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An Efficient Staggered Scheme for Solving the Poromechanics Problem of Quasi-Static Cardiac Perfusion

International Journal for Numerical Methods in Biomedical Engineering 2025年第4期41卷 e70030页

作者： Wang, Xuan Cai, Li Ma, Pengfei Gao, Hao Xi'an Key Laboratory of Scientific Computation and Applied Statistics Xi'an China NPU-UoG International Cooperative Lab for Computation and Application in Cardiology Xi'an China School of Mathematics and Statistics Northwestern Polytechnical University Xi'an China School of Mathematics and Statistics University of Glasgow Glasgow United Kingdom

The ventricles can be considered a type of poroelastic material, where the mass and pressure of the interstitial fluid, along with the displacement of the skeleton, are the three primary physical quantities of interest. Based on the free energy function of the poroelastic material, we propose a simplified model that requires only two fields to be directly solved, with another quantity obtained through post-processing. To solve this model, we first discretize the equations with the backward Euler scheme and finite element method, leading to a nonlinear system of equations, which can be solved using the Newton method in a monolithic way. For computational efficiency, we proposed a staggered scheme, where the large nonlinear system is divided into two smaller independent systems, and each only solves for one field using the Newton method. The numerical results showed the staggered scheme is more efficient than the monolithic scheme and that the two schemes achieve the same results, and are also in good agreement with those reported in the literature. Finally, we applied the staggered scheme to ventricular myocardial perfusion models and obtained the blood perfusion patterns in the myocardium during the cardiac systole. © 2025 John Wiley & Sons Ltd.

关键词： cardiac perfusion finite element method poroelastic material staggered scheme

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Cooperative networked systems: Multiple graphs, coalitional games, new probabilistic models

Cooperative networked systems: Multiple graphs, coalitional ...

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Mediterranean Conference on Control and Automation

作者： Baras, John S. Applied Mathematics Statistics and Scientific Computation Program Institute for Systems Research University of Maryland College Park United States

ISBN: (纸本)9781457701252

Networked systems are ubiquitous. A taxonomy of networked systems includes infrastructure and communication networks, social and economic networks, biological networks and biological swarms, robotic swarms, and several other categories. Most networked systems include physical components and cyber components implemented in various ways. Thus many networked systems come from the domain of cyberphysical systems (CPS). Cooperative networked systems represent from a certain abstract point of view a distributed and (at least partially) asynchronous implementation of the well known cycle "sense-decide-actuate" of control systems. Yet the interaction of dynamics, sensing, control and decision making, with network structures has created the need for a new scientific basis for the modeling, analysis, design and performance evaluation of such networked systems. For example, efforts to develop a new "Network Science" have emerged. Similarly, efforts to develop new theories of computation that emphasize multiple agents interacting over networks, beyond the conventional concepts and principles of computation and computability, have been also undertaken very recently. In another direction, several efforts have been undertaken very recently to develop models for such systems that integrate continuous and event-triggered dynamics within a framework that permits validation and testing of correctness. Thus the consideration of cooperative networked systems have raised fundamental new questions and challenges. © 2011 IEEE.

关键词： Decision making

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Realistic-science, technology, engineering, and mathematics assisted by google classroom as a learning innovation in the new normal era to improve statistical thinking skill 7

Realistic-science, technology, engineering, and mathematics ...

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7th International Conference on mathematics, Science, and Education 2020, ICMSE 2020

作者： Ardiansyah, A.S. Novita, N.A. Zhintya, H. Kurnianto, D. Mathematics Education Study Program Universitas Negeri Semarang Indonesia Applied Statistics and Computation Study Program Universitas Negeri Semarang Indonesia

Based on government policies regarding the implementation of learning from home, it is necessary the learning innovation to continue learning in the new normal era by utilizing existing technological advances. In this digital era, statistics thinking is important because it is needed to be able to interpret and understand and make good decisions from the statistical data obtained. From these problems, one of the innovations that can be done is by implementing Realistic mathematics Education integrated Science, Technology, Engineering, and mathematics assisted by Google Classroom (R-STEM-GC). This paper aims to determine the effect of R-STEM-GC learning on students' statistical thinking skills. This paper uses literature review method research that identifies, assesses, and interprets all findings on a research topic to answer existing research questions. It can concluded that realistic learning was more effective in terms of students' mathematical reasoning and communication than conventional learning;learning with the application of STEM can improve students' problem solving abilities compared to conventional learning;and the use of google classrooms that can improve communication skills. From the results of this analysis, the application of R-STEM-GC learning can be an innovative solution in improving students' statistical thinking skills in new normal era. © Published under licence by IOP Publishing Ltd.

关键词： Students

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A high order conservative upwind algorithm for the incompressible Navier Stokes equations

A high order conservative upwind algorithm for the incompres...

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作者： Ghosh, Debojyoti Baeder, James D. University of Maryland College Park MD 20742 United States Applied Mathematics and Statistics and Scientific Computation Australia Department of Aerospace Engineering Australia

ISBN: (纸本)9781617389221

The incompressible Navier Stokes equations are solved numerically using the Fractional Step algorithm. A Cartesian staggered-grid solver based on a high order upwind reconstruction of the convective flux is developed for high Reynolds number and inviscid flows. The Weighted Essentially Non-Oscillatory Schemes are used in conjunction with Runge-Kutta time-stepping. Upwinding based on velocity components is necessary for non-oscillatory and stable solutions at high Reynolds numbers. The conservative and non-conservative flux formulations are compared since differences are expected due to the numerical error in satisfying the continuity equation. The algorithm is validated against benchmark flow problems. The accuracy and convergence properties are analyzed on an isolated vortex convection problem. Finally, the performance of the algorithm on inviscid problems with strong gradients is demonstrated by simulating the evolution of a shear layer and leapfrogging of vortex rings. © 2010 by the American Institute of Aeronautics and Astronautics, Inc.

关键词： Reynolds number

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A lumped parameter model for evaluating coronary artery blood supply capacity

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Mathematical Biosciences and Engineering 2024年第4期21卷 5838-5862页

作者： Cai, Li Zhong, Qian Xu, Juan Huang, Yuan Gao, Hao School of Mathematics and Statistics Northwestern Polytechnical University Xi’an710129 China NPU-UoG International Cooperative Lab for Computation and Application in Cardiology Xi’an710129 China Xi’an Key Laboratory of Scientific Computation and Applied Statistics Xi’an710129 China Department of Mathematics University of Cambridge CambridgeCB2 1TN United Kingdom School of Mathematics and Statistics University of Glasgow GlasgowG12 8QQ United Kingdom

The coronary artery constitutes a vital vascular system that sustains cardiac function, with its primary role being the conveyance of indispensable nutrients to the myocardial tissue. When coronary artery disease occurs, it will affect the blood supply of the heart and induce myocardial ischemia. Therefore, it is of great significance to numerically simulate the coronary artery and evaluate its blood supply capacity. In this article, the coronary artery lumped parameter model was derived based on the relationship between circuit system parameters and cardiovascular system parameters, and the blood supply capacity of the coronary artery in healthy and stenosis states was studied. The aortic root pressure calculated by the aortic valve fluid-structure interaction (AV FSI) simulator was employed as the inlet boundary condition. To emulate the physiological phenomenon of sudden pressure drops resulting from an abrupt reduction in blood vessel radius, a head loss model was connected at the coronary artery’s entrance. For each coronary artery outlet, the symmetric structured tree model was appended to simulate the terminal impedance of the missing downstream coronary arteries. The particle swarm optimization (PSO) algorithm was used to optimize the blood flow viscous resistance, blood flow inertia, and vascular compliance of the coronary artery model. In the stenosis states, the relative flow and fractional flow reserve (FFR) calculated by numerical simulation corresponded to the published literature data. It was anticipated that the proposed model can be readily adapted for clinical application, serving as a valuable reference for diagnosing and treating patients. © 2024 the Author(s), licensee AIMS Press.

关键词： Blood vessels

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Preconditioning techniques for reduced basis methods for parameterized elliptic partial differential equations

Preconditioning techniques for reduced basis methods for par...

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作者： Elman, Howard C. Forstall, Virginia Department of Computer Science Institute for Advanced Computer Studies University of Maryland College ParkMD20742 United States Applied Mathematics and Statistics and Scientific Computation Program University of Maryland College ParkMD20742 United States

The reduced basis methodology is an efficient approach to solve parameterized discrete partial differential equations when the solution is needed at many parameter values. An offline step approximates the solution space, and an online step utilizes this approximation, the reduced basis, to solve a smaller reduced problem, which provides an accurate estimate of the solution. Traditionally, the reduced problem is solved using direct methods. However, the size of the reduced system needed to produce solutions of a given accuracy depends on the characteristics of the problem, and it may happen that the size is significantly smaller than that of the original discrete problem but large enough to make direct solution costly. In this scenario, it may be more effective to use iterative methods to solve the reduced problem. We construct preconditioners for reduced iterative methods which are derived from preconditioners for the full problem. This approach permits reduced basis methods to be practical for larger bases than direct methods allow. We illustrate the effectiveness of iterative methods for solving reduced problems by considering two examples, the steady-state diffusion and convection-diffusion-reaction equations. © 2015 Society for Industrial and applied mathematics.

关键词： Iterative methods

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A multiobjective optimization approach to smart growth in land development

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Socio-Economic Planning Sciences 2006年第3期40卷 212-248页

作者： Gabriel, Steven A. Faria, José A. Moglen, Glenn E. Department of Civil and Environmental Engineering University of Maryland College Park MD 20742 United States Applied Mathematics and Scientific Computation Program University of Maryland College Park MD 20742 United States

In this paper we apply a multiobjective optimization model of Smart Growth to land development. The term Smart Growth is meant to describe development strategies-that do not promote urban sprawl. However, the term is somewhat open to interpretation. The multiobjective aspects arise when considering the conflicting interests of the various stakeholders involved in land development decisions: the government planner, the environmentalist, the conservationist, and the land developer. We present a formulation-employing linear and convex quadratic objective functions subject to polyhedral and binary constraints for the stakeholders. The resulting optimization problems are convex, quadratic mixed integer programs that are NP-complete. We report numerical results with this model for Montgomery County, Maryland, and present them using a geographic information system (GIS). © 2005 Elsevier Ltd. All rights reserved.

关键词： Geographic Information System Integer programming Land use planning Large Scale Optimization Multiple objective programming Quadratic programming Smart Growth

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Fluid-structure interaction simulation of pathological mitral valve dynamics in a coupled mitral valve-left ventricle model

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Intelligent Medicine 2023年第2期3卷 104-114页

作者： Li Cai Tong Zhao Yongheng Wang Xiaoyu Luo Hao Gao NPU-UoG International Cooperative Lab for Computation and Application in Cardiology School of Mathematics and StatisticsNorthwestern Polytechnical UniversityXi’anShaanxi 710129China Xi’an Key Laboratory of Scientific Computation and Applied Statistics Xi’anShaanxi 710129China School of Mathematics and Statistics University of GlasgowGlasgowG128QQUnited Kingdom

Background Understanding the interaction between the mitral valve(MV)and the left ventricle(LV)is very important in assessing cardiac pump function,especially when the MV is *** dysfunction is a major medical problem owing to the essential role of the MV in cardiac pump *** modelling can provide new approaches to gain insight into the functions of the MV and *** In this study,a previously developed LV-MV model was used to study cardiac dynamics of MV leaflets under normal and pathological conditions,including hypertrophic cardiomyopathy(HOCM)and calcification of the *** coupled LV-MV model was implemented using a hybrid immersed boundary/finite element method to enable assessment of MV haemodynamic *** parameters of the HOCM and calcified valves were inversely determined from published experimental *** LV compensation mechanism was further studied in the case of the calcified *** Our results showed that MV dynamics and LV pump function could be greatly affected by MV *** example,the HOCM case showed bulged MV leaflets at the systole owing to low stiffness,and the calcified MV was associated with impaired diastolic filling and much-reduced stroke *** further demonstrated that either increasing the LV filling pressure or increasing myocardial contractility could enable a calcified valve to achieve near-normal pump *** The modelling approach developed in this study may deepen our understanding of the interactions between the MV and the LV and help in risk stratification of heart valve disease and in silico treatment planning by exploring intrinsic compensation mechanisms.

关键词： Mitral valve Left ventricle Valve disease Hybrid immersed boundary/finite element method Calcification Hypertrophic cardiomyopathy

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∈-subgradient algorithms for bilevel convex optimization

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Inverse Problems 2017年第5期33卷

作者： Helou, Elias S. Simões, Lucas E.A. Department of Applied Mathematics and Statistics Institute of Mathematical Sciences and Computation USP São Carlos Brazil Institute of Mathematics Statistics and Scientific Computing UNICAMP Campinas Brazil

This paper introduces and studies the convergence properties of a new class of explicit ∈-subgradient methods for the task of minimizing a convex function over a set of minimizers of another convex minimization problem. The general algorithm specializes to some important cases, such as first-order methods applied to a varying objective function, which have computationally cheap iterations. We present numerical experimentation concerning certain applications where the theoretical framework encompasses efficient algorithmic techniques, enabling the use of the resulting methods to solve very large practical problems arising in tomographic image reconstruction. © 2017 IOP Publishing Ltd.

关键词： Convex optimization

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Morphological perceptron learning

Morphological perceptron learning

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IEEE International Symposium on Intelligent Control (ISIC)

作者： P. Sussner Institute for Mathematics Statisticsand Scientific Computation Department of Applied Mathematics State University of Campinas Sao Paulo Brazil

Perceptrons have been used to classify patterns into different classes. Several researchers introduced a novel class of artificial neural networks, called morphological neural networks. In this new theory, the first step in computing the next state of a neuron or in performing the next layer neural network computation involves the nonlinear operation of adding neural values and their synaptic strengths followed by forming the maximum of the results. Ritter et al. (1997) have shown that the properties of morphological neural networks differ drastically from those of traditional neural network models. In this paper, the author introduces a learning algorithm for multilayer morphological perceptrons which is capable of solving arbitrary classification problems of patterns into two classes.

关键词： Neural networks Artificial neural networks Computer networks Multi-layer neural network Neurons Biological system modeling Electric potential Algebra mathematics Mathematical model

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