Nestor G. Sepulveda

Current injection into a two-dimensional anisotropic bidomain

A two-dimensional sheet of anisotropic cardiac tissue is represented with the bidomain model, and the finite element method is used to solve the bidomain equations. When the anisotropy ratios of the intracellular and extracellular spaces are not equal, the injection of current into the tissue induces a transmembrane potential that has a complicated spatial dependence, including adjacent regions of depolarized and hyperpolarized tissue. This behavior may have important implications for the electrical stimulation of cardiac tissue and for defibrillation.

Using a magnetometer to image a two‐dimensional current distribution

We describe a mathematical algorithm to obtain an image of a two‐dimensional current distribution from measurements of its magnetic field. The spatial resolution of this image is determined by the signal‐to‐noise ratio of the magnetometer data and the distance between the magnetometer and the plane of the current distribution. In many cases, the quality of the image can be improved more by decreasing the current‐to‐magnetometer distance than by decreasing the noise in the magnetometer.

Finite element analysis of cardiac defibrillation current distributions

A two-dimensional finite element model of the canine heart and thorax developed to examine different aspects of the distribution of current through cardiac tissue during defibrillation is discussed. This model allows comparison of the various electrode configurations for the implantable cardioverter/defibrillator. Since the electrical criteria for predicting defibrillation thresholds are not known, defibrillation energy in dogs was measured to determine the voltages to apply to the model for calculating current distribution. Analyzing isopotential contours, current lines, power distributions, current lines, power distributions, current density histograms, and cumulative current distributions allowed the critical fraction and threshold current density for defibrillation to be estimated, various electrode configurations to be compared, and the sensitivity of the defibrillation threshold to electrode position, patch size, and tissue conductivity to be assessed. It was found that blood can shunt defibrillation current away from the myocardium, that myocardial tissue conductivity strongly affects the current distributions, and that epicardial patch size is more important than subcutaneous patch size.<<ETX>>

Magnetic susceptibility tomography for three-dimensional imaging of diamagnetic and paramagnetic objects

A tomographic technique for reconstructing the three-dimensional distribution of magnetic susceptibility in an object is described, A SQUID magnetometer may be used to measure the perturbations imposed by the object on an applied magnetic field and these data contain information about the susceptibility distribution. To assess the technique, a model object was defined, simulated magnetic field data were generated, and a matrix inversion was carried out with singular value decomposition to yield a least-squares solution for the susceptibility distribution. Various relative geometries of the three interacting physical systems (the applied field, the object and the measurement space) were used and the algorithms performance was investigated for each of the cases in which one of the systems was moved while keeping the other two fixed. With either strategy involving relative motion between the object and the measurement space, accurate, convergent solutions were obtained, but the algorithm failed when only the direction of the uniform applied field was varied. A suitable nonuniform applied field may make the algorithm robust. Applications for a tomographic imaging susceptometer in biomedical imaging, nondestructive evaluation, and geophysics are envisaged. >

Electric and magnetic fields from two-dimensional anisotropic bisyncytia

Cardiac tissue can be considered macroscopically as a bidomain, anisotropic conductor in which simple depolarization wavefronts produce complex current distributions. Since such distributions may be difficult to measure using electrical techniques, we have developed a mathematical model to determine the feasibility of magnetic localization of these currents. By applying the finite element method to an idealized two-dimensional bisyncytium with anisotropic conductivities, we have calculated the intracellular and extracellular potentials, the current distributions, and the magnetic fields for a circular depolarization wavefront. The calculated magnetic field 1 mm from the tissue is well within the sensitivity of a SQUID magnetometer. Our results show that complex bisyncytial current patterns can be studied magnetically, and these studies should provide valuable insight regarding the electrical anisotropy of cardiac tissue.

Instrumentation and techniques for high-resolution magnetic imaging

Abstract not available.

Bipolar Stimulation of Cardiac Tissue Using an Anisotropic Bidomain Model

Bipolar Stimulation of the Cardiac Bidomain. Introduction: One of the fundamental electrophysiologic problems that has not yet been completely elucidated is the response of cardiac tissue to externally applied electric currents. A limited number of theoretical and experimental techniques has been used to study the electric behavior of cardiac tissue in the presence of stimulating currents, and to demonstrate that the anisotropy in the passive electrical properties of the tissue plays an important role in the genesis and propagation of the activation wave‐front and the resulting potential distributions.

Magnetic susceptibility imaging for nondestructive evaluation (using SQUID magnetometer)

High-resolution superconducting magnetometers such as MicroSQUID (superconducting quantum interference device) have been shown to be effective for nondestructive evaluation. MicroSQUID can also be used with a room-temperature magnet to image the magnetic susceptibility of materials. A diamagnetic or paramagnetic sample is scanned in the applied field, and the local perturbations are measured. For thin samples, such as plates, sheets, or thin sections of rock, the data are deconvolved to generate two-dimensional susceptibility images. Three-dimensional structures can be imaged with magnetic susceptibility tomography: deconvolution of a large data set obtained by applying the field and scanning in multiple orientations. Extremely small surface defects on nonmagnetic or weakly magnetic samples are imaged by decorating the sample with paramagnetic microspheres prior to scanning. Magnetic susceptibility imaging demonstrates the feasibility of SQUID nondestructive evaluation on materials that could previously be examined only with X-rays or ultrasound.<<ETX>>

An improved method for magnetic identification and localization of cracks in conductors

A SQUID magnetometer can be used to measure the magnetic field produced by flaws in a two-dimensional, conducting plate carrying a current. Identification of the flaw-induced magnetic field is difficult because of the large magnetic field associated with the edges of the plate and the current in the leads that connect the plate to the power supply. We have developed a technique by which the wire and edge fields can be cancelled prior to mapping the magnetic field. In this technique, a similar unflawed conducting sheet is placed adjacent to the flawed plate, with a connection between the sheet and the plate at one edge, and with the opposite edges of the sheet and of the plate connected to the two conductors of a coaxial cable. Thus, an applied current will flow along one conductor of the cable, across the cancelling sheet, cross into the flawed plate, return along the plate, and then return to the power supply along the other conductor of the coaxial cable. As a result of this geometry, there is no magnetic field from the lead-in wires because they are coaxial, and the magnetic field due to the edges of the plate is cancelled by the opposing magnetic field of the edges in the adjacent sheet. The extent of cancellation is determined primarily by the separation between the plate and the cancelling sheet, by the thickness of the plate, and by macroscopic inhomogeneities in their electrical conductivities.

A mathematical analysis of the magnetic field produced by flaws in two-dimensional current-carrying conductors

We examine the magnetic field produced by small flaws in a two-dimensional, conducting plate carrying an otherwise-uniform current. We use a conjugate function approach to calculate the current and voltage distributions about the circular and elliptical flaws in the conducting plate, and examine the dependence of the normal component of the magnetic field upon distance, hole size, elliptical eccentricity, and elliptical orientation. We show that when the field is calculated, far from the hole, the field falls off as 1/z3, wherez is the distance above the plate, and as 1/r2, wherer is the distance from the center of the hole to the observation point. We also show that for circular and elliptical flaws, the normal component of the magnetic field in the far-field region is linearly related to the area of the flaw.