Ren Hai-Peng, Yang Yan, Baptista Murilo S, Grebogi Celso
Shaanxi Key Laboratory of CSCIIP, Xi'an University of Technology, Xi'an 710048, People's Republic of China
Shaanxi Key Laboratory of CSCIIP, Xi'an University of Technology, Xi'an 710048, People's Republic of China.
Philos Trans A Math Phys Eng Sci. 2017 Mar 6;375(2088). doi: 10.1098/rsta.2016.0221.
Chemotherapy is a widely accepted method for tumour treatment. A medical doctor usually treats patients periodically with an amount of drug according to empirical medicine guides. From the point of view of cybernetics, this procedure is an impulse control system, where the amount and frequency of drug used can be determined analytically using the impulse control theory. In this paper, the stability of a chemotherapy treatment of a tumour is analysed applying the impulse control theory. The globally stable condition for prescription of a periodic oscillatory chemotherapeutic agent is derived. The permanence of the solution of the treatment process is verified using the Lyapunov function and the comparison theorem. Finally, we provide the values for the strength and the time interval that the chemotherapeutic agent needs to be applied such that the proposed impulse chemotherapy can eliminate the tumour cells and preserve the immune cells. The results given in the paper provide an analytical formula to guide medical doctors to choose the theoretical minimum amount of drug to treat the cancer and prevent harming the patients because of over-treating.This article is part of the themed issue 'Horizons of cybernetical physics'.
化疗是一种被广泛接受的肿瘤治疗方法。医生通常根据经验医学指南定期给患者使用一定量的药物进行治疗。从控制论的角度来看，这个过程是一个脉冲控制系统，其中使用的药物量和频率可以通过脉冲控制理论进行分析确定。在本文中，应用脉冲控制理论分析了肿瘤化疗治疗的稳定性。推导了周期性振荡化疗药物处方的全局稳定条件。使用李雅普诺夫函数和比较定理验证了治疗过程解的持久性。最后，我们给出了化疗药物需要应用的强度和时间间隔的值，以便所提出的脉冲化疗能够消除肿瘤细胞并保留免疫细胞。本文给出的结果提供了一个解析公式，以指导医生选择治疗癌症的理论最小药物量，并防止因过度治疗而伤害患者。本文是主题为“控制论物理学的前沿”的特刊的一部分。
