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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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Dimensionless ratios: Characteristics of quantum liquids and their phase transitions

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Physical Review B 2016年第19期94卷 195129-195129页

作者： Yi-Cong Yu Yang-Yang Chen Hai-Qing Lin Rudolf A. Römer Xi-Wen Guan State Key Laboratory of Magnetic Resonance and Atomic and Molecular Physics Wuhan Institute of Physics and Mathematics Chinese Academy of Sciences Wuhan 430071 China Beijing Computational Science Research Center Beijing 100094 China Department of Physics and Centre for Scientific Computing University of Warwick Coventry CV4 7AL United Kingdom Center for Cold Atom Physics Chinese Academy of Sciences Wuhan 430071 China Department of Theoretical Physics Research School of Physics and Engineering Australian National University Canberra ACT 0200 Australia

Dimensionless ratios of physical properties can characterize low-temperature phases in a wide variety of materials. As such, the Wilson ratio (WR), the Kadowaki-Woods ratio, and the Wiedemann-Franz law capture essential features of Fermi liquids in metals, heavy fermions, etc. Here we prove that the phases of many-body interacting multicomponent quantum liquids in one dimension (1D) can be described by WRs based on the compressibility, susceptibility, and specific heat associated with each component. These WRs arise due to additivity rules within subsystems reminiscent of the rules for multiresistor networks in series and parallel—a novel and useful characteristic of multicomponent Tomonaga-Luttinger liquids (TLL) independent of microscopic details of the systems. Using experimentally realized multispecies cold atomic gases as examples, we prove that the Wilson ratios uniquely identify phases of TLL, while providing universal scaling relations at the boundaries between phases. Their values within a phase are solely determined by the stiffnesses and sound velocities of subsystems and identify the internal degrees of freedom of said phase such as its spin degeneracy. This finding can be directly applied to a wide range of 1D many-body systems and reveals deep physical insights into recent experimental measurements of the universal thermodynamics in ultracold atoms and spins.

关键词： Fermi gases Specific heat Fermi liquid theory

Probabilistic methods for approximate archetypal analysis

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arXiv 2021年

作者： Han, Ruijian Osting, Braxton Wang, Dong Xu, Yiming Department of Statistics The Chinese University of Hong Kong Hong Kong Department of Mathematics University of Utah Salt Lake City United States School of Science and Engineering The Chinese University of Hong Kong Shenzhen China Guangdong Provincial Key Laboratory of Big Data Computing The Chinese University of Hong Kong Shenzhen China Scientific Computing and Imaging Institute University of Utah Salt Lake City United States

Archetypal analysis is an unsupervised learning method for exploratory data analysis. One major challenge that limits the applicability of archetypal analysis in practice is the inherent computational complexity of the existing algorithms. In this paper, we provide a novel approximation approach to partially address this issue. Utilizing probabilistic ideas from high-dimensional geometry, we introduce two preprocessing techniques to reduce the dimension and representation cardinality of the data, respectively. We prove that provided the data is approximately embedded in a low-dimensional linear subspace and the convex hull of the corresponding representations is well approximated by a polytope with a few vertices, our method can effectively reduce the scaling of archetypal analysis. Moreover, the solution of the reduced problem is near-optimal in terms of prediction errors. Our approach can be combined with other acceleration techniques to further mitigate the intrinsic complexity of archetypal analysis. We demonstrate the usefulness of our results by applying our method to summarize several moderately large-scale datasets. Copyright © 2021, The Authors. All rights reserved.

关键词： Large dataset

Development and illustration of a framework for computational thinking practices in introductory physics

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Physical Review Physics Education Research 2022年第2期18卷 020106-020106页

作者： Daniel P. Weller Theodore E. Bott Marcos D. Caballero Paul W. Irving Department of Physics and Astronomy Michigan State University East Lansing Michigan 48824 USA School of Mathematical and Physical Sciences University of New England Biddeford Maine 04005 USA Department of Computational Mathematics Science and Engineering and CREATE for STEM Institute Michigan State University East Lansing Michigan 48824 USA Department of Physics and Center for Computing in Science Education University of Oslo Oslo 0316 Norway

Physics classes with computation integrated into the curriculum are a fitting setting for investigating computational thinking. In this paper, we present a framework for exploring this topic in introductory physics courses. The framework, which was developed by reviewing relevant literature and acquiring video data from high school classrooms, comprises 14 practices that students could engage in when working with Glowscript VPython activities. For every practice, we provide in-class video data to exemplify the practice. In doing this work, we hope to provide ways for teachers to assess their students’ development of computational thinking and give physics education researchers a foundation to study the topic in greater depth.

关键词： Technology K-12 students K-12 teachers

Quantum Circuits for the Heat Equation with Physical Boundary Conditions Via Schrödingerisation

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SSRN

SSRN 2024年

作者： Jin, Shi Liu, Nana Yu, Yue School of Mathematical Sciences Institute of Natural Sciences MOE-LSC Shanghai Jiao Tong University Shanghai200240 China University of Michigan Shanghai Jiao Tong University Joint Institute Shanghai200240 China School of Mathematics and Computational Science Hunan Key Laboratory for Computation and Simulation in Science and Engineering Key Laboratory of Intelligent Computing and Information Processing of Ministry of Education National Center for Applied Mathematics in Hunan Xiangtan University Hunan Xiangtan411105 China

This paper explores the explicit design of quantum circuits for quantum simulation of partial differential equations (PDEs) with physical boundary conditions. These equations and/or their discretized forms usually do not evolve via unitary dynamics, thus are not suitable for quantum simulation. Boundary conditions (either time-dependent or independent) make the problem more difficult. To tackle this challenge, the Schrödingerisation method can be employed, which converts linear partial and ordinary differential equations with non-unitary dynamics into systems of Schrödinger-type equations, via the so-called warped phase transformation that maps the equation into one higher dimension. Despite advancements in Schrödingerisation techniques, the explicit implementation of quantum circuits for solving general PDEs, especially with physical boundary conditions, remains underdeveloped. We present two methods for handling the inhomogeneous terms arising from time-dependent physical boundary conditions. One approach utilizes Duhamel's principle to express the solution in integral form and employs linear combination of unitaries (LCU) for coherent state preparation. Another method applies an augmentation to transform the inhomogeneous problem into a homogeneous one. We then apply the quantum simulation technique from [CJL23] to transform the resulting non-autonomous system to an autonomous system in one higher dimension. We provide detailed implementations of these two methods and conduct a comprehensive complexity analysis in terms of queries to the time evolution input oracle. © 2024, The Authors. All rights reserved.

关键词： Boundary conditions

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

Why is Grain Growth Not Curvature Flow?

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arXiv 2024年

作者： Qiu, Caihao Srolovitz, David J. Rohrer, Gregory S. Han, Jian Salvalaglio, Marco Department of Materials Science and Engineering City University of Hong Kong Hong Kong Department of Mechanical Engineering The University of Hong Kong Pokfulam Road Hong Kong The University of Hong Kong Shenzhen China Department of Materials Science and Engineering Carnegie Mellon University PittsburghPA United States Institute of Scientific Computing TU Dresden Dresden01062 Germany Dresden Center for Computational Materials Science TU Dresden Dresden01062 Germany

Grain growth describes the increase in the mean grain size with time during the annealing of a polycrystal;it is widely accepted that this is driven by capillarity (surface tension). Although classically modeled and interpreted as mean curvature flow, a growing body of evidence has demonstrated that this is overly simplistic and inconsistent with experimental observations. Despite many proposals for the source of this failure, it remains a subject of ongoing debate. By considering the fundamental microscopic mechanism of grain boundary (GB) migration, we demonstrate that internal stress (shear coupling) associated with GB motion is the primary factor causing deviations in grain growth from mean curvature flow. This is achieved through the application of a two-dimensional bicrystallography-respecting continuum model for GB migration to grain growth, implemented in a diffuse-interface approach. These results are validated by comparison with atomistic simulations and the scatter in the curvature-velocity relationship is shown to be in excellent agreement with experimental results for grain growth in 3D polycrystals (not possible based on other proposed explanations). This work also demonstrates how to account for the mechanical effects that are integral to grain growth in crystalline solids. Copyright © 2024, The Authors. All rights reserved.

关键词： Polycrystals

Constraint energy minimizing generalized multiscale finite element method for dual continuum model

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arXiv 2018年

作者： Cheung, Siu Wun Chung, Eric T. Efendiev, Yalchin Leung, Wing Tat Vasilyeva, Maria Department of Mathematics Texas A&M University College StationTX77843 United States Department of Mathematics Chinese University of Hong Kong Shatin New Territories Hong Kong Texas A&M University College StationTX United States Institute of Computational Engineering and Sciences University of Texas at Austin Austin United States Institute for Scientific Computation Texas A&M University College StationTX77843 United States 677980 Russia

The dual continuum model serves as a powerful tool in the modeling of subsurface applications. It allows a systematic coupling of various components of the solutions. The system is of multiscale nature as it involves high heterogeneous and high contrast coefficients. To numerically compute the solutions, some types of reduced order methods are necessary. We will develop and analyze a novel multiscale method based on the recent advances in multiscale finite element methods. Our method will compute multiple local multiscale basis functions per coarse region. The idea is based on some local spectral problems, which are important to identify high contrast channels, and an energy minimization principle. Using these concepts, we show that the basis functions are localized, even in the presence of high contrast long channels and fractures. In addition, we show that the convergence of the method depends only on the coarse mesh size. Finally, we present several numerical tests to show the performance. Copyright © 2018, The Authors. All rights reserved.

关键词： Functions

Single Relaxation Time and Multiple Revised Matrix Lattice Boltzmann Simulations of Forced Isotropic Turbulence

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arXiv 2022年

作者： Kareem, Waleed Abdel Asinari, Pietro Succi, Sauro Izawa, Seiichiro Fukunishi, Yu Department of Mathematics Faculty of Science Suez University Egypt Academy of Scientific Research & Technology Egypt Politecnico di Torino Department of Energy Corso Duca degli Abruzzi 24 Torino10129 Italy Instituto Applicazioni Calcolo CNR Italy Department of Mechanical Engineering and Sciences University of Toyama Japan Institute of Computational Fluid Dynamics Japan

The single relaxation time (SRT) and the revised matrix (RM) lattice Boltzmann models are compared for simulations of three dimensional forced isotropic turbulence with resolutions of 1283 and 2563, respectively. The forcing technique by Guo et al. (2002) is applied with the two models using the same parameters and conditions. Some new aspects and results have been confirmed such as the superiority of the MRT model to simulate forced turbulence and using the Courant-Friedichs-Lewy condition (CFL) (Courant et al., 1967) by multiplying the velocity input with the coefficient CFL −4 for all cases. The single relaxation time is set to τ = 0.503 in all SRT simulations. Results show that the obtained turbulent velocity fields yield universal characteristics as proven in previous theoretical, experimental and numerical studies. The Taylor Reynolds number for the simulations are found as SRT: Rλ = 62 and MRT: Rλ = 65 for 1283 and SRT: Rλ = 107 and MRT: Rλ = 82 for the case of 2563, respectively. To test the weak incompressibility for the SRT model in comparison to the MRT model, the density probability distribution function (PDF) is depicted and it is found that ρ is almost unity at all timesteps for the MRT case, while a clear disturbance about unity is observed for the SRT case. Time variation's statistics such as the Taylor Reynolds number Rλ, the Taylor microscale λ, the Kolmogrov microscale η and energy spectra are calculated and depicted for all cases. One of the disadvantages of the MRT case is the simulations time which is found about twice the SRT simulations time, where about 80 hours are needed for simulating 12000 timesteps in the 2563 case in comparison to 42 hours for the SRT model using the same hardware resources. © 2022, CC BY.

关键词： Velocity