一个包含2/3D位移和变形的心血管系统弹性数值模型

Q3 Mathematics

International Journal for Simulation and Multidisciplinary Design Optimization Pub Date : 2020-01-01 DOI:10.1051/smdo/2020014

Ayoub Azzayani

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引用次数: 0

摘要

在此工作中，我们考虑变形位移的方向，在二维和三维维度上处理约束下变形的弹性模型。这项工作是一篇文章的结果[a]。Azzayani等人，Br。j .数学。第一版。科学。(2016)]其中我们通过固定纤维方向使用相同的数学模型。然后，如果我们考虑特征值和特征向量的情况，也就是这项工作的情况，我们就可以在图像处理中控制心脏的变形。该数学模型可用于描述考虑纤维方向的心脏变形，以估计左心室功能的整体和局部参数。首先，我们提出了在一个域Ω∧∈n (n = 2或3)上的数学模型，并给出了该数学模型解的存在唯一性(二维和三维)。其次，利用FreeFem软件进行了数值模拟，最后给出了仿真结果和评价。最后，我们将讨论该模型的图像处理及其帮助医生诊断心脏病的可行性。

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A numerical model of elasticity for cardiovascular system that includes 2/3D displacements and deformations

In this work, we deal an elasticity model in 2D and 3D dimension for deformation under constraint by taking into account the direction of the deformation displacement. This work is a result of an article [A. Azzayani et al., Br. J. Math. Comput. Sci. (2016)] in which we use the same mathematical model by fixing the fiber orientation. Then, if we considered the case of eignvalue and eigenvector, and which is the case of this work, we can be able to control the deformation of the heart in the image processing. This mathematical model can be used to describe the heart deformation taking into account the orientation of the fibers for estimating global and regional parameters of the left ventricular function. In first, we start by presenting the proposed mathematical model on a domain Ω ⊂ ℝn (n = 2 or 3), and we give the existence and uniqueness of solution to the mathematical model is given (in both 2D and 3D dimension). Secondly, we give numerical simulations with FreeFem software, simulations results and comments are given in the end. In the end, we will discuss about the image treatment with this model and its feasibility to help doctors in the diagnosis of heart disease.

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来源期刊

International Journal for Simulation and Multidisciplinary Design Optimization Mathematics-Control and Optimization

CiteScore

2.00

自引率

0.00%

发文量

审稿时长

16 weeks

期刊介绍： The International Journal for Simulation and Multidisciplinary Design Optimization is a peer-reviewed journal covering all aspects related to the simulation and multidisciplinary design optimization. It is devoted to publish original work related to advanced design methodologies, theoretical approaches, contemporary computers and their applications to different fields such as engineering software/hardware developments, science, computing techniques, aerospace, automobile, aeronautic, business, management, manufacturing,... etc. Front-edge research topics related to topology optimization, composite material design, numerical simulation of manufacturing process, advanced optimization algorithms, industrial applications of optimization methods are highly suggested. The scope includes, but is not limited to original research contributions, reviews in the following topics: Parameter identification & Surface Response (all aspects of characterization and modeling of materials and structural behaviors, Artificial Neural Network, Parametric Programming, approximation methods,…etc.) Optimization Strategies (optimization methods that involve heuristic or Mathematics approaches, Control Theory, Linear & Nonlinear Programming, Stochastic Programming, Discrete & Dynamic Programming, Operational Research, Algorithms in Optimization based on nature behaviors,….etc.) Structural Optimization (sizing, shape and topology optimizations with or without external constraints for materials and structures) Dynamic and Vibration (cover modelling and simulation for dynamic and vibration analysis, shape and topology optimizations with or without external constraints for materials and structures) Industrial Applications (Applications Related to Optimization, Modelling for Engineering applications are very welcome. Authors should underline the technological, numerical or integration of the mentioned scopes.).