Thornton B S, Langtry T N
Foundation for Australian Resources, School of Mathematical Sciences, Sydney, Australia.
J Med Syst. 1988 Feb;12(1):31-41. doi: 10.1007/BF01002374.
The paper describes an adaptive control approach to the problem of the treatment of solid tumors. The evolution with time t of the state of a tumor is modelled by a two-compartment system, governed by two differential equations forming an autonomous system under therapy control u, (formula; see text) where y1 and y2 are the number of proliferating and nonproliferating cells, respectively. The output is analyzed in the phase plane y1y2. The control problem is that of restricting the tumor state to a predetermined region of the plane by selecting a suitable change in therapy control u, e.g., modality and dosage, when the state solution intersects the boundary of this region and the ratio y1/y2 of proliferating to nonproliferating cells is displayed together with an elapsed time scale. Then, consequent selection of a suitable therapeutic sequence may be assisted by the use of a data base as part of an expert system. The process is repeated at each intersection of the prescribed boundary. Such sequences may lead to stabilization of the system through the appearance on a computer display screen of a stable equilibrium point or a limit cycle.
本文描述了一种针对实体瘤治疗问题的自适应控制方法。肿瘤状态随时间t的演变由一个双室系统建模，该系统由两个微分方程控制，在治疗控制u下构成一个自治系统，（公式；见原文）其中y1和y2分别是增殖细胞和非增殖细胞的数量。在相平面y1y2中分析输出。控制问题是当状态解与该区域的边界相交且增殖细胞与非增殖细胞的比率y1/y2与经过的时间尺度一起显示时，通过选择治疗控制u的合适变化（例如方式和剂量），将肿瘤状态限制在平面的预定区域内。然后，作为专家系统一部分的数据库的使用可以辅助随后选择合适的治疗序列。在规定边界的每个交点处重复该过程。这样的序列可能会通过在计算机显示屏上出现稳定平衡点或极限环而导致系统稳定。
