Nonlinear simulation of vascular tumor growth with chemotaxis and the control of necrosis
Nonlinear simulation of vascular tumor growth with chemotaxis and the control of necrosis
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DOI：
10.1016/j.jcp.2022.111153
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发表时间：
2021-07
期刊：
影响因子：
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通讯作者：
M. Lu;Wenrui Hao;Chun Liu;J. Lowengrub;Shuwang Li
中科院分区：
文献类型：
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作者：
M. Lu;Wenrui Hao;Chun Liu;J. Lowengrub;Shuwang Li
在本文中，我们开发了一个二维锐界面肿瘤生长模型，以研究使用受控坏死核心的瘤内结构和脉管系统的瘤外营养供应对肿瘤形态的影响。我们首先表明我们的模型使用线性稳定性分析扩展了文献中的基准结果。然后，我们在演化的环形域中使用光谱精确的边界积分方法对这个广义模型进行数值求解，不仅在模拟肿瘤脉管系统的营养场的外边界上采用 Robin 边界条件，而且在模拟肿瘤坏死控制的压力场的内边界上采用静态边界条件。通过跟踪 GMRES 迭代次数，压力场和养分场的离散线性系统显示出良好的条件。我们的非线性模拟揭示了如果坏死核心固定为圆形，则血管生成的稳定作用以及趋化性和坏死的不稳定作用在肿瘤形态不稳定性的发展中。当坏死核心被控制为非圆形时，可以观察到增殖的稳定作用和凋亡的不稳定作用。最后，在边界处精确求解的营养物浓度及其通量和压力水平及其正常导数的值，有助于我们表征相应的肿瘤形态以及保持肿瘤坏死区域的各种形状所需的界面上的生物物理量的水平。有趣的是，我们注意到，当坏死区域固定为三重非圆形形状时，即使肿瘤的初始形状是圆形，肿瘤也会演变成与固定坏死区域形状的三重对称相对应的形状。
In this paper, we develop a sharp interface tumor growth model in two dimensions to study the effect of both the intratumoral structure using a controlled necrotic core and the extratumoral nutrient supply from vasculature on tumor morphology. We first show that our model extends the benchmark results in the literature using linear stability analysis. Then we solve this generalized model numerically using a spectrally accurate boundary integral method in an evolving annular domain, not only with a Robin boundary condition on the outer boundary for the nutrient field which models tumor vasculature, but also with a static boundary condition on the inner boundary for pressure field which models the control of tumornecrosis. The discretized linear systems for both pressure and nutrient fields are shown to be well-conditioned through tracing GMRES iteration numbers. Our nonlinear simulations reveal the stabilizing effects ofangiogenesisand the destabilizing ones ofchemotaxisandnecrosisin the development of tumor morphological instabilities if the necrotic core is fixed in a circular shape. When the necrotic core is controlled in a non-circular shape, the stabilizing effects ofproliferationand the destabilizing ones ofapoptosisare observed. Finally, the values of the nutrient concentration with its fluxes and the pressure level with its normal derivatives, which are solved accurately at the boundaries, help us to characterize the corresponding tumor morphology and the level of the biophysical quantities on interfaces required in keeping various shapes of the necrotic region of the tumor. Interestingly, we notice that when the necrotic region is fixed in a 3-fold non-circular shape, even if the initial shape of the tumor is circular, the tumor will evolve into a shape corresponding to the 3-fold symmetry of the shape of the fixed necrotic region.