Mathematical analysis of hydrodynamics and tissue deformation inside an isolated solid tumor

IF 0.7 Q4 MECHANICS
Meraj Alam, Bibaswan Dey, G. Raja
{"title":"Mathematical analysis of hydrodynamics and tissue deformation inside an isolated solid tumor","authors":"Meraj Alam, Bibaswan Dey, G. Raja","doi":"10.2298/TAM180810014A","DOIUrl":null,"url":null,"abstract":"In this article, we present a biphasic mixture theory based mathematical model for the hydrodynamics of interstitial fluid motion and mechanical behavior of the solid phase inside a solid tumor. The tumor tissue considered here is an isolated deformable biological medium. The solid phase of the tumor is constituted by vasculature, tumor cells, and extracellular matrix, which are wet by a physiological extracellular fluid. Since the tumor is deformable in nature, the mass and momentum equations for both the phases are presented. The momentum equations are coupled due to the interaction (or drag) force term. These governing equations reduce to a one-way coupled system under the assumption of infinitesimal deformation of the solid phase. The well-posedness of this model is shown in the weak sense by using the inf-sup (Babuska–Brezzi) condition and Lax–Milgram theorem in 2D and 3D. Further, we discuss a one-dimensional spherical symmetry model and present some results on the stress fields and energy of the system based on L2 and Sobolev norms. We discuss the so-called phenomena of “necrosis” inside a solid tumor using the energy of the system.","PeriodicalId":44059,"journal":{"name":"Theoretical and Applied Mechanics","volume":null,"pages":null},"PeriodicalIF":0.7000,"publicationDate":"2018-01-01","publicationTypes":"Journal Article","fieldsOfStudy":null,"isOpenAccess":false,"openAccessPdf":"","citationCount":"3","resultStr":null,"platform":"Semanticscholar","paperid":null,"PeriodicalName":"Theoretical and Applied Mechanics","FirstCategoryId":"1085","ListUrlMain":"https://doi.org/10.2298/TAM180810014A","RegionNum":0,"RegionCategory":null,"ArticlePicture":[],"TitleCN":null,"AbstractTextCN":null,"PMCID":null,"EPubDate":"","PubModel":"","JCR":"Q4","JCRName":"MECHANICS","Score":null,"Total":0}
引用次数: 3

Abstract

In this article, we present a biphasic mixture theory based mathematical model for the hydrodynamics of interstitial fluid motion and mechanical behavior of the solid phase inside a solid tumor. The tumor tissue considered here is an isolated deformable biological medium. The solid phase of the tumor is constituted by vasculature, tumor cells, and extracellular matrix, which are wet by a physiological extracellular fluid. Since the tumor is deformable in nature, the mass and momentum equations for both the phases are presented. The momentum equations are coupled due to the interaction (or drag) force term. These governing equations reduce to a one-way coupled system under the assumption of infinitesimal deformation of the solid phase. The well-posedness of this model is shown in the weak sense by using the inf-sup (Babuska–Brezzi) condition and Lax–Milgram theorem in 2D and 3D. Further, we discuss a one-dimensional spherical symmetry model and present some results on the stress fields and energy of the system based on L2 and Sobolev norms. We discuss the so-called phenomena of “necrosis” inside a solid tumor using the energy of the system.
孤立实体瘤内流体力学和组织变形的数学分析
在本文中,我们提出了一个基于双相混合理论的数学模型,用于计算实体瘤内部的流体运动和固相力学行为。这里考虑的肿瘤组织是一个孤立的可变形的生物培养基。肿瘤的固相由脉管系统、肿瘤细胞和细胞外基质组成,细胞外基质被生理细胞外液润湿。由于肿瘤本质上是可变形的,因此给出了这两个阶段的质量和动量方程。动量方程由于相互作用(或阻力)力项而耦合。这些控制方程在固相无限小变形的假设下简化为单向耦合系统。利用二维和三维的f-sup (Babuska-Brezzi)条件和Lax-Milgram定理,在弱意义上证明了该模型的适定性。进一步讨论了一维球对称模型,并给出了基于L2范数和Sobolev范数的系统应力场和能量的一些结果。我们利用系统的能量来讨论实体肿瘤内部所谓的“坏死”现象。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
求助全文
约1分钟内获得全文 求助全文
来源期刊
CiteScore
0.90
自引率
0.00%
发文量
4
审稿时长
32 weeks
期刊介绍: Theoretical and Applied Mechanics (TAM) invites submission of original scholarly work in all fields of theoretical and applied mechanics. TAM features selected high quality research articles that represent the broad spectrum of interest in mechanics.
×
引用
GB/T 7714-2015
复制
MLA
复制
APA
复制
导出至
BibTeX EndNote RefMan NoteFirst NoteExpress
×
提示
您的信息不完整,为了账户安全,请先补充。
现在去补充
×
提示
您因"违规操作"
具体请查看互助需知
我知道了
×
提示
确定
请完成安全验证×
copy
已复制链接
快去分享给好友吧!
我知道了
右上角分享
点击右上角分享
0
联系我们:info@booksci.cn Book学术提供免费学术资源搜索服务,方便国内外学者检索中英文文献。致力于提供最便捷和优质的服务体验。 Copyright © 2023 布克学术 All rights reserved.
京ICP备2023020795号-1
ghs 京公网安备 11010802042870号
Book学术文献互助
Book学术文献互助群
群 号:481959085
Book学术官方微信