Bifurcation analysis of a free boundary problem modelling tumour growth under the action of inhibitors
Bifurcation analysis of a free boundary problem modelling tumour growth under the action of inhibitors
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DOI：
10.1088/0951-7715/25/10/2971
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发表时间：
2012-10
期刊：
影响因子：
1.7
通讯作者：
Junde Wu;Fujun Zhou
中科院分区：
文献类型：
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作者：
Junde Wu;Fujun Zhou
在本文中，我们研究了在抑制剂作用下模拟肿瘤生长的自由边界问题的非径向稳态解。该模型由两个椭圆方程描述的营养物质和抑制剂的浓度，分别和一个斯托克斯方程的肿瘤细胞的速度和内部压力。增殖率μ与细胞间增殖率γ的比值μ/γ起着分岔参数的作用。我们证明了在某些情形下存在一个正序列，使得对于每个（μ/γ）n（n为偶数）n*，存在从径向平稳解分支出来的非径向平稳解，而在其他情形下至多存在有限个分支点.这与相应的无边界模型中总是存在无穷多个非径向定常分岔解的分支是一个显著的区别。我们的分析还表明，抑制剂的供应可能会降低肿瘤的侵袭能力，甚至使肿瘤的非侵袭性和稳定性。
In this paper we investigate non-radial stationary solutions of a free boundary problem modelling tumour growth under the action of inhibitors. The model consists of two elliptic equations describing the concentration of nutrients and inhibitors, respectively, and a Stokes equation for the velocity of tumour cells and internal pressure. The ratio μ/γ of the proliferation rate μ and the cell-to-cell adhesiveness γ plays the role of the bifurcation parameter. We prove that in certain situations there exists a positive sequence such that for each (μ/γ)n(n even ⩾n*) there exist non-radial stationary solutions bifurcating from the radial stationary solution, while in the other situations there exists at most a finite number of bifurcation points. This is a remarkable difference from the corresponding inhibitor-free model where there always exist infinitely many branches of non-radial stationary bifurcation solutions. Our analysis also indicates that inhibitor supply may lower the ability of tumour invasion, and even make the tumour unaggressive and stable.