Fedotov Sergei, Iomin Alexander
School of Mathematics, The University of Manchester, Manchester M60 1QD, United Kingdom.
Phys Rev Lett. 2007 Mar 16;98(11):118101. doi: 10.1103/PhysRevLett.98.118101. Epub 2007 Mar 12.
We propose a two-component reaction-transport model for the migration-proliferation dichotomy in the spreading of tumor cells. By using a continuous time random walk (CTRW), we formulate a system of the balance equations for the cancer cells of two phenotypes with random switching between cell proliferation and migration. The transport process is formulated in terms of the CTRW with an arbitrary waiting-time distribution law. Proliferation is modeled by a standard logistic growth. We apply hyperbolic scaling and Hamilton-Jacobi formalism to determine the overall rate of tumor cell invasion. In particular, we take into account both normal diffusion and anomalous transport (subdiffusion) in order to show that the standard diffusion approximation for migration leads to overestimation of the overall cancer spreading rate.
我们提出了一个用于肿瘤细胞扩散中迁移 - 增殖二分法的双组分反应 - 传输模型。通过使用连续时间随机游走（CTRW），我们建立了一个关于两种表型癌细胞的平衡方程组，这两种表型的细胞在增殖和迁移之间随机切换。传输过程根据具有任意等待时间分布律的CTRW来表述。增殖由标准逻辑斯蒂增长模型描述。我们应用双曲缩放和哈密顿 - 雅可比形式主义来确定肿瘤细胞侵袭的总体速率。特别地，我们同时考虑了正常扩散和反常传输（亚扩散），以表明迁移的标准扩散近似会导致对癌症总体扩散速率的高估。
