Universidade de Sao Paulo, Depto de Matematica Aplicada e Estatistica, ICMC, USP, 13560-970, Sao Carlos, Brazil.
Math Biosci Eng. 2013 Feb;10(1):221-34. doi: 10.3934/mbe.2013.10.221.
Dosage and frequency of treatment schedules are important for successful chemotherapy. However, in this work we argue that cell-kill response and tumoral growth should not be seen as separate and therefore are essential in a mathematical cancer model. This paper presents a mathematical model for sequencing of cancer chemotherapy and surgery. Our purpose is to investigate treatments for large human tumours considering a suitable cell-kill dynamics. We use some biological and pharmacological data in a numerical approach, where drug administration occurs in cycles (periodic infusion) and surgery is performed instantaneously. Moreover, we also present an analysis of stability for a chemotherapeutic model with continuous drug administration. According to Norton and Simon [22], our results indicate that chemotherapy is less efficient in treating tumours that have reached a plateau level of growing and that a combination with surgical treatment can provide better outcomes.
治疗方案的剂量和频率对于成功的化疗至关重要。然而，在这项工作中，我们认为细胞杀伤反应和肿瘤生长不应被视为独立的，因此在数学癌症模型中是必不可少的。本文提出了一种用于癌症化疗和手术排序的数学模型。我们的目的是研究考虑合适的细胞杀伤动力学的大型人类肿瘤的治疗方法。我们在数值方法中使用了一些生物学和药理学数据，其中药物给药发生在周期（周期性输注）中，手术是瞬时进行的。此外，我们还对具有连续药物给药的化疗模型的稳定性进行了分析。根据 Norton 和 Simon [22] 的说法，我们的结果表明，化疗在治疗已经达到生长平台水平的肿瘤方面效率较低，而与手术治疗相结合可以提供更好的结果。
