Vermolen F J, Meijden R P van der, Es M van, Gefen A, Weihs D
Delft Institute of Applied Mathematics, Delft University of Technology, Delft, The Netherlands,
Ann Biomed Eng. 2015 Jul;43(7):1680-94. doi: 10.1007/s10439-015-1271-1. Epub 2015 Feb 11.
A phenomenological model is formulated to model the early stages of tumor formation. The model is based on a cell-based formalism, where each cell is represented as a circle or sphere in two-and three dimensional simulations, respectively. The model takes into account constituent cells, such as epithelial cells, tumor cells, and T-cells that chase the tumor cells and engulf them. Fundamental biological processes such as random walk, haptotaxis/chemotaxis, contact mechanics, cell proliferation and death, as well as secretion of chemokines are taken into account. The developed formalism is based on the representation of partial differential equations in terms of fundamental solutions, as well as on stochastic processes and stochastic differential equations. We also take into account the likelihood of seeding of tumors. The model shows the initiation of tumors and allows to study a quantification of the impact of various subprocesses and possibly even of various treatments.
建立了一个现象学模型来模拟肿瘤形成的早期阶段。该模型基于一种基于细胞的形式体系，在二维和三维模拟中，每个细胞分别表示为一个圆或球体。该模型考虑了组成细胞，如上皮细胞、肿瘤细胞以及追踪并吞噬肿瘤细胞的T细胞。还考虑了基本的生物学过程，如随机游走、趋触性/趋化性、接触力学、细胞增殖和死亡以及趋化因子的分泌。所开发的形式体系基于用基本解表示的偏微分方程，以及随机过程和随机微分方程。我们还考虑了肿瘤播种的可能性。该模型展示了肿瘤的起始，并能够研究各种子过程甚至各种治疗的影响的量化。
