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Capturing the Influence of Conduction Velocity on Epicardial Activation Patterns Using Uncertainty Quantification

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Capturing the Influence of Conduction Velocity on Epicardial...

Computers in Cardiology (CinC)

作者： Anna Busatto Lindsay C Rupp Karli Gillette Akil Narayan Gernot Plank Rob S MacLeod Scientific Computing and Imaging Institute University of Utah SLC UT USA Nora Eccles Cardiovascular Research and Training Institute University of Utah SLC UT USA Department of Biomedical Engineering University of Utah SLC UT USA University of Utah Salt Lake City UT Institute of Biophysics Medical University of Graz Graz Austria Department of Mathematics University of Utah SLC UT USA

Individual variability in parameter settings, due to either user selection or disease states, can impact accuracy when simulating the electrical behavior of the heart. Here, we aim to test the impact of inevitable uncertainty in conduction velocities (CVs) on the output of simulations of cardiac propagation, given three stimulus locations on the left ventricular (LV) free wall. To understand the role of physiological variability in CV in simulations of cardiac activation, we generated detailed maps of the variability in propagation simulations by implementing bi-ventricular activation simulations and quantified the effects by deploying robust uncertainty quantification techniques based on polynomial chaos expansion (PCE). PCE allows efficient stochastic exploration with reduced computational demand by utilizing an emulator for the underlying forward model. Our results suggest that CV within healthy physiological ranges plays a small role in the activation times across all stimulation locations. However, we noticed differences in variation coefficients depending on the stimulation site, i.e., LV endocardium, midmyocardium, and epicardium. We observed low levels of variation in activation times near the earliest activation sites, whereas there was higher variation toward the termination sites. These results suggest that CV variability can play a role when simulating healthy and diseased states.

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Finding stationary points on bounded-rank matrices: A geometric hurdle and a smooth remedy

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arXiv 2021年

作者： Levin, Eitan Kileel, Joe Boumal, Nicolas Department of Computing and Mathematical Sciences California Institute of Technology United States Department of Mathematics Oden Institute for Computational Engineering and Sciences University of Texas Austin United States Switzerland

We consider the problem of provably finding a stationary point of a smooth function to be minimized on the variety of bounded-rank matrices. This turns out to be unexpectedly delicate. We trace the difficulty back to a geometric obstacle: On a nonsmooth set, there may be sequences of points along which standard measures of stationarity tend to zero, but whose limit points are not stationary. We name such events apocalypses, as they can cause optimization algorithms to converge to non-stationary points. We illustrate this explicitly for an existing optimization algorithm on bounded-rank matrices. To provably find stationary points, we modify a trust-region method on a standard smooth parameterization of the variety. The method relies on the known fact that second-order stationary points on the parameter space map to stationary points on the variety. Our geometric observations and proposed algorithm generalize beyond bounded-rank matrices. We give a geometric characterization of apocalypses on general constraint sets, which implies that Clarke-regular sets do not admit apocalypses. Such sets include smooth manifolds, manifolds with boundaries, and convex sets. Our trust-region method supports parameterization by any complete Riemannian *** Codes 65K10, 49J53, 90C26, 90C46 Copyright © 2021, The Authors. All rights reserved.

关键词： Matrix algebra

A low-degree strictly conservative finite element method for incompressible flows

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arXiv 2021年

作者： Zeng, Huilan Zhang, Chen-Song Zhang, Shuo LSEC Institute of Computational Mathematics and Scientific/Engineering Computation Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing100190 China University of Chinese Academy of Sciences Beijing100049 China

In this paper, a new P2 − P1 finite element pair is proposed for incompressible fluid. For this pair, the discrete inf-sup condition and the discrete Korn's inequality hold on general triangulations. It yields exactly divergence-free velocity approximations when applied to models of incompressible flows. The robust capacity of the pair for incompressible flows are verified theoretically and numerically. © 2021, CC BY.

关键词： Navier Stokes equations

AutoCT: Automated CT registration, segmentation, and quantification

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arXiv 2023年

作者： Bai, Zhe Essiari, Abdelilah Perciano, Talita Bouchard, Kristofer E. Applied Mathematics and Computational Research Division Lawrence Berkeley National Laboratory United States Scientific Data Division Lawrence Berkeley National Laboratory United States Biological Systems and Engineering Division Lawrence Berkeley National Laboratory United States Helen Wills Neuroscience Institute Redwood Center for Theoretical Neuroscience UC Berkeley United States

The processing and analysis of computed tomography (CT) imaging is important for both basic scientific development and clinical applications. In AutoCT, we provide a comprehensive pipeline that integrates an end-to-end automatic preprocessing, registration, segmentation, and quantitative analysis of 3D CT scans. The engineered pipeline enables atlas-based CT segmentation and quantification leveraging diffeomorphic transformations through efficient forward and inverse mappings. The extracted localized features from the deformation field allow for downstream statistical learning that may facilitate medical diagnostics. On a lightweight and portable software platform, AutoCT provides a new toolkit for the CT imaging community to underpin the deployment of artificial intelligence-driven applications. © 2023, CC BY-NC-ND.

关键词： Image segmentation

Construction and Validation of an Obstetric Risk Classification Engine to Support Intensive Care Unit (ICU) Admission Using Machine Learning

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SSRN

SSRN 2022年

作者： Soares, Fabiano Miguel Rose, Lívia Ohana da Rocha Oak Cecatti, José Guilherme Luz, Adriana Gomes Awe, Oluwafunmilola Deborah Esmi, Estevão Laureano de Carvalho Pacagnella, Rodolfo Department of Obstetrics and Gynecology Faculty of Medical Sciences State University of Campinas SP Campinas Brazil Department of Applied and Computational Mathematics Institute of Mathematics Statistics and Scientific Computing State University of Campinas SP Campinas Brazil Campus Universitário R. Alexander Flemming 101. Barão Geraldo Campinas SP. 13083-872 Brazil

Introduction: Maternal mortality remains a global problem, despite the efforts of many international organizations such as the World Health Organization to reduce it. In recent times, scientific evidence useful in the reduction of maternal mortality has become well established, which include implementation of bundles in emergency, and provision of Intensive Care Units (ICU) for obstetric complications. This is a major factor in the management of pregnant women, however, there is a need for optimization of the Intensive Care Unit (ICU) when the need arises. We aimed to develop a clinical support tool to guide decisions on which obstetric population required ICU ***: This study describes the development and validation of an obstetric risk classification engine among patients with maternal morbidity We used a supervised machine learning technique in a multicentric database of pregnant population including 9,550 women with Severe Maternal Morbidity. A decision tree model and two regression tree models were tested (Random Forest, Gradient boosting Machine -GBM, and Extreme Gradient Boosting -XGBoost) and after application, the accuracy, sensitivity and specificity were compared and the differences between the predictions were analyzed using Wilcoxon ***: The XGBoost algorithm showed the highest efficiency with an accuracy of 85%, sensitivity of 42%, specificity of 97%, AUC on the ROC curve of 86.7% and the estimated prevalence of ICU use (11.6%, in contrast to the actual prevalence of ICU, 21.52%), indicating the need to optimize the use of intensive ***: The Risk engine developed showed positive results, hence, can serve as a reinforcement factor in the management of women with complications so that those who need intensive care can be correctly identified, thereby optimizing the use of intensive beds. © 2022, The Authors. All rights reserved.

关键词： Intensive care units

Convergence and Complexity of an Adaptive Planewave Method for Eigenvalue Computations

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arXiv 2021年

作者： Dai, Xiaoying Pan, Yan Yang, Bin Zhou, Aihui LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China School of Mathematical Sciences University of Chinese Academy of Sciences Beijing100049 China NCMIS Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing100190 China

In this paper, we study the adaptive planewave discretization for a cluster of eigenvalues of second-order elliptic partial differential equations. We first design an a posteriori error estimator and prove both the upper and lower bounds. Based on the a posteriori error estimator, we propose an adaptive planewave method. We then prove that the adaptive planewave approximations have the linear convergence rate and quasi-optimal complexity. Copyright © 2021, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

Time-Division Energy Beamforming for Multiuser Wireless Power Transfer with Non-Linear Energy Harvesting

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arXiv 2020年

作者： Ma, Ganggang Xu, Jie Liu, Ya-Feng Vedady Moghadam, Mohammad R. Shenzhen China Shenzhen China State Key Laboratory of Scientific and Engineering Computing Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and Systems Science Chinese Academy of Sciences Beijing China TransferFi Pte Ltd Singapore

Energy beamforming has emerged as a promising technique for enhancing the energy transfer efficiency of wireless power transfer (WPT). However, the performance of conventional energy beamforming may seriously degrade due to the nonlinear radio frequency (RF) to direct current (DC) conversion at energy receivers (ERs). To tackle this issue, this letter proposes a new time-division energy beamforming, in which different energy beamforming matrices (of high ranks in general) are time shared to exploit the "convex-concave" shape of the RF-DC power relation at ERs. By considering a particular time duration for WPT, we maximize the minimum harvested DC energy among all ERs, by jointly optimizing the energy beamforming matrices and the corresponding time allocation. In order to solve the non-convex min-DC-energy maximization problem, we propose an efficient solution by using the techniques of alternating optimization and successive convex approximation (SCA). Numerical results show that the proposed time-division energy beamforming design indeed outperforms the conventional multi-beam and time-division-multiple-access (TDMA)-based energy transmissions. Copyright © 2020, The Authors. All rights reserved.

关键词： Energy harvesting

A simple low-degree optimal finite element scheme for the elastic transmission eigenvalue problem

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arXiv 2021年

作者： Xi, Yingxia Ji, Xia Zhang, Shuo School of Science Nanjing University of Science and Technology Nanjing210094 China School of Mathematics and Statistics Beijing Institute of Technology Beijing100081 China Beijing Key Laboratory on MCAACI Beijing Institute of Technology Beijing100081 China LSEC Institute of Computational Mathematics and Scientific/Engineering Computing Academy of Mathematics and System Sciences Chinese Academy of Sciences Beijing100190 China

The paper presents a finite element scheme for the elastic transmission eigenvalue problem written as a fourth order eigenvalue problem. The scheme uses piecewise cubic polynomials and obtains optimal convergence rate. Compared with other low-degree and nonconforming finite element schemes, the scheme inherits the continuous bilinear form which does not need extra stabilizations and is thus simple to *** Codes 31A30, 65N30, 47B07 Copyright © 2021, The Authors. All rights reserved.

关键词： Eigenvalues and eigenfunctions

The directional isotropy of LIGO-Virgo binaries

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arXiv 2023年

作者： Isi, Maximiliano Farr, Will M. Varma, Vijay Center for Computational Astrophysics Flatiron Institute 162 5th Ave New YorkNY10010 United States Department of Physics and Astronomy Stony Brook University Stony BrookNY11794 United States Am Mühlenberg 1 Potsdam14476 Germany Department of Mathematics Center for Scientific Computing and Data Science Research University of Massachusetts DartmouthMA02747 United States

We demonstrate how to constrain the degree of absolute alignment of the total angular momenta of LIGO-Virgo binary black holes, looking for a special direction in space that would break isotropy. We also allow for inhomogeneities in the distribution of black holes over the sky. Making use of dipolar models for the spatial distribution and orientation of the sources, we analyze 57 signals with false-alarm rates ≤ 1/yr from the third LIGO-Virgo observing run. Accounting for selection biases, we find the population of LIGO-Virgo black holes to be fully consistent with both homogeneity and isotropy. We additionally find the data to constrain some directions of alignment more than others, and produce posteriors for the directions of total angular momentum of all binaries in our set. All code and data are made publicly available in https://***/maxisi/gwisotropy/. © 2023, CC BY.

关键词： Black holes