加权Sobolev空间中点源线性化弹性模型分析:在组织收缩中的应用

IF 1.9 3区 数学 Q2 Mathematics
W. Boon, F. Vermolen
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引用次数: 1

摘要

为了模拟成纤维细胞在真皮组织中施加的收缩力,我们提出并分析了在线性化弹性假设下的两种建模方法。第一种方法在成纤维细胞的边界上引入了点力的集合,而第二种方法在成纤维细胞的中心采用了各向同性的应力点源。我们用加权Sobolev空间分析了得到的偏微分方程,并确定了各自解的奇异性。提出了两种有限元方法,一种是基于直接应用的方法,另一种是减去奇异点并计算修正场的方法。最后,我们验证了建模方法的有效性,证明了数值方法的收敛性,并通过数值实验验证了分析结果。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Analysis of linearized elasticity models with point sources in weighted Sobolev spaces: applications in tissue contraction
In order to model the contractive forces exerted by fibroblast cells in dermal tissue, we propose and analyze two modeling approaches under the assumption of linearized elasticity. The first approach introduces a collection of point forces on the boundary of the fibroblast whereas the second approach employs an isotropic stress point source in its center. We analyze the resulting partial differential equations in terms of weighted Sobolev spaces and identify the singular behavior of the respective solutions. Two finite element method approaches are proposed, one based on a direct application and another in which the singularity is subtracted and a correction field is computed. Finally, we confirm the validity of the modeling approach, demonstrate convergence of the numerical methods, and verify the analysis through the use of numerical experiments.
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来源期刊
CiteScore
2.70
自引率
5.30%
发文量
27
审稿时长
6-12 weeks
期刊介绍: M2AN publishes original research papers of high scientific quality in two areas: Mathematical Modelling, and Numerical Analysis. Mathematical Modelling comprises the development and study of a mathematical formulation of a problem. Numerical Analysis comprises the formulation and study of a numerical approximation or solution approach to a mathematically formulated problem. Papers should be of interest to researchers and practitioners that value both rigorous theoretical analysis and solid evidence of computational relevance.
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