Bertuzzi Alessandro, D'Onofrio Alberto, Fasano Antonio, Gandolfi Alberto
Istituto di Analisi dei Sistemi ed Informatica del CNR, Viale Manzoni 30, 00185 Roma, Italy.
Bull Math Biol. 2003 Sep;65(5):903-31. doi: 10.1016/S0092-8240(03)00054-5.
In this paper, the evolution of a tumour cord after treatment is investigated by extensive numerical simulations on the basis of a mathematical model developed by Bertuzzi et al. (submitted). The model is formulated in cylindrical symmetry adopting the continuum approach, and takes into account the influence of oxygen level on the proliferation and death rate of cells, the volume reduction due to disgregation of dead cells, and the cell killing effects of radiation and drugs. Some extensions of the model are proposed to represent more accurately the radioresistance of hypoxic cells and the cytotoxic action of anticancer drugs. The steady state of the cord, and the cord evolution from the steady state after the delivery of a single dose of an anticancer agent, are computed for various combinations of model parameters and for different choices of the functions describing the effects of treatments. The results of the numerical computations show that, in spite of its many simplifications, the model behaviour appears to be reasonable in view of the available experimental observations. The model allows having a better insight into some complex treatment-related events, such as cell reoxygenation and repopulation.
在本文中，基于Bertuzzi等人（已提交）开发的数学模型，通过广泛的数值模拟研究了肿瘤条索在治疗后的演变。该模型采用连续介质方法在圆柱对称中进行公式化，并考虑了氧水平对细胞增殖和死亡率的影响、由于死细胞解体导致的体积减小以及辐射和药物的细胞杀伤作用。提出了该模型的一些扩展，以更准确地表示缺氧细胞的放射抗性和抗癌药物的细胞毒性作用。针对模型参数的各种组合以及描述治疗效果的函数的不同选择，计算了条索的稳态以及在单次给予抗癌剂后从稳态开始的条索演变。数值计算结果表明，尽管该模型有许多简化之处，但鉴于现有的实验观察结果，其行为似乎是合理的。该模型有助于更好地洞察一些与治疗相关的复杂事件，如细胞再氧合和再增殖。
