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Is a single lethal electric field threshold sufficient to characterize the lesion size in computational modeling of cardiac pulsed-field ablation?

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Heart Rhythm O2 2025年第5期6卷 671-677.0页

作者： Petras, Argyrios Amoros Figueras, Gerard Moreno Weidmann, Zoraida García-Sánchez, Tomás Viladés Medel, David Ivorra, Antoni Guerra, Jose M. Gerardo-Giorda, Luca RICAM–Johann Radon Institute for Computational and Applied Mathematics Linz Austria Department of Cardiology Hospital de la Santa Creu i Sant Pau Universitat Autònoma de Barcelona CIBER CV Barcelona Spain Department of Information and Communication Technologies Universitat Pompeu Fabra Barcelona Spain Institute for Mathematical Methods in Medicine and Data-Based Modelling Johannes Kepler University Linz Austria

Background: Pulsed-field ablation (PFA) is a novel cardiac ablation technology based on irreversible electroporation (IRE). PFA computational models rely on identification of a lethal electric field threshold to predict the IRE area. However, the predicted lesion anisotropy ratios (width over depth) vary extensively among recent studies, and these discrepancies remain a subject of discussion. Objective: This work aims to evaluate the predicted lesion anisotropy ratios using a PFA computational model by applying it to an open-chest in vivo porcine model geometry. Methods: Six domestic swine underwent epicardial PFA applications using a previously described waveform protocol. Animals were killed at least 3 hours after the last ablation, and lesions were assessed using triphenyltetrazolium chloride (TTC) staining. Numeric simulations were performed on a segmented and meshed porcine thoracic computed tomography (CT) scan, mimicking the open-chest experimental setup. Results: The maximum width of all simulated lesions was observed at the epicardial surface. The anisotropy ratios (AR) of the experimental lesions were smaller than the simulated ones (AR experimental vs simulated, 1.0–1.7 vs 2–2.7;Q1–Q3 quartiles). Increasing the peak voltage resulted in larger lesions;however, the computational model clearly underestimated the increase in lesion depth compared with the experimental data. Conclusion: Our computational model shows that a single lethal electric field threshold is insufficient to accurately predict both lesion depth and width in cardiac PFA. Our study suggests that for the given PFA waveforms, a threshold between 270 and 500 V/cm provides satisfactory lesion depth estimations, and a higher threshold between 790 and 1000 V/cm better captures the lesion width. © 2025 Heart Rhythm Society

关键词： Cardiac ablation Computer simulations Electric field threshold Mathematical modeling Pulsed field ablation

Entropic van der Corput’s Difference Theorem

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arXiv 2024年

作者： Gu, Weichen Li, Xiang Department of Mathematics and Statistics University of New Hampshire DurhamNH03824 United States Integrated Applied Mathematics Program University of New Hampshire DurhamNH03824 United States

We prove an entropy version of van der Corput’s difference theorem: the entropy of a sequence is equal to the entropy of its differences. This reveals a potential correspondence between the theory of uniform distribution mod 1 and entropy. As applications, we establish the corresponding entropy versions for several other results on uniform distribution. Copyright © 2024, The Authors. All rights reserved.

关键词： Entropy

Solving Non Linear Differential Equations by Using A G - Homotopy Analysis Method 2

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Solving Non Linear Differential Equations by Using A G - Hom...

2nd International Conference on Mathematical Modeling and computational Methods in Science and Engineering, ICMMCMSE 2020

作者： Saratha, S.R. Bagyalakshmi, M. Sai Sundara Krishnan, G. Department of Mathematics Kumaraguru College of Technology Tamilnadu Coimbatore India Department of Mathematics PSG College of Technology Tamilnadu Coimbatore India Department of Applied Mathematics and Computational Sciences PSG College of Technology Tamilnadu Coimbatore India

This paper proposes an efficient hybrid analytical method named the Generalized Homotopy Analysis Method (GHAM) for solving nonlinear differential equations. The proposed hybrid method consists of topology based Homotopy Analysis Method (HAM) and Laplace typed integral transform (G-transform). Compared with HAM, GHAM does not require the effort to perform repeated integration and differentiation, when it is applied to solve higher order differential equations. Compared with G-transform, GHAM serves as an effective approach to tackle higher-order nonlinear differential equations. The effectiveness of GHAM is illustrated through the analysis of numerical examples, and the obtained results are graphically depicted. Also, GHAM is effectively utilized to analyze the density of the forest cover incorporating various parameters, which include the seed reproduction, seed deposition, seed establishment rates, old trees due to aging and the coefficients of mortality due to space variables. © Published under licence by IOP Publishing Ltd.

关键词： Mathematical transformations

A QUADRATURE SCHEME FOR STEADY-STATE DIFFUSION EQUATIONS INVOLVING FRACTIONAL POWER OF REGULARLY ACCRETIVE OPERATOR

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arXiv 2023年

作者： Duan, Beiping Yang, Zongze Faculty of Computational Mathematics and Cybernetics Shenzhen MSU-BIT University Shenzhen518172 China Department of Applied Mathematics The Hong Kong Polytechnic University Kowloon Hong Kong

In this paper we construct a quadrature scheme to numerically solve the nonlocal diffusion equation (Aα + bI)u = f with Aα the α-th power of the regularly accretive operator A. Rigorous error analysis is carried out and sharp error bounds (up to some negligible constants) are obtained. The error estimates include a wide range of cases in which the regularity index and spectral angle of A, the smoothness of f, the size of b and α are all involved. The quadrature scheme is exponentially convergent with respect to the step size and is root-exponentially convergent with respect to the number of solves. Some numerical tests are presented in the last section to verify the sharpness of our estimates. Furthermore, both the scheme and the error bounds can be utilized directly to solve and analyze time-dependent *** Codes 65N12, 65R20, 65N30, 65N50, 35S15 Copyright © 2023, The Authors. All rights reserved.

关键词： Error analysis

STABLE RECOVERY OF COEFFICIENTS IN AN INVERSE FAULT FRICTION PROBLEM

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arXiv 2023年

作者： de Hoop, Maarten V. Lassas, Matti Lu, Jinpeng Oksanen, Lauri Computational and Applied Mathematics and Earth Science Rice University HoustonTX77005 United States Department of Mathematics and Statistics University of Helsinki HelsinkiFI-00014 Finland

We consider the inverse fault friction problem of determining the friction coefficient in the Tresca friction model, which can be formulated as an inverse problem for differential inequalities. We show that the measurements of elastic waves during a rupture uniquely determine the friction coefficient at the rupture surface with explicit stability *** Codes 35R30, 35Q86 Copyright © 2023, The Authors. All rights reserved.

关键词： Elastic waves

Predator Prey Scavenger Model using Holling’s Functional Response of Type III and Physics-Informed Deep Neural Networks

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arXiv 2024年

作者： Panchal, Aneesh Beniwal, Kirti Kumar, Vivek Department of Computational and Data Sciences Indian Institute of Science Karnataka Bangalore560012 India Department of Applied Mathematics Delhi Technological University Delhi110042 India

Nonlinear mathematical models introduce the relation between various physical and biological interactions present in nature. One of the most famous models is the Lotka-Volterra model which defined the interaction between predator and prey species present in nature. However, predators, scavengers, and prey populations coexist in a natural system where scavengers can additionally rely on the dead bodies of predators present in the system. Keeping this in mind, the formulation and simulation of the predator prey scavenger model is introduced in this paper. For the predation response, respective prey species are assumed to have Holling’s functional response of type III. The proposed model is tested for various simulations and is found to be showing satisfactory results in different scenarios. After simulations, the American forest dataset is taken for parameter estimation which imitates the real-world case. For parameter estimation, a physics-informed deep neural network is used with the Adam backpropagation method which prevents the avalanche effect in trainable parameters updation. For neural networks, mean square error and physics-informed informed error are considered. After the neural network, the hence-found parameters are fine-tuned using the Broyden–Fletcher–Goldfarb–Shanno algorithm. Finally, the hence-found parameters using a natural dataset are tested for stability using Jacobian stability analysis. Future research work includes minimization of error induced by parameters, bifurcation analysis, and sensitivity analysis of the parameters. Copyright © 2024, The Authors. All rights reserved.

关键词： Sensitivity analysis

Identification of candidate paleotsunami deposit from sediment layers drilled in Seubadeh located in South Aceh of Indonesia 5

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Identification of candidate paleotsunami deposit from sedime...

5th International Conference on Research and Learning of Physics, ICRLP 2022

作者： Vethra Prasetyo, A. Mirda Sukman, M. Vahreza, A. Mitaphonna, R. Fauzi Rajibussalim Ismail, N. Lahna, K. Ramli, M. Idris, N. Graduate Program of Physics Department of Physics Faculty of Mathematics and Natural Sciences Universitas Syiah Kuala Jl. Syech Abdurrauf No. 3 Darussalam Banda Aceh23111 Indonesia Department of Physics Faculty of Mathematics and Natural Sciences Universitas Syiah Kuala Jl. Syech Abdurrauf No. 3 Darussalam Banda Aceh Aceh23111 Indonesia Graduate School of Mathematics and Applied Sciences Universitas Syiah Kuala Banda Aceh23111 Indonesia Department of Chemistry Universitas Syiah Kuala Faculty of Mathematics and Natural Sciences Banda Aceh23111 Indonesia

This study is conducted to identify prehistoric tsunami deposit (paleotsunami) in Seubadeh village, located in South Aceh Regency, Aceh province, Indonesia. Regional morphologic and seismic characteristics suggest that Seubadeh village is an area that stores tsunami deposits, both new tsunami deposits and prehistoric tsunami deposits. Therefore, in this study, the search for paleotsunami deposits was carried out in Seubadeh village. The tsunami deposit samples were taken at several points in Seubadeh village using a hand drill with a depth of more than 2 m. Sediment classification of the collected samples using Troels-Smith method shows a candidate layer of paleotsunami tsunami deposit was found between two clay deposits. The layer is dominated by plant roots and shell material. In addition, the sediment samples were sieved using a mesh to evaluate the grain size distribution of clay, silt and sand. The results of the grain size distribution and color evaluation of the respective layer are presented. The results of the analysis of the particle size distribution in the sample and the color of the sample indicate that there are 2 layers that show characteristics as a paleotsunami deposit, namely at a depth of about 170-200 cm and 280-292 cm. The paleotsunami deposit found will be further characterized by an emission spectroscopic technique. © Published under licence by IOP Publishing Ltd.

关键词： Deposits

ORBITS OF SECOND ORDER LINEAR RECURRENCES OVER FINITE FIELDS

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arXiv 2024年

作者： Panraksa, Chatchawan Somasunderam, Naveen Applied Mathematics Program Mahidol University International College Salaya Nakhon Pathom73170 Thailand Department of Mathematics State University of New York PlattsburghNY12901 United States

Let Q be the matrix (a1 0b )in GL2(Fq) where Fq is a finite field, and let G be the finite cyclic group generated by Q. We consider the action of G on the set Fq × Fq. In particular, we study certain relationships between the lengths of the non-trivial orbits of G, and their frequency of occurrence. This is done in part by investigating the order of elements of a product in an abelian group when the product has prime power order. For q a prime and b = 1, the orbits correspond to Fibonacci type linear recurrences modulo q for different initial conditions. We also derive certain conditions under which the roots of the characteristic polynomial of Q are generators of F×q . Examples are included to illustrate the *** Codes 11B37, 11B39, 11B50, 11T06, 11T30, 20K01, 37P25 © 2024, CC BY.

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Usable boundary for visibility-based surveillance-evasion games

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arXiv 2023年

作者： Esteve-Yagüe, Carlos Tsai, Richard Department of Applied Mathematics and Theoretical Physics University of Cambridge Cambridge United Kingdom Department of Mathematics Oden Institute for Computational Engineering and Sciences The University of Texas at Austin Austin United States

We consider a surveillance-evasion game in an environment with obstacles. In such an environment, a mobile pursuer seeks to maintain the visibility with a mobile evader, who tries to get occluded from the pursuer in the shortest time possible. In this two-player zero-sum game setting, we study the discontinuities of the value of the game near the boundary of the target set (the non-visibility region). In particular, we describe the transition between the usable part of the boundary of the target (where the value vanishes) and the non-usable part (where the value is positive). We show that the value enjoys a different behaviour depending on the regularity of the obstacles involved in the game. Namely, we prove that the boundary profile is continuous for the case of smooth obstacles, and that it exhibits a jump discontinuity when the obstacle contains corners. Moreover, we prove that, in the latter case, there is a semi-permeable barrier emanating from the interface between the usable and the non-usable part of the boundary of the target *** Codes 91A23, 49L12, 49L25, 49N70 Copyright © 2023, The Authors. All rights reserved.

关键词： Visibility