癌症是威胁人类生命的主要疾病之一.应用数学和物理理论,结合计算机技术,将各种影响肿瘤生长的因素综合考虑,建立可靠的肿瘤生长趋势模型,对于获得肿瘤生物学过程的知识及优化治疗方案都有着重要的意义.综合考虑肿瘤细胞间黏着能量、细胞运动速度、细胞间压强、肿瘤内部质量交换及营养浓度分布等多个因素,以遵循质量守恒定律的对流-反应-扩散偏微分方程为基础,详细描述肿瘤细胞生长模型的建立原理和过程,并分析其合理性和实际意义.通过仿真实验,分析讨论模型中的重要参数,如肿瘤细胞维持可生长的最低营养浓度、黏着能量参数和肿瘤初始形状等的意义以及对肿瘤细胞生长趋势的影响.仿真结果表明,构建的肿瘤细胞生长模型能够演化肿瘤向外生长扩张的趋势,并能够根据营养浓度的变化等条件演化出相应的结果,模拟出肿瘤生长过程中出现的突起结构,说明这是符合实际肿瘤细胞生长的基本模式.此课题的研究具有预测肿瘤生长趋势,辅助临床肿瘤治疗的实际意义.%Cancer has been one of the major diseases threatening human life. Considering various factors influencing tumor invasion to construct a rational tumor growth model, through integrating mathematical and physical theories with computer technology, it is important to understand the invasion procedure of cancerous tissue and help for optimizing clinical tumor therapy plan. Based on an advection-diffusion-reaction equation which describes the mass conservation laws, this paper detailed the modeling of the tumor cells growth and analyzed its rationality and practical significance by considering many factors including tumor cells adhesion energy, cell moving velocity, solid pressure, mass exchange and nutrition distribution. The simulation results showed the effects of some factors in the model, including the lowest nutrition concentration supporting viable tumor cells, adhesion energy parameter and initial tumor shape, on tumor cells growth, and proved that our model can simulate the evolution of tumors growing outward expansion trend; and according to the nutrient concentration changes and other conditions alterations, the corresponding evolution results can be obtained; simulating tumor cells growth results appear the protuberant structures, which is consistent with the actual tumor growth. This study is significant for predicting tumor growth evolution and assisting clinical tumor therapy.
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