Nonlinear studies of tumor morphological stability using a two-fluid flow model
Nonlinear studies of tumor morphological stability using a two-fluid flow model
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DOI：
10.1007/s00285-018-1212-3
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发表时间：
2018-03
影响因子：
1.9
通讯作者：
K. Pham;Emma Turian;Kai Liu;Shuwang Li;J. Lowengrub
中科院分区：
文献类型：
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作者：
K. Pham;Emma Turian;Kai Liu;Shuwang Li;J. Lowengrub
我们使用双流体斯托克斯模型在组织尺度上考虑无血管肿瘤的非线性动力学，其中肿瘤和宿主微环境的粘度可能不同。粘度反映了细胞和细胞外基质混合物的综合特性。我们对肿瘤进行线性形态稳定性分析，并使用二维边界积分模拟研究非线性的作用。尽管细胞死亡可能通过细胞凋亡发生，但肿瘤是非坏死的。我们证明肿瘤进化受到一组减少的无量纲参数的调节，这些参数表征细胞凋亡、细胞-细胞/细胞-细胞外基质粘附、血管化以及肿瘤与宿主粘度的比率。方程的新颖重新表述使得能够使用标准边界积分技术对方程进行数值求解。非线性模拟结果与近圆形肿瘤的线性预测一致。随着扰动的发展和增长，线性和非线性结果会出现偏差，线性理论往往会低估扰动的增长。模拟揭示了两种基本类型的肿瘤形状，具体取决于肿瘤的粘度和微环境。当肿瘤比其环境更粘稠时，肿瘤往往会形成侵入性指状结构和分支状结构。随着肿瘤和宿主粘度的相对比例降低，肿瘤往往会以更紧凑的形状生长，并形成健康区域的复杂内陷，这些内陷可能被包裹在肿瘤内部。尽管我们的模型使用了肿瘤和宿主生物力学的简化描述，但我们的结果与各种肿瘤类型的实验一致，表明肿瘤硬度和肿瘤侵袭性之间存在正相关。
We consider the nonlinear dynamics of an avascular tumor at the tissue scale using a two-fluid flow Stokes model, where the viscosity of the tumor and host microenvironment may be different. The viscosities reflect the combined properties of cell and extracellular matrix mixtures. We perform a linear morphological stability analysis of the tumors, and we investigate the role of nonlinearity using boundary-integral simulations in two dimensions. The tumor is non-necrotic, although cell death may occur through apoptosis. We demonstrate that tumor evolution is regulated by a reduced set of nondimensional parameters that characterize apoptosis, cell–cell/cell-extracellular matrix adhesion, vascularization and the ratio of tumor and host viscosities. A novel reformulation of the equations enables the use of standard boundary integral techniques to solve the equations numerically. Nonlinear simulation results are consistent with linear predictions for nearly circular tumors. As perturbations develop and grow, the linear and nonlinear results deviate and linear theory tends to underpredict the growth of perturbations. Simulations reveal two basic types of tumor shapes, depending on the viscosities of the tumor and microenvironment. When the tumor is more viscous than its environment, the tumors tend to develop invasive fingers and a branched-like structure. As the relative ratio of the tumor and host viscosities decreases, the tumors tend to grow with a more compact shape and develop complex invaginations of healthy regions that may become encapsulated in the tumor interior. Although our model utilizes a simplified description of the tumor and host biomechanics, our results are consistent with experiments in a variety of tumor types that suggest that there is a positive correlation between tumor stiffness and tumor aggressiveness.