Fred Greensite

University of California, Irvine

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Geertjan Huiskamp

University Medical Center Utrecht

Yao‐Jin Qian

University of California, Irvine

Richard B. Buxton

University of California, San Diego

R B Dietrich

University of California, Irvine Medical Center

Anton N. Hasso

University of California, Irvine

Ira T. Lott

University of California, Irvine

Andrew J. Pullan

University of Auckland

A. van Oosterom

Radboud University Nijmegen

Yu‐Kun Tsui

Chi Mei Medical Center

Fong Y. Tsai

University of California, Irvine

Cooperative Institutions

University of California, Irvine Medical Center

University of California, Irvine

University of California, San Diego

Neurological Surgery

University of California San Diego Medical Center

University Medical Center Utrecht

University of California System

Irvine University

Resonance Research (United States)

Harvard University

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

IEEE Transactions on Biomedical Engineering (1993)

Fred Greensite

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.< >

Classification of discontinuities

Body surface

Regularization

10.1109/10.250576

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Citations (10)

TECHNIQUES IN TREATING THE BIOELECTROMAGNETIC SOURCE IMAGING PROBLEMS AND THEIR APPLICATION

World Scientific Publishing Company eBooks (2005)

Fred Greensite Andrew J. Pullan G. HUISKAMP

10.1142/9789812701077_0006

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Citations (0)

Cortical CSF volume fluctuations by MRI in brain aging, dementia and hydrocephalus

Neuroreport (1994)

Jane F. Emerson Po-Chou Chen William R. Shankle Fred Greensite Eldon L. Foltz

DYNAMIC MR imaging has revealed dramatic fluctuations in the appearance of CSF in the cortical sulci and cortical subarachnoid spaces in aging individuals and patients with hydrocephalus, dementia and Down syndrome in contrast to young healthy volunteers. The changes have been interpreted as volume fluctuations that represent undamped CSF hydrodynamics and have implications with respect to the origin of CSF in the cortical regions and with respect to the similarity between aging and dementia and edematous states of the brain.

10.1097/00001756-199409080-00003

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Citations (9)

Spinal Subdural Hematoma Associated with Attempted Epidural Anesthesia and Subsequent Continuous Spinal Anesthesia

Anesthesia & Analgesia (1980)

Fred Greensite Jordan Katz

*Resident, Department of Anesthesiology, University of California, San Diego. †Professor and Vice Chairman, Department of Anesthesiology, University of California, San Diego; Chief, Anesthesia Service, VA Medical Center, San Diego. Anesthesiology Service, VA Medical Center, La Jolla, California 92161. Reprint requests to Dr. Katz, Anesthesiology Service, VA Medical Center, 3350 La Jolla Village Dr, San Diego CA 92161. Accepted for publication September 5, 1979.

10.1213/00000539-198001000-00017

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Citations (97)

Cosmology from a non-physical standpoint: an algebraic analysis

arXiv (Cornell University) (2022)

Fred Greensite

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".

Wedge (geometry)

Algebraic structure

10.48550/arxiv.2209.14127

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Partial inverse problems

Inverse Problems (2006)

Fred Greensite

We develop consequences of the generalization of 'ordinary' to 'partial' inverse problems—where the latter are inverse problems in which the unknown has domain dimension higher than 1 and is thereby subject to operators whose components individually do not address all the variables. This is analogous to the transition from ordinary to partial differential equations—the difference in this case being that the relevant operators are compact rather than unbounded. Accordingly, the significance of this generalization is in its implications for regularization technique. Previously, such problems (which arise in widespread scientific settings) have been approached with a variety of ad hoc methodologies. In contrast, we derive a favoured methodology based on the changes in group structures naturally associated with actions on vectors (the unknowns in discretized ordinary inverse problems) versus those associated with actions on higher order arrays (the unknowns in discretized partial inverse problems). A principal finding of this approach is that the set of admissible random matrices for treatment of a discretized partial inverse problem is a particular homogeneous space whose isotropy group determines the favoured estimation mechanism. A number of surprising results are obtained, including identification of situations where a favoured nontrivial regularization matrix can be entirely determined from treatment of (discretized) second kind Fredholm equations. The derived methodology is contrasted with various standard treatments. Numerical examples illustrate the method and demonstrate its potential for providing improved accuracy compared with usual regularization technique.

10.1088/0266-5611/22/2/005

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Citations (2)

When is the Inverse Problem of Electrocardiography Well-Posed

Fred Greensite Jinping Qian

The inverse problem of electrocardiography [1] can be formulated as a reconstruction of maps of epicardial potentials and/or activation times from observed body-surface potential distributions. The problem is formulated as a Fredholm equation of the first kind, where the kernel has a finite L2-norm. Therefore, the body-surface potential data—being the "convolution" of the source with a well-behaved transfer function—is a smoothed version of the desired source and the least-squares solution is unstable in the presence of measurement and modelling noise. Thus, when the inverse problem of electrocardiography is formulated in this manner it is ill-posed, i.e. the solution does not depend continuously on the data, and regularization methods produce severely filtered solution candidates [2, 3, 4, 5]. Almost since the inverse problem of electrocardiography was first stated, mechanisms for incorporating inherent time constraints have been proposed, but none has led to a well-posed formulation. We will demonstrate in this chapter that the ill-posedness of the inverse problem of electrocardiography resolves when one supplements the usual bidomain assumptions with the assumption that phase 0 of the ventricular action potential is a step discontinuity. This extends work found in [6, 7, 8].

Well-posed problem

Regularization

Bidomain model

Convolution (computer science)

10.1007/978-3-322-85017-1_20

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Citations (1)

Two mechanisms for electrocardiographic deconvolution

Fred Greensite

Electrocardiographic imaging requires computation of a time-varying "source" (e.g. epicardial potentials) from measurements (body surface potentials) with a known linear dependence on the source. The problem has been usually treated in a time-independent fashion, but since it is ill-posed, and since solutions at adjacent time points must be codependent, it has been suggested that time-dependent information be incorporated into the regularization procedure. The authors supply two different mechanisms for incorporating time in a natural fashion based on treatment of the data as a generalized convolution.

Convolution (computer science)

Regularization

Body surface

10.1109/iembs.1996.647487

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Citations (8)

Susceptibility-weighted imaging for differential diagnosis of cerebral vascular pathology: A pictorial review

Journal of the Neurological Sciences (2009)

Yu‐Kun Tsui Fong Y. Tsai Anton N. Hasso Fred Greensite Binh V. Nguyen

Susceptibility Weighted Imaging

Quantitative Susceptibility Mapping

Maximum intensity projection