Marcel Wellner

Synthesis of voltage-sensitive fluorescence signals from three-dimensional myocardial activation patterns.

Voltage-sensitive fluorescent dyes are commonly used to measure cardiac electrical activity. Recent studies indicate, however, that optical action potentials (OAPs) recorded from the myocardial surface originate from a widely distributed volume beneath the surface and may contain useful information regarding intramural activation. The first step toward obtaining this information is to predict OAPs from known patterns of three-dimensional (3-D) electrical activity. To achieve this goal, we developed a two-stage model in which the output of a 3-D ionic model of electrical excitation serves as the input to an optical model of light scattering and absorption inside heart tissue. The two-stage model permits unique optical signatures to be obtained for given 3-D patterns of electrical activity for direct comparison with experimental data, thus yielding information about intramural electrical activity. To illustrate applications of the model, we simulated surface fluorescence signals produced by 3-D electrical activity during epicardial and endocardial pacing. We discovered that OAP upstroke morphology was highly sensitive to the transmural component of wave front velocity and could be used to predict wave front orientation with respect to the surface. These findings demonstrate the potential of the model for obtaining useful 3-D information about intramural propagation.

Minimal principle for rotor filaments

Three-dimensional rotors, or scroll waves, provide essential insight into the activity of excitable media. They also are a suspected cause in the formation and maintenance of ventricular fibrillation, whose lethality is well known. It is therefore of considerable interest to find out what configurations can be adopted by such pathologies. A scrolls behavior is embodied in its organizing center or filament, a largely quiescent tube about which the scroll rotates. Predicting filament shape has normally required computer-intensive simulations of the whole scroll in time. We have found a fast and robust principle that yields the prediction for stationary filaments on a purely geometrical basis, blind to the reaction parameters of the medium. The procedure is to calculate the filament shape as a minimal path. We work in singly diffusive media whose diffusivity tensor—and no other feature—varies spatially. Mathematical and numerical evidence is presented for the proposition that a stable filament is a geodesic in a three-dimensional space whose metric is given by the inverse diffusivity tensor of the medium. Away from the boundaries, a stable filament is unaffected by the reaction parameters. The algorithmic aspects of this work are subsidiary to our main purpose of drawing attention to the universal and unexpectedly exact fit of an elementary geodesic principle within reaction–diffusion theories.

Multiplicative optical tomography of cardiac electrical activity

Cardiac electrical activity can be mapped today through the response of voltage-sensitive dyes; but poor transparency of muscle tissue has enforced shallow-depth imaging. We present a three-dimensional (3D) reconstruction method for electrical activity deep inside the myocardial wall. Our approach is nonlinear and differs substantially from standard diffusive optical tomography. It does not require matrix inversion, data regularization or a priori information concerning the original object. Opposite sides of a slab-shaped preparation are scanned in parallel by detection and illumination points with a constant vector offset between illumination and detection axes (biaxial scanning). Scanning is performed in two perpendicular directions. In each direction, a pair of 2D images is obtained under offsets of opposite signs. These two pairs are the input for a multiplicative reconstruction algorithm, whose output is a 3D image. The overall procedure was successfully tested on computer-generated sources that include points, lines and hemispheres, patterned after actual electrophysiological excitations. The algorithm is computationally efficient and stable with respect to varying noise levels in the raw data.

Probing Field-Induced Tissue Polarization Using Transillumination Fluorescent Imaging

Despite major successes of biophysical theories in predicting the effects of electrical shocks within the heart, recent optical mapping studies have revealed two major discrepancies between theory and experiment: 1), the presence of negative bulk polarization recorded during strong shocks; and 2), the unexpectedly small surface polarization under shock electrodes. There is little consensus as to whether these differences result from deficiencies of experimental techniques, artifacts of tissue damage, or deficiencies of existing theories. Here, we take advantage of recently developed near-infrared voltage-sensitive dyes and transillumination optical imaging to perform, for the first time that we know of, noninvasive probing of field effects deep inside the intact ventricular wall. This technique removes some of the limitations encountered in previous experimental studies. We explicitly demonstrate that deep inside intact myocardial tissue preparations, strong electrical shocks do produce considerable negative bulk polarization previously inferred from surface recordings. We also demonstrate that near-threshold diastolic field stimulation produces activation of deep myocardial layers 2-6 mm away from the cathodal surface, contrary to theory. Using bidomain simulations we explore factors that may improve the agreement between theory and experiment. We show that the inclusion of negative asymmetric current can qualitatively explain negative bulk polarization in a discontinuous bidomain model.

The Electric Potential

We have just seen how a force motivates the idea of an electric field (the electric force per unit test charge).

Waves in excitable media: Effects of wave geometry

We consider waves in two-dimensional excitable media. The correct form of the eikonal equation (i.e. the formula that predicts propagation speed as a function of curvature) is a question that has surfaced and resurfaced during the last twenty years or so. Good answers have become available in limiting cases and under certain approximations, notably weak curvatures, low frequencies, and sharp wave fronts. The solution is important in some cardiac pathologies, as well as in our basic understanding of excitable-medium mathematics. After a brief review of curvature effects, particularly in heart tissue, we demonstrate how to obtain a drastically corrected formula that is free of restrictions on frequency and sharpness. (In the original limiting cases the result is unchanged.) Our derivation uses a finite-renormalization method. We illustrate the formula in the context of cardiac tissue. For the sake of definiteness we work in terms of FitzHugh–Nagumo-like models.

Rotation and Torque

Rotational motion, or spin, is visible everywhere; it is involved whenever an object changes its orientation. Our technical civilization relies on wheels and levers, and will continue to do so despite the modern engineer’s justified abhorrence of “moving parts.” In the natural world, rotation may be observed on levels from astronomical to subatomic. All astronomical entities, such as the Earth, the Galaxy, the stars, etc., rotate to some extent about their own axis. This rotation is quite independent of their orbital motion (“revolution”), as the familiar example of the Earth reminds us. On the molecular, atomic, and subatomic scale, particle spin is a key to many important and beautiful phenomena, some of which will be touched upon later in this book.

Manifest gauge and Poincare covariance

Manifest gauge invariance is known to be incompatible with manifest Poincare covariance (Strocchis theorem). By extending the notion of gauge invariance to that of gauge covariance, we circumvent that incompatibility, at least for free electromagnetic potentials. In the new formulation the potentials, AG, for all permissible gauges G. act on a common Hilbert space. This formulation is shown to be inequivalent to the more conventional ones. (In particular, the Coulomb gauge is now inaccessible.) The abstract gauges G are represented by c-number potentials VG, which play a central role in the theory. Even without interaction, they obey a field equation with a source, and thus they anticipate the existence of electric charges.

A theory of elementary couplings III

Abstract Some recent attempts at constructing a detailed dynamical theory (“compensation theory”) of strong interactions are revised, extended, and systematized. It is hoped that this article, which aims at being self-contained, may serve as an introduction to the subject.

Three-dimensional reconstruction of electrical activity in the heart using optical parallax

Until recently, optical mapping of electrical activity in the heart muscle using voltage-sensitive dyes has mainly been applied to subsurface imaging. Here we present a method for the three-dimensional (3D) reconstruction of electrical activity deep inside the myocardial wall. We propose an alternative approach to diffusive optical tomography, based on ideas from binocular vision. Detection and illumination occur on opposite sides of the preparation. Staining with absorptive voltage-sensitive dyes is assumed. Data acquisition follows a paraxial scanning procedure, which modifies coaxial scanning by the introduction of a vector offset between illumination and detection axes. Pairs of 2D images are obtained corresponding to offsets of opposite signs. Those image pairs created by parallax are used as an input for the reconstruction algorithm, whose output is a 3D optical image of intramural electrical excitation. We apply this method to the slab geometry. The procedure was tested for a variety of computer-generated sources including particles, lines, bubbles, and simulated electrophysiological patterns such as scroll waves. The limitations of the method and possible improvements are discussed.