On viable therapy strategy for a mathematical spatial cancer model describing the dynamics of malignant and healthy cells.
On viable therapy strategy for a mathematical spatial cancer model describing the dynamics of malignant and healthy cells.
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关于描述恶性和健康细胞动态的数学空间癌症模型的可行治疗策略。
DOI：
10.3934/mbe.2015.12.163
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发表时间：
2014
期刊：
影响因子：
--
通讯作者：
E. Fimmel
中科院分区：
文献类型：
--
作者：
A. Bratus;S. Kovalenko;E. Fimmel
被认为是一种药物和恶性和健康细胞之间的相互作用的数学空间癌症模型。据推测，该药物影响阴性恶性细胞以及健康细胞。所考虑的数学模型由三个非线性抛物型偏微分方程组成，该方程描述了恶性细胞和健康细胞的空间动力学以及药物的浓度。此外，我们假设在整个治疗过程中，恶性和健康细胞的数量以及药物的总剂量有一些阶段限制。我们搜索了在应用最大强度的药物（强化治疗阶段）和停止给药（放松阶段）之间切换的所有治疗过程，目的是实现最大可能的治疗（生存）时间。我们将称该疗法为可行的治疗策略。
A mathematical spatial cancer model of the interaction between a drug and both malignant and healthy cells is considered. It is assumed that the drug influences negative malignant cells as well as healthy ones. The mathematical model considered consists of three nonlinear parabolic partial differential equations which describe spatial dynamics of malignant cells as well as healthy ones, and of the concentration of the drug. Additionally, we assume some phase constraints for the number of the malignant and the healthy cells and for the total dose of the drug during the whole treatment process. We search through all the courses of treatment switching between an application of the drug with the maximum intensity (intensive therapy phase) and discontinuing administering of the drug (relaxation phase) with the objective of achieving the maximum possible therapy (survival) time. We will call the therapy a viable treatment strategy.
影响因子：
5
作者：
Swierniak, Andrzej;Kimmel, Marek;Smieja, Jaroslaw
通讯作者：
Smieja, Jaroslaw
神经胶质瘤三维数学模型中生长速率和扩散系数的相互作用。
DOI：
--
发表时间：
1997
期刊：
Journal of neuropathology and experimental neurology.
影响因子：
--
作者：
Burgess,PK;Kulesa,PM;Murray,JD;AlvordJr,EC
通讯作者：
AlvordJr,EC