Department of Applied Mathematics, Illinois Institute of Technology, Chicago, IL, 60616, USA.
Departments of Mathematics and Biomedical Engineering, Center for Complex Biological Systems, Chao Family Comprehensive Cancer Center, University of California at Irvine, Irvine, CA, 92617, USA.
Bull Math Biol. 2020 Mar 12;82(3):39. doi: 10.1007/s11538-020-00716-z.
In this paper, we develop a sharp interface tumor growth model to study the effect of the tumor microenvironment using a complex far-field geometry that mimics a heterogeneous distribution of vasculature. Together with different nutrient uptake rates inside and outside the tumor, this introduces variability in spatial diffusion gradients. Linear stability analysis suggests that the uptake rate in the tumor microenvironment, together with chemotaxis, may induce unstable growth, especially when the nutrient gradients are large. We investigate the fully nonlinear dynamics using a spectrally accurate boundary integral method. Our nonlinear simulations reveal that vascular heterogeneity plays an important role in the development of morphological instabilities that range from fingering and chain-like morphologies to compact, plate-like shapes in two dimensions.
本文开发了一个锐利界面肿瘤生长模型，使用模拟血管异质性分布的复杂远场几何结构来研究肿瘤微环境的影响。同时，肿瘤内外不同的营养摄取率导致空间扩散梯度的变化。线性稳定性分析表明，肿瘤微环境中的摄取率和趋化性可能会导致不稳定的生长，尤其是在营养梯度较大的情况下。我们使用谱精确边界积分方法研究完全非线性动力学。我们的非线性模拟表明，血管异质性在形态不稳定性的发展中起着重要作用，这些不稳定性从指状和链状形态到二维中的紧凑、板状形态不等。
