Fassoni Artur C, Yang Hyun M
Instituto de Matemática e Computação, UNIFEI, Itajubá, Minas Gerais, Brazil.
Instituto de Matemática, Estatística e Computação Científica, UNICAMP, Campinas, São Paulo, Brazil.
Math Med Biol. 2019 Jun 13;36(2):241-267. doi: 10.1093/imammb/dqy010.
Tumorigenesis has been described as a multistep process, where each step is associated with a genetic alteration, in the direction to progressively transform a normal cell and its descendants into a malignant tumour. Into this work, we propose a mathematical model for cancer onset and development, considering three populations: normal, premalignant and cancer cells. The model takes into account three hallmarks of cancer: self-sufficiency on growth signals, insensibility to anti-growth signals and evading apoptosis. By using a nonlinear expression to describe the mutation from premalignant to cancer cells, the model includes genetic instability as an enabling characteristic of tumour progression. Mathematical analysis was performed in detail. Results indicate that apoptosis and tissue repair system are the first barriers against tumour progression. One of these mechanisms must be corrupted for cancer to develop from a single mutant cell. The results also show that the presence of aggressive cancer cells opens way to survival of less adapted premalignant cells. Numerical simulations were performed with parameter values based on experimental data of breast cancer, and the necessary time taken for cancer to reach a detectable size from a single mutant cell was estimated with respect to some parameters. We find that the rates of apoptosis and mutations have a large influence on the pace of tumour progression and on the time it takes to become clinically detectable.
肿瘤发生被描述为一个多步骤过程，其中每个步骤都与一种基因改变相关联，朝着将正常细胞及其后代逐渐转变为恶性肿瘤的方向发展。在这项工作中，我们提出了一个癌症发生和发展的数学模型，考虑了三种细胞群体：正常细胞、癌前细胞和癌细胞。该模型考虑了癌症的三个特征：生长信号的自给自足、对生长抑制信号的不敏感以及逃避细胞凋亡。通过使用非线性表达式来描述从癌前细胞到癌细胞的突变，该模型将基因不稳定性作为肿瘤进展的一个促成特征。我们进行了详细的数学分析。结果表明，细胞凋亡和组织修复系统是肿瘤进展的首要障碍。癌症要从单个突变细胞发展起来，这些机制中的一个必须被破坏。结果还表明，侵袭性癌细胞的存在为适应性较差的癌前细胞的存活开辟了道路。我们根据乳腺癌的实验数据使用参数值进行了数值模拟，并针对一些参数估计了癌症从单个突变细胞发展到可检测大小所需的时间。我们发现，细胞凋亡率和突变率对肿瘤进展的速度以及临床可检测所需的时间有很大影响。
