Volume 10, Issue 3
Numerical Simulation of Tumor Growth Based on the Free Boundary Element Discretization

Adv. Appl. Math. Mech., 10 (2018), pp. 529-553.

Published online: 2018-10

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• Abstract

We present an iterative method to numerically simulate the growth and shrinkage of tumor. We transform the free boundary problem describing tumor growth into the boundary integral equations which reduce the dimensionality of the problem by one. By boundary element method, we discretize the boundary integral equations by grid points on the moving boundaries of tumor. We estimate the error of the numerical integration. We design an iterative scheme and implement successfully this scheme to visually and graphically show the evolution of the interface between the tumor and the external tissue at different moments of time. In this paper, the proliferation rate $μ$ is a function of space $x$ and time $t$. Our numerical method professor Bei Hu proposed is novel and our numerical results are in agreement with the tumor growth in vivo.

35R35, 62P10, 65M38

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@Article{AAMM-10-529, author = {Zhang , YarongHe , Yinnian and Chen , Hongbin}, title = {Numerical Simulation of Tumor Growth Based on the Free Boundary Element Discretization}, journal = {Advances in Applied Mathematics and Mechanics}, year = {2018}, volume = {10}, number = {3}, pages = {529--553}, abstract = {

We present an iterative method to numerically simulate the growth and shrinkage of tumor. We transform the free boundary problem describing tumor growth into the boundary integral equations which reduce the dimensionality of the problem by one. By boundary element method, we discretize the boundary integral equations by grid points on the moving boundaries of tumor. We estimate the error of the numerical integration. We design an iterative scheme and implement successfully this scheme to visually and graphically show the evolution of the interface between the tumor and the external tissue at different moments of time. In this paper, the proliferation rate $μ$ is a function of space $x$ and time $t$. Our numerical method professor Bei Hu proposed is novel and our numerical results are in agreement with the tumor growth in vivo.

}, issn = {2075-1354}, doi = {https://doi.org/10.4208/aamm.OA-2016-0165}, url = {http://global-sci.org/intro/article_detail/aamm/12224.html} }
TY - JOUR T1 - Numerical Simulation of Tumor Growth Based on the Free Boundary Element Discretization AU - Zhang , Yarong AU - He , Yinnian AU - Chen , Hongbin JO - Advances in Applied Mathematics and Mechanics VL - 3 SP - 529 EP - 553 PY - 2018 DA - 2018/10 SN - 10 DO - http://doi.org/10.4208/aamm.OA-2016-0165 UR - https://global-sci.org/intro/article_detail/aamm/12224.html KW - Free boundary problem, mathematical model of tumor growth, boundary integral equations, Green functions, singular integrals. AB -

We present an iterative method to numerically simulate the growth and shrinkage of tumor. We transform the free boundary problem describing tumor growth into the boundary integral equations which reduce the dimensionality of the problem by one. By boundary element method, we discretize the boundary integral equations by grid points on the moving boundaries of tumor. We estimate the error of the numerical integration. We design an iterative scheme and implement successfully this scheme to visually and graphically show the evolution of the interface between the tumor and the external tissue at different moments of time. In this paper, the proliferation rate $μ$ is a function of space $x$ and time $t$. Our numerical method professor Bei Hu proposed is novel and our numerical results are in agreement with the tumor growth in vivo.

Yarong Zhang, Yinnian He & Hongbin Chen. (2020). Numerical Simulation of Tumor Growth Based on the Free Boundary Element Discretization. Advances in Applied Mathematics and Mechanics. 10 (3). 529-553. doi:10.4208/aamm.OA-2016-0165
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