The Laplacian inverse problem of electrocardiography: an eccentric spheres study

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.

An implanted spherical head model exposed to electromagnetic fields at a mobile communication frequency

Can cellular phones and personal communication systems base station antennas affect the active or passive implantable medical devices adversely? Concerns over the possible harmful effects of nonionizing irradiaton upon implanted medical devices have been present for many years. Key issues to address are the questions of whether mobile phones have a detrimental effect on implants, and how the interaction of the handset with the body can be minimized in order to both alleviate public fears and improve handset antenna performance and new implant designs. This paper presents a thorough investigation of the scattering of an electromagnetic (EM) wave from a perfectly conducting implant (a cylindrical wire and a very thin cylindrical disk) of electrically small radius (of resonant length), embedded eccentrically into a dielectric spherical head model by a dipole antenna (0.4 wavelength) at 900 MHz. The dyadic Green's function (DGF) for spherical vector wave functions is employed. Analytical expressions for the scattered fields of an implant embedded head model is obtained. Numerical results from analytical expressions are computed for this problem and then compared with the results from the same model using the finite-difference time-domain, EMU-FDTD electromagnetic simulator. Good agreement is observed between the analytical results on the proposed method in comparison with the FDTD method.

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.

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 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.

Application of high-order boundary elements to the electrocardiographic inverse problem

Eight-noded quadrilateral boundary elements are applied to the electrocardiographic inverse problem as an example for high-order boundary elements. It is shown that the choice of the shape functions used for approximation of the potentials has a remarkable influence on the solution obtained if the number of electrodes is smaller than the number of primary source points (under-determined equation system). Three different formulations are investigated considering a concentric spheres problem where an analytic solution is available: (a) the isoparametric formulation; (b) the quasi-first-order formulation; and (c) the pseudo-subparametric formulation as a new method. In a second step the pseudo-subparametric formulation (which provided the best results in the test problem) is applied to real word data. The transmembrane potential pattern of a 40 years old female suffering from severe heart failure and ventricular tachycardia after large anterior wall myocardial infarction is reconstructed for one time instant. Furthermore, an algorithm for the calculation of the transfer matrix is presented which avoids restrictions to the boundary element mesh caused by the placement of the electrodes.