials are excluded due to noise or artifact.

SIGNIFICANCE

The present method promises to provide a useful alternative as a general purpose classification procedure for MI classification.

Electrophysiological indices of orienting attention toward pain

This study examined the effects of orienting on two pain-related components of the sural nerve-evoked somatosensory evoked potential: the NDP (80-230 ms), which is generated in part by the anterior cingulate cortex (ACCc), and SP6 (280-340 ms). NDP and SP6 amplitudes were larger when subjects oriented their attention away from an invalidly cued location and toward the sural nerve pain than when their attention remained focused on the pain. These results and our earlier studies suggest that the ACCc activity generating the NDP is involved in detecting transient painful stimuli. This activity is enhanced when the pain occurs outside the focus of attention, and it may signal other brain areas that attention should be oriented away from its current focus and toward the pain. SP6 appears to be a pain-evoked P3a event-related potential, with an anterior component involved in orienting attention away from some other task and toward the pain, and an posterior component involved in evaluating the pain.

Non-invasive estimation of myocardial infarction by means of a heart-model-based imaging approach: A simulation study

In the study, a new myocardial infarction (MI) estimation method was developed for estimating MI in the three-dimensional myocardium by means of a heart-model-based inverse approach. The site and size of MI are estimated from body surface electrocardiograms by minimising multiple objective functions of the measured body surface potential maps (BSPMs) and the heart-model-generated BSPMs. Computer simulations were conducted to evaluate the performance of the developed method, using a single-site MI and dual-site MI protocols. The simulation results show that, for the single-site MI, the averaged spatial distance (SD) between the weighting centres of the 'true' and estimated MIs, and the averaged relative error (RE) between the numbers of the 'true' and estimated infarcted units are 3.0 +/- 0.6/3.6 +/- 0.6 mm and 0.11 +/- 0.02/0.14 +/- 0.02, respectively, when 5 microV/10 microV Gaussian white noise was added to the body surface potentials. For the dual-site MI, the averaged SD between the weighting centres of the 'true' and estimated MIs, and the averaged RE between the numbers of the 'true' and estimated infarcted units are 3.8 +/- 0.7/3.9 +/- 0.7mm and 0.12 +/- 0.02/0.14 +/- 0.03, respectively, when 5 microV/10 microV Gaussian white noise was added to the body surface potentials. The simulation results suggest the feasibility of applying the heart-model-based imaging approach to the estimation of myocardial infarction from body surface potentials.

Noninvasive imaging of cardiac transmembrane potentials within three-dimensional myocardium by means of a realistic geometry anisotropic heart model

We have developed a new approach for imaging cardiac transmembrane potentials (TMPs) within the three-dimensional (3-D) myocardium by means of an anisotropic heart model. The cardiac TMP distribution is estimated from body surface electrocardiograms by minimizing objective functions of the "measured" body surface potential maps (BSPMs) and the heart-model-generated BSPMs. Computer simulation studies have been conducted to evaluate the present 3-D TMP imaging approach using pacing protocols. Simulations of single-site pacing at 24 sites throughout the ventricles, as well as dual-site pacing at 12 pairs of sites in the vicinity of atrio-ventricular ring were performed. The present simulation results show that the correlation coefficient (CC) and relative error (RE) between the "true" and inversely estimated TMP distributions were 0.9915 +/- 0.0041 and 0.1266 +/- 0.0326, for single-site pacing, and 0.9889 +/- 0.0034 and 0.1473 +/- 0.0237 for dual-site pacing, respectively, when 10 microV Gaussian white noise (GWN) was added to the BSPMs. The effects of heart and torso geometry uncertainty were also evaluated by shifting the heart position by 10 mm and altering the torso size by 10%. The CC between the "true" and inversely estimated TMP distributions was above 0.97 when these geometry uncertainties were considered. The present simulation results demonstrate the feasibility of noninvasive estimation of TMP distribution throughout the ventricles from body surface electrocardiographic measurements, and suggest that the present method may become a useful alternative in noninvasive imaging of distributed cardiac electrophysiological processes within the 3-D myocardium.

Noninvasive three-dimensional activation time imaging of ventricular excitation by means of a heart-excitation model

We propose a new method for imaging activation time within three-dimensional (3D) myocardium by means of a heart-excitation model. The activation time is estimated from body surface electrocardiograms by minimizing multiple objective functions of the measured body surface potential maps (BSPMs) and the heart-model-generated BSPMs. Computer simulation studies have been conducted to evaluate the proposed 3D myocardial activation time imaging approach. Single-site pacing at 24 sites throughout the ventricles, as well as dual-site pacing at 12 pairs of sites in the vicinity of atrioventricular ring, was performed. The present simulation results show that the average correlation coefficient (CC) and relative error (RE) for single-site pacing were 0.9992+/-0.0008/0.9989+/-0.0008 and 0.05+/-0.02/0.07+/-0.03, respectively, when 5 microV/10 microV Gaussian white noise (GWN) was added to the body surface potentials. The average CC and RE for dual-site pacing were 0.9975+/-0.0037 and 0.08+/-0.04, respectively, when 10 microV GWN was added to the body surface potentials. The present simulation results suggest the feasibility of noninvasive estimation of activation time throughout the ventricles from body surface potential measurement, and suggest that the proposed method may become an important alternative in imaging cardiac electrical activity noninvasively.

Body surface Laplacian mapping of atrial depolarization in healthy human subjects

In the present study, we report body surface Laplacian mapping of atrial depolarization under sinus rhythm in 8 healthy male subjects. For each subject, 95 unipolar disk electrodes with inter-electrode distance of 2 cm were used to record simultaneously potential ECGs over the anterior chest. The Laplacian ECG was then estimated during the P wave using a novel spline Laplacian technique. The body surface potential map (BSPM) and body surface Laplacian map (BSLM) at different time instants or time intervals of the P wave were constructed and compared. The present results showed that the BSPMs during the P wave were characterized by the rotation of a pair of positive/negative potential distribution from right to left around the anterior torso. On the other hand, the corresponding BSLMs revealed more spatial details, including two positive activities (denoted as P1 and P2, appeared in all 8 subjects), and three negative activities (denoted as N1, N2, and N3, appeared in 7, 7, and 4 subjects, respectively). The separation of these activities and their evolving patterns were also compared and confirmed by computer simulation using a realistic geometry heart-torso model. The above findings may be directly related to the underlying activation sequence during atrial depolarization in healthy subjects, suggesting the potential clinical applications of the Laplacian ECG technique.

A new method for incorporating weighted temporal and spatial smoothing in the inverse problem of electrocardiography

In this paper, we present a method for incorporating temporal smoothing (TS) into the estimate of epicardial potentials from body surface potential data. Our algorithm employs a different spatial smoothing parameter, chosen by the composite residual error and smoothing operator criteria, at each time step in the sequence. The total spatial smoothing term is then simply partitioned between temporal and spatial smoothing. The algorithm appears to be quite robust with regard to this partitioning. The new method was evaluated in the setting of additive Gaussian noise, but otherwise realistic conditions of body geometry and reference epicardial potentials. In examining the match between estimated and measured electrograms, or the match between estimated isopotential maps and measured isopotential maps, the estimates constructed using the new TS algorithm produced consistently smaller relative errors than those constructed using a quasi-static (QS) algorithm or those constructed by postprocessing the QS estimate with a moving average filter.

A spline Laplacian ECG estimator in a realistic geometry volume conductor

We have developed a spline-based Laplacian estimator over an arbitrarily shaped surface of a volume conductor and tested its applicability to Laplacian electrocardiogram (ECG) mapping. In the newly developed algorithm, estimation of the parameters associated with the spline Laplacian is formulated by seeking the general inverse of a transfer matrix. Only one spline-parameter needs to be determined through regularization in order to estimate the realistic geometry surface Laplacian from the body surface potentials. It has been demonstrated that the rich knowledge on regularization in the inverse problems can be directly applied to estimate the spline Laplacian ECG (LECG), such as the discrepancy principle. Computer simulations have been conducted to validate the new approach in a spherical volume conductor and test the feasibility of mapping cardiac electrical sources in a realistic geometry heart-torso model. The present results demonstrate that the realistic geometry spline LECG can be estimated conveniently from the body surface potentials, is more robust against measurement noise and has better performance than the conventional five-point local Laplacian estimator.

Imaging and visualization of 3-D cardiac electric activity

Noninvasive imaging of cardiac electric activity is of importance for better understanding the underlying mechanisms and for aiding clinical diagnosis and intervention of cardiac abnormalities. We propose to image the three-dimensional (3-D) cardiac bioelectric source distribution from body-surface electrocardiograms. Cardiac electrical sources were modeled by a current dipole distribution throughout the entire myocardium, and estimated by using the Laplacian weighted minimum norm (LWMN) algorithm from body-surface potentials. The estimated inverse solution of the current distribution was further improved by using a recursive weighting strategy for localized sources, such as origins of cardiac arrhythmias. Computer simulations were conducted to test the feasibility of the proposed approach by using a 3-D ventricle model embedded in a realistically shaped torso model. The boundary element method was used to solve the forward problem from assumed cardiac sources to the body-surface potentials. Two testing dipoles were placed in the left and right ventricles, simulating the early activation associated with ventricular arrhythmias. The LWMN inverse solution showed an equivalent source distribution over the entity of both ventricles, with spread areas of activity overlying the positions of the testing dipoles. The sharpened inverse image provides well-localized focal sources near the testing dipole positions. In summary, the present computer simulation suggests that the proposed 3-D cardiac current source imaging and localization approach appears to be a promising candidate for localizing and imaging sites of origins of cardiac activation.

Localization of the site of origin of cardiac activation by means of a heart-model-based electrocardiographic imaging approach

We have developed a new approach to solve the inverse problem of electrocardiography in terms of heart model parameters. The inverse solution of the electrocardiogram (ECG) inverse problem is defined, in the present study, as the parameters of the heart model, which are closely related to the physiological and pathophysiological status of the heart, and is estimated by using an optimization system of heart model parameters, instead of solving the matrix equation relating the body surface ECGs and equivalent cardiac sources. An artificial neural network based preliminary diagnosis system has been developed to limit the searching space of the optimization algorithm and to initialize the model parameters in the computer heart model. The optimal heart model parameters were obtained by minimizing the objective functions, as functions of the observed and model-generated body surface ECGs. We have tested the feasibility of the newly developed technique in localizing the site of origin of cardiac activation using a pace mapping protocol. The present computer simulation results show that, the present approach for localization of the site of origin of ventricular activation achieved an averaged localization error of about 3 mm [for 5-muV Gaussian white noise (GWN)] and 4 mm (for 10-muV GWN), with standard deviation of the localization errors of being about 1.5 mm. The present simulation study suggests that this newly developed approach provides a robust inverse solution, circumventing the difficulties of the ECG inverse problem, and may become an important alternative to other ECG inverse solutions.

Fusion of body surface potential and body surface Laplacian signals for electrocardiographic imaging

Various approaches to the solution to the inverse problem of electrocardiography have been proposed over the years. Recently, the use of inverse algorithms using measured body surface Laplacians has been proposed, and in various studies this technique has been shown to outperform the traditional use of body surface potentials in certain model problems. In this paper, we compare the use of body surface potentials and body surface Laplacians on two model problems with different assumed cardiac sources. For the spherical cap model problems with an anterior source, the epicardial estimates using body surface potentials had smaller average relative errors than when body surface Laplacians were used. For the spherical cap model problems with a posterior source, the epicardial estimates using body surface potential or body surface Laplacian sensors generally produced similar relative errors. For the radial dipole model, the epicardial estimates using body surface Laplacians had smaller errors than when body surface potentials were used. We introduce a fusion algorithm that combines the different types of signals and generally produces a good estimate for both model problems.

Electrocorticographic coherence patterns

The availability of implantable subdural electrode arrays has made systematic studies of electrocorticographic (ECoG) coherence possible. Studies of coherence patterns recorded directly from human cortex are reviewed along with the presentation of original human clinical data, which reveal reliable and characteristic patterns of coherence. A data-driven technique for discriminating between reliable and unreliable coherence and phase values is described and used to reveal the relationship between coherence and cortical anatomy, such as in the region of the central sulcus, where low phase coherence declines and high phase-shifted coherence increases. Analysis of coherence magnitude and phase makes it possible to determine which signals likely arise from the cortical surface, and which arise from the depths of a sulcus. Alterations in coherence patterns caused by tumors or epilepsy are described and may be used to identify normal and pathological functional relationships between distant cortical areas. Some electrophysiologic/pathologic correlations indicate at least two types of epileptic abnormality, implying a sequence in breakdown of epileptic tissue. The relationship between coherence patterns and behavior and cognition is introduced and compared to similar studies of single-unit binding in animals.