论文标题
建模肿瘤生长：一个简单的基于个体的模型及其分析
Modeling tumor growth: a simple individual-based model and its analysis
论文作者
论文摘要
恶性肿瘤的起始和发育是一种复杂的现象，具有决定其长时间行为的关键阶段。通过各种模型来描述这种现象：从简单的启发式模型到采用随机过程的模型。在本章中，我们通过分析一个简单的基于个体的模型来讨论此类建模的某些方面，其中将肿瘤细胞作为点粒子以$ \ Mathbf {r} _ {+}的形式漂移，：= [0，+\ iffty）$以单位速度来源。在原点上，每个粒子分成两个新粒子，这些粒子立即出现在随机位置下以$ \ mathbf {r} _ {+} $。在它们的漂移过程中，颗粒在分裂之前会随机死亡。在此模型中，给定单元的特征$ x \ in \ mathbf {r} _ {+} $与时间相对应与其分裂相对应，死亡是由治疗因素引起的。在其基础上，我们演示了如何得出疾病（涉及与治疗相关的死亡率和细胞周期分布参数）的疾病，肿瘤大小在时间上保持界限，这实际上意味着打击疾病。
Initiation and development of a malignant tumor is a complex phenomenon that has critical stages determining its long time behavior. This phenomenon is mathematically described by means of various models: from simple heuristic models to those employing stochastic processes. In this chapter, we discuss some aspects of such modeling by analyzing a simple individual-based model, in which tumor cells are presented as point particles drifting in $\mathbf{R}_{+}:=[0,+\infty)$ towards the origin with unit speed. At the origin, each of them splits into two new particles that instantly appear in $\mathbf{R}_{+}$ at random positions. During their drift the particles are subject to a random death before splitting. In this model, trait $x\in \mathbf{R}_{+}$ of a given cell corresponds to time to its division and the death is caused by therapeutic factors. On its base we demonstrate how to derive a condition -- involving the therapy related death rate and cell cycle distribution parameters -- under which the tumor size remains bounded in time, which practically means combating the disease.
