Biomedical subjects

F Greensite

Publications and source records attributed to F Greensite.

13 recordsLinked to original sources

PubMed2000

Temporally unconstrained space-time treatment of linear formulations of the inverse problem of electroencephalography.

This paper provides an optimal mechanism for the introduction of temporal constraints into linear imaging formulations of the inverse electroencephalography problem. The method is based on derivation of a "virtual-SVD," an extension of generalized singular value decomposition to the setting of random matrices. Surprisingly, the formalism is superior, in principle, to standard regularization methods even in the absence of known temporal constraints. Investigation of this basic temporally unconstrained setting was undertaken to illustrate the application of the method, and as a necessary first step in its systematic evaluation. Although abstract simulations demonstrate superior accuracy for the virtual-SVD method as compared with standard methods, investigation of a particular realistic simulation involving spatiotemporally distributed temporal lobe interictal spikes indicates that significant improvement in solution estimate quality under temporally unconstrained conditions may be limited to a very narrow range of the signal-to-noise ratio (particularly in the context of a markedly row-deficient transfer matrix). These results underline the prospective importance of investigation of the efficacy and feasibility of application of temporal constraints (such as those resulting from knowledge of the general time series format of epilepsy associated wave forms, evoked potentials, etc.) within the derived formalism.

Biomedical Engineering↗

PubMed1998

An improved method for estimating epicardial potentials from the body surface.

We present a new method for regularizing the illposed 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.

Computer Simulation↗

PubMed1997

A new method for myocardial activation imaging.

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.

Algorithms↗

PubMed1995

A theorem concerning myocardial activation imaging.

We present a theorem which is the basis of a new approach to imaging ventricular surface activation. Application of the theorem in realistic simulations and with human data is presented elsewhere in this conference.

Algorithms↗

PubMed1994

Thymic rebound in a patient with scrotal mesothelioma.

Benign enlargement of the thymus, termed "thymic rebound," is a well-documented phenomenon in children. It typically follows a period of stress. Thymic rebound in an adult is not described in the literature. We present the first documented account of an adult with malignant disease who exhibited thymic rebound without chemotherapy, infection, or other obvious cause for this phenomenon.

Adult↗

PubMed1994

The mathematical basis for imaging cardia electrical function.

The essential difficulty of the source-imaging problem in electrocardiology is that the data (body surface potentials) depend continuously on the properties of complex uniquely determined equivalent sources (e.g., epicardial potentials) while such sources do not depend continuously on the data (precluding utility of direct inversion of the operator relating sources and data). This is in distinction to the standard digital tomographic imaging problems in radiology, which superficially resemble the electrocardiographic imaging problem in their requirement for solution of a linear integral equation. From the mathematical standpoint, the electrocardiographic imaging problem requires that an operator with a continuous inverse be constructed from the original operator. This may be accomplished either by slightly perturbing the original operator (the regularization approach), or by performing a calculation on the data (based on inherent source evolution singularities) which allows restriction of the admissible solution domain to a compact set (the topological approach). An understanding of the mathematical questions fundamental to this imaging problem is helpful in assessing its present status and in identifying promising directions for the development of a clinically useful technique.

Electrocardiography↗

PubMed1993

Demonstration of "discontinuities" in the time derivatives of body surface potentials, and their prospective role in noninvasive imaging of the ventricular surface activation map.

The ill-posed nature of the inverse electrocardiography problem has necessitated use of regularization techniques as a means of rendering epicardial potential maps. Significant inaccuracies are introduced by such methods (on the order of 50% error relative to the actual map), due to imposition of the regularizing functionals. It has been previously shown that the generator of topological changes in epicardial potential maps during ventricular activation is of much lower order than the epicardial maps themselves, yet sufficiently constrains the full ventricular surface activation mapping problem so as to obviate the need for further regularization. The mathematical formalism for reconstructing this generator has previously been presented under the assumption of negligible depolarization wavefront thickness, and requires identification and processing of "step discontinuities" predicted to occur in body surface potential derivatives. Using principal component analysis and spatial averaging methods, we have examined this fundamental prediction of the formalism in the context of a nonzero depolarization wavefront thickness (leading to prediction of dominant body surface potential derivative deflections with rise times comparable to those of ventricular electrogram intrinsic deflections). Studies of the body surface potential data obtained in three normal subjects supports the predictions of the theory, thereby suggesting the possible usefulness of the approach as an alternative to traditional regularization methods.

Adult↗

PubMed1992

A new method for regularization of the inverse problem of electrocardiography.

The inverse problem of electrocardiography (specifically, that part concerned with the computation of the ventricular surface activation isochrones) is shown to be formally equivalent to the problem of identification and measurement of discontinuities in derivatives of body surface potentials. This is based on the demonstration that such measurements allow localization of the relative extrema of the ventricular surface activation map (given a forward problem solution), which in turn restricts the space of admissible solution maps to a compact set. Although the inverse problem and the problem of identifying derivative discontinuities are both ill-posed, it is possible that the latter may be more easily or justifiably resolved with available information, particularly as current methods for regularizing the inverse problem typically rely on a regularization parameter chosen in an a posteriori fashion. An example of the power of the approach is the demonstration that a recent Uniform Dipole Layer Hypothesis-based method for producing the ventricular surface activation map is largely independent on that hypothesis and capable in principle of generating maps that are very similar in a precise sense to those that would result from the usual epicardial potential formulation (assuming the latter were capable of producing intrinsic deflections in computed epicardial electrograms sufficiently steep to accurately compute the activation map). This is consistent with the preliminary success of the former method, despite the significant inaccuracy of its underlying assumption.

Animals↗

PubMed1992

Some imaging parameters of the oblique dipole layer cardiac generator derivable from body surface electrical potentials.

The goal of noninvasively imaging the cardiac electrical generator is considerably complicated by the conductive anistropy of the cardiac muscle which, as featured in the oblique dipole layer model of ventricular depolarization, introduces muscle fiber geometry and a conductivity tensor as additional unknowns. The ventricular surface activation map has been previously presented as a description of the cardiac generator in image form, but the integral equation defining its relationship to the body surface potentials is valid only under the less accurate uniform dipole layer hypothesis. Using an argument from differential geometry, which allows the integral equation approach to be bypassed, we show that the critical points of this map can still be localized on the heart surface from the body surface potentials in a manner fully consistent with the oblique dipole layer model. Thus, in principle, a realistic and useful "image-like" output is possible in a limited way even without explicit information regarding conductivity anisotropy. The realization of this output will require improvements in the temporal resolution presently available from existing body surface potential mapping systems.

Action Potentials↗

PubMed1991

Target-point combination of MR images.

A method is described for combining multiple magnetic resonance images of the same anatomic slice to produce a single image which incorporates the favorable contrast features of each of the original images. The target-point method is a general method that includes linear combination as a subset and is designed to deal with the clinical need to maximize the contrast-to-noise ratio between several pairs of tissue simultaneously. Although it is intrinsically a nonlinear method, noise propagates approximately uniformly into the combined image. In examples of brain images the target-point method produces images with higher mutual contrast than the first principal component weighted sun image.

Brain↗

PubMed1991

Fatty infiltration of the liver: quantification with phase-contrast MR imaging at 1.5 T vs biopsy.

Quantification of hepatic fat content by application of MR phase-contrast imaging (Dixon method) at 1.5 T was compared with results of biopsy in 16 patients with a variety of liver abnormalities. Motion artifact was suppressed by employing six or eight averages of short TR in-phase (echo offset, 0 msec), out-of-phase (echo offset, 1.1 msec), and in-phase (echo offset, 2.2 msec) spin-echo pulse sequences. The 360 degree out-of-phase sequence was used to assess the impact of T2* decay on this method of estimating fat fraction. A standard two-echo long TR sequence also was obtained in all patients. Histologic preparations from the biopsy specimens were examined by a pathologist who had no knowledge of the MR results and were graded according to overall visual assessment as belonging to one of four categories of fat fraction. Results of the MR-calculated apparent fat fraction were compared directly with biopsy category and were also placed in MR fat fraction categories, allowing estimation of the statistical correlation between the biopsy and MR grading systems. Eight of eight patients with biopsy categories indicating a fat fraction of less than 0.25 were computed by MR to have a fat fraction of less than 0.1. Seven of eight patients with biopsy categories indicating a fat fraction of greater than 0.25 were computed by MR to have a fat fraction of at least 0.24. The MR-calculated apparent fat fraction category correlated significantly with the histologic biopsy category (r = .86, p less than .01). When compared with the in-phase image, decreased signal from liver was visually apparent on the 180 degree out-of-phase images in all cases in which the fat fraction was at least 0.24, but there was no indication of fatty liver on the standard T1- or T2-weighted images. Calculated T2 also showed no correlation with degree of fatty deposition. Correction for T2* decay by using the 360 degree out-of-phase acquisition in addition to the standard 0 degree and 180 degree out-of-phase images had little effect on fat fraction computation. Phase-contrast MR is a promising noninvasive method for quantitative assessment of fatty deposition in the liver.

Adult↗

PubMedDate not supplied

Well-posed formulation of the inverse problem of electrocardiography.

It has long been speculated that incorporation of available time constraints into the inverse electrocardiography problem could improve the accuracy of maps of epicardial potential or activation reconstructed from body surface potential measurements. However, all prior formulations of this problem have remained ill-posed, and the best way to utilize these constraints has been unclear. By making proper use of the timing information, we show that the inverse electrocardiography problem (for calculation of ventricular surface activation isochrones) is formally well-posed under anisotropic bidomain conditions and the assumption that ventricular muscle action potential phase 0 is a step discontinuity. In practical terms, this implies that non-regularized stable activation map solutions are possible if correlates of derived body surface potential derivative discontinuity times can be identified from the noisy analog signals, and only a small number of ventricular surface activation function extrema occur during a unit of time resolution defined by phase zero duration over the spatial extent of a bidomain point. We include a quasi-realistic numerical example illustrating the ease with which the extrema of the endocardial and epicardial activation maps are computed via Jump Maps derived from body surface potentials (this being the crucial step in rendering images of ventricular surface activation in this approach). The efficient signal processing algorithm used to accomplish this task is well suited to the setting of multiple extrema occurring during overlapping phase zero time intervals.

Algorithms↗

PubMedDate not supplied

New quantitative and qualitative approaches to the inverse problem of electrocardiology: their theoretical relationship and experimental consistency.

In addition to formidable theoretical obstacles that a proposed solution to the inverse electrocardiology problem must overcome, there are great practical difficulties in establishing its accuracy in actual clinical application. However, the recent appearance of two fundamentally independent treatments of the inverse problem raises the possibility that they may be used in tandem to help establish their individual accuracy. Thus, if the two methods give incompatible results in application then one of the methods must be inaccurate. Conversely, if the two methods give compatible results then the accuracy of both methods is supported (for the particular quantities measured) subject only to the validity of the assumptions common to both methods. We have compared results from the application of a quantitative "integral equations based" method with that of a qualitative "differential topology inspired" approach in three healthy volunteers. The output examined consists of measurements of the times of appearance of epicardial sources (depolarization wavefront breakthroughs) and sinks of the ventricular surface activation map. The extent of agreement on source/sink times between the methods was consistent with the resolution limits imposed by noise and discrete sampling on derivatives of the electrocardiogram. When events defined by the integral method occurring within 2 ms of each other are grouped together (and their times averaged), the two methods agreed on source/sink times to within 3 ms except in two instances where they differed by 5 ms. The measurements made by the two methods were found to be highly correlated (R = 0.95). While the quantitative method alone rests on a variety of modeling and procedural assumptions, the only assumption common to both methods is the uniform dipole layer hypothesis. Thus, subject to this single assumption, one may infer the accuracy of the quantitative method in healthy individuals for epicardial source/sink times. On the other hand, coupling with the far more detailed quantitative method allows further useful characterization of the output of the qualitative method. In particular, this study provides convincing evidence that the major deflections of the spatial velocity electrocardiogram are coupled to particular epicardial sources and sinks, as has been previously conjectured on theoretical grounds. This raises the possibility of bedside evaluation of these epicardial events.

Electrocardiography↗