Numerical Simulation of Tumor Growth Based on the Free Boundary Element Discretization

Numerical Simulation of Tumor Growth Based on the Free Boundary Element  Discretization

Year:    2018

Author:    Yarong Zhang, Yinnian He, Hongbin Chen

Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 3 : pp. 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.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/aamm.OA-2016-0165

Advances in Applied Mathematics and Mechanics, Vol. 10 (2018), Iss. 3 : pp. 529–553

Published online:    2018-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    25

Keywords:    Free boundary problem mathematical model of tumor growth boundary integral equations Green functions singular integrals.

Author Details

Yarong Zhang

Yinnian He

Hongbin Chen