F. Greensite

Bio: F. Greensite is an academic researcher from University of California, Irvine. The author has contributed to research in topics: Mathematics & Inverse problem. The author has an hindex of 3, co-authored 3 publications receiving 348 citations.

A new method for myocardial activation imaging

Abstract: Noninvasive images of the myocardial activation sequence are acquired, based on a new formulation of the inverse problem of electrocardiography in terms of the critical points of the ventricular surface activation map. It is shown that the method is stable with respect to substantial amounts of correlated noise common in the measurements and modeling of electrocardiography and that problems associated with conventional regularization techniques can be circumvented. Examples of application of the method to measured human data are presented. This first invasive validation of results compares well to previously published results obtained by using a standard approach. The method can provide additional constraints on, and thus improve, traditional methods aimed at solving the inverse problem of electrocardiography.

An improved method for estimating epicardial potentials from the body surface

Abstract: The authors present a new method for regularizing the ill-posed problem of computing epicardial potentials from body surface potentials. The method simultaneously regularizes the equations associated with all time points, and relies on a new theorem which states that a solution based on optimal regularization of each integral equation associated with each principal component of the data will be more accurate than a solution based on optimal regularization of each integral equation associated with each time point. The theorem is illustrated with simulations mimicking the complexity of the inverse electrocardiography problem. As must be expected from a method which imposes no additional a priori constraints, the new approach addresses uncorrelated noise only, and in the presence of dominating correlated noise it is only successful in producing a "cleaner" version of a necessarily compromised solution. Nevertheless, in principle, the new method is always preferred to the standard approach, since it (without penalty) eliminates pure noise that would otherwise be present in the solution estimate.

Cosmology from a non-physical standpoint: an algebraic analysis

Abstract: We present a non-physical interpretation of the Cosmological Constant based on a particular algebraic analysis. This also introduces some novel algebraic structures, such as ``unital norms", ``uncurling metrics", and ``partial wedge products".

Use of group theory in the selection and description of regularization methods for functional source imaging

Abstract: Commonly, functional source imaging problems are "partial" rather than "ordinary" inverse problems-wherein the defining operator consists of component operators that individually do not address all variables of the unknown. When this ordinary-to-partial transition is minimally constrained, algebraic principles can be used to derive a favored methodology-which we do here. The resulting Isotropy method is compared to two other regularization methods proposed for functional source imaging (Kalman and Joint Regularization). This theoretical support for the favored status of the Isotropy method is consistent with its favorable computational performance in low prior information settings, as indicated in recent publications

Characterizations of real finite-dimensional unital algebras

Abstract: . We provide novel characterizations of the inversion operation on the units of real finite-dimensional unital associative algebras, based on the ways an algebra’s inversion operation can be uncurled. Using an associated functor, these augment the tools available for providing a negative answer to the (recursively undecidable) question of whether two such algebras are related by an epimorphism. Various other features are presented, arising from the extended notion of an algebra norm resulting from these characterizations.

The forward and inverse problems of electrocardiography

Abstract: This article summarizes the theoretical underpinnings of both the forward and inverse problems of electrocardiography. Space limitations prohibit describing all of the research work done in these areas, and the author apologizes in advance for any omissions on this account or due to oversight. The article should enable one to gain a better qualitative and quantitative understanding of the heart's electrical activity.

Geometrical aspects of the interindividual variability of multilead ECG recordings

Abstract: The ECG as measured from healthy subjects shows a considerable interindividual variability. This variability is caused by geometrical as well as by physiological factors. In this study, the relative contribution of the geometrical factors is estimated. In addition a method aimed at correcting for these factors is described. First, a measure (RV) for quantifying the overall variability is presented, and for healthy individuals its value is estimated as 0.52. Next, based on a simulation study using the individual (heart-lung-torso) geometry of 25 subjects, the variability caused by geometrical factors is estimated as 0.40, indicating that in healthy subjects the RV for healthy individuals resulting from electrophysiology is of the order of 0.33. In an evaluation of the correction procedure, applied to realistic, simulated body surface potentials, it is shown that RV caused by geometrical factors can be reduced from 0.40 to 0.06. When applying the correction procedure to measured ECG data no reduction of the RV value could be demonstrated. These results indicate that the involved procedure of the inverse computation of a cardiac equivalent source, at the present time, is of insufficient quality to cash in on the substantial reduction of RV values from 0.52 down to 0.33 that might be obtainable.

Non-Invasive Imaging of Cardiac Activation and Recovery

Abstract: The sequences of activation and recovery of the heart have physiological and clinical relevance. We report on progress made over the last years in the method that images these timings based on an equivalent double layer on the myocardial surface serving as the equivalent source of cardiac activity, with local transmembrane potentials (TMP) acting as their strength. The TMP wave forms were described analytically by timing parameters, found by minimizing the difference between observed body surface potentials and those based on the source description. The parameter estimation procedure involved is non-linear, and consequently requires the specification of initial estimates of its solution. Those of the timing of depolarization were based on the fastest route algorithm, taking into account properties of anisotropic propagation inside the myocardium. Those of recovery were based on electrotonic effects. Body surface potentials and individual geometry were recorded on: a healthy subject, a WPW patient and a Brugada patient during an Ajmaline provocation test. In all three cases, the inversely estimated timing agreed entirely with available physiological knowledge. The improvements to the inverse procedure made are attributed to our use of initial estimates based on the general electrophysiology of propagation. The quality of the results and the required computation time permit the application of this inverse procedure in a clinical setting.

Application of L1-Norm Regularization to Epicardial Potential Solution of the Inverse Electrocardiography Problem

Abstract: The electrocardiographic inverse problem of computing epicardial potentials from multi-electrode body-surface ECG measurements, is an ill-posed problem. Tikhonov regularization is commonly employed, which imposes penalty on the L2-norm of the potentials (zero-order) or their derivatives. Previous work has indicated superior results using L2-norm of the normal derivative of the solution (a first order regularization). However, L2-norm penalty function can cause considerable smoothing of the solution. Here, we use the L1-norm of the normal derivative of the potential as a penalty function. L1-norm solutions were compared to zero-order and first-order L2-norm Tikhonov solutions and to measured 'gold standards' in previous experiments with isolated canine hearts. Solutions with L1-norm penalty function (average relative error [RE] = 0.36) were more accurate than L2-norm (average RE = 0.62). In addition, the L1-norm method localized epicardial pacing sites with better accuracy (3.8 +/- 1.5 mm) compared to L2-norm (9.2 +/- 2.6 mm) during pacing in five pediatric patients with congenital heart disease. In a pediatric patient with Wolff-Parkinson-White syndrome, the L1-norm method also detected and localized two distinct areas of early activation around the mitral valve annulus, indicating the presence of two left-sided pathways which were not distinguished using L2 regularization.

Noninvasive Electrocardiographic Imaging

Abstract: Background:Cardiac arrhythmias continue to be a leading cause of death and disability. Despite this alarming fact, a noninvasive imaging modality for cardiac electrophysiology (EP) has not been developed. Standard electrocardiographic techniques attempt to infer electrophysiological processes in the heart from a limited number of recordings on the body surface. This traditional approach is limited in its ability to provide information on regional electrocardiac activity and to localize electrophysiological events in the heart (e.g., arrhythmogenic foci; regions of elevated dispersion of myocardial repolarization). This article reviews the development of a novel imaging modality (electrocardiographic imaging [ECGI]) for the reconstruction of cardiac electrical activity from potentials measured away from the heart (i.e., on the torso surface). The results presented demonstrate that ECGI can noninvasively reconstruct epicardial potentials, electrograms, and isochrones with good accuracy and resolution. Results:The locations of ectopic pacing sites are reconstructed within 10 mm of their actual positions. Dual epicardial pacing sites separated by 52 mm, 35 mm, and 17 mm can be resolved. The depth of intramural ectopic activity can be estimated and the direction of intramural activation spread can be determined from the reconstructed epicardial potential pattern and its evolution in time. Results from infarcted hearts demonstrate that ECGI can detect and reconstruct the abnormal electrophysiological substrate associated with the infarct. The figure-of-eight pattern of reentrant activation in the epicardial border zone during ventricular tachycardia is also reconstructed by ECGI noninvasively. Conclusions:These results demonstrate the potential of ECGI as a clinical noninvasive imaging modality for identifying patients at risk of cardiac arrhythmias and for guiding and evaluating antiarrhythmic interventions in such patients. A.N.E. 1999;4(3):340–359