{"title":"新型心脏组织电-热-射频耦合模型的数学研究","authors":"","doi":"10.1016/j.cnsns.2024.108281","DOIUrl":null,"url":null,"abstract":"<div><p>This paper presents a nonlinear reaction–diffusion-fluid system that simulates radiofrequency ablation within cardiac tissue. The model conveys the dynamic evolution of temperature and electric potential in both the fluid and solid regions, along with the evolution of velocity within the solid region. By formulating the system that describes the phenomena across the entire domain, encompassing both solid and fluid phases, we proceed to an analysis of well-posedness, considering a broad class of right-hand side terms. The system involves parameters such as heat conductivity, kinematic viscosity, and electrical conductivity, all of which exhibit nonlinearity contingent upon the temperature variable. The mathematical analysis extends to establishing the existence of a global solution, employing the Faedo–Galerkin method in a three-dimensional space. To enhance the practical applicability of our theoretical results, we complement our study with a series of numerical experiments. We implement the discrete system using the finite element method for spatial discretization and an Euler scheme for temporal discretization. Nonlinear parameters are linearized through decoupling systems, as introduced in our continuous analysis. These experiments are conducted to demonstrate and validate the theoretical findings we have established.</p></div>","PeriodicalId":50658,"journal":{"name":"Communications in Nonlinear Science and Numerical Simulation","volume":null,"pages":null},"PeriodicalIF":3.4000,"publicationDate":"2024-08-17","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"0","resultStr":"{\"title\":\"Mathematical study of a new coupled electro-thermo radiofrequency model of cardiac tissue\",\"authors\":\"\",\"doi\":\"10.1016/j.cnsns.2024.108281\",\"DOIUrl\":null,\"url\":null,\"abstract\":\"<div><p>This paper presents a nonlinear reaction–diffusion-fluid system that simulates radiofrequency ablation within cardiac tissue. The model conveys the dynamic evolution of temperature and electric potential in both the fluid and solid regions, along with the evolution of velocity within the solid region. By formulating the system that describes the phenomena across the entire domain, encompassing both solid and fluid phases, we proceed to an analysis of well-posedness, considering a broad class of right-hand side terms. The system involves parameters such as heat conductivity, kinematic viscosity, and electrical conductivity, all of which exhibit nonlinearity contingent upon the temperature variable. The mathematical analysis extends to establishing the existence of a global solution, employing the Faedo–Galerkin method in a three-dimensional space. To enhance the practical applicability of our theoretical results, we complement our study with a series of numerical experiments. We implement the discrete system using the finite element method for spatial discretization and an Euler scheme for temporal discretization. Nonlinear parameters are linearized through decoupling systems, as introduced in our continuous analysis. These experiments are conducted to demonstrate and validate the theoretical findings we have established.</p></div>\",\"PeriodicalId\":50658,\"journal\":{\"name\":\"Communications in Nonlinear Science and Numerical Simulation\",\"volume\":null,\"pages\":null},\"PeriodicalIF\":3.4000,\"publicationDate\":\"2024-08-17\",\"publicationTypes\":\"Journal Article\",\"fieldsOfStudy\":null,\"isOpenAccess\":false,\"openAccessPdf\":\"\",\"citationCount\":\"0\",\"resultStr\":null,\"platform\":\"Semanticscholar\",\"paperid\":null,\"PeriodicalName\":\"Communications in Nonlinear Science and Numerical Simulation\",\"FirstCategoryId\":\"100\",\"ListUrlMain\":\"https://www.sciencedirect.com/science/article/pii/S1007570424004660\",\"RegionNum\":2,\"RegionCategory\":\"数学\",\"ArticlePicture\":[],\"TitleCN\":null,\"AbstractTextCN\":null,\"PMCID\":null,\"EPubDate\":\"\",\"PubModel\":\"\",\"JCR\":\"Q1\",\"JCRName\":\"MATHEMATICS, APPLIED\",\"Score\":null,\"Total\":0}","platform":"Semanticscholar","paperid":null,"PeriodicalName":"Communications in Nonlinear Science and Numerical Simulation","FirstCategoryId":"100","ListUrlMain":"https://www.sciencedirect.com/science/article/pii/S1007570424004660","RegionNum":2,"RegionCategory":"数学","ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q1","JCRName":"MATHEMATICS, APPLIED","Score":null,"Total":0}
Mathematical study of a new coupled electro-thermo radiofrequency model of cardiac tissue
This paper presents a nonlinear reaction–diffusion-fluid system that simulates radiofrequency ablation within cardiac tissue. The model conveys the dynamic evolution of temperature and electric potential in both the fluid and solid regions, along with the evolution of velocity within the solid region. By formulating the system that describes the phenomena across the entire domain, encompassing both solid and fluid phases, we proceed to an analysis of well-posedness, considering a broad class of right-hand side terms. The system involves parameters such as heat conductivity, kinematic viscosity, and electrical conductivity, all of which exhibit nonlinearity contingent upon the temperature variable. The mathematical analysis extends to establishing the existence of a global solution, employing the Faedo–Galerkin method in a three-dimensional space. To enhance the practical applicability of our theoretical results, we complement our study with a series of numerical experiments. We implement the discrete system using the finite element method for spatial discretization and an Euler scheme for temporal discretization. Nonlinear parameters are linearized through decoupling systems, as introduced in our continuous analysis. These experiments are conducted to demonstrate and validate the theoretical findings we have established.
期刊介绍:
The journal publishes original research findings on experimental observation, mathematical modeling, theoretical analysis and numerical simulation, for more accurate description, better prediction or novel application, of nonlinear phenomena in science and engineering. It offers a venue for researchers to make rapid exchange of ideas and techniques in nonlinear science and complexity.
The submission of manuscripts with cross-disciplinary approaches in nonlinear science and complexity is particularly encouraged.
Topics of interest:
Nonlinear differential or delay equations, Lie group analysis and asymptotic methods, Discontinuous systems, Fractals, Fractional calculus and dynamics, Nonlinear effects in quantum mechanics, Nonlinear stochastic processes, Experimental nonlinear science, Time-series and signal analysis, Computational methods and simulations in nonlinear science and engineering, Control of dynamical systems, Synchronization, Lyapunov analysis, High-dimensional chaos and turbulence, Chaos in Hamiltonian systems, Integrable systems and solitons, Collective behavior in many-body systems, Biological physics and networks, Nonlinear mechanical systems, Complex systems and complexity.
No length limitation for contributions is set, but only concisely written manuscripts are published. Brief papers are published on the basis of Rapid Communications. Discussions of previously published papers are welcome.