文章：

癌症的数学：整合定量模型

The mathematics of cancer: integrating quantitative models

原文发布日期：2015-11-24

DOI: 10.1038/nrc4029

类型: Review Article

开放获取: 否

要点：

1. Mathematical models have become an integral part of cancer biology. They are useful tools for deriving a mechanistic understanding of dynamic processes in cancer.
2. The somatic evolutionary process, which maintains tissues and can initiate cancer, has served as a hallmark of mathematical descriptions of tumours. Mathematical models have helped in the understanding of interactions among homeostatic mechanisms, environmental factors and mutation accumulation that drive tumorigenesis.
3. Using cell-based hierarchical models of tissue structure, theoretical insights have influenced the prediction of the cell of origin of human cancers, which may drive an understanding of metastasis and treatment response.
4. The temporal order of events during tumour development can be recapitulated using mathematical modelling and genomics data sets.
5. Mathematical models have also been used to explore the role of the tumour microenvironment in cancer progression. Such models help to elucidate important microenvironmental barriers to effective cancer treatment and how to overcome them.
6. Metastasis evolution and immunotherapy have attracted increasing interest but still offer a wide range of opportunities for mathematical modelling.
7. In combination with pharmacological considerations, quantitative models have a decisive role in the exploration of novel treatment modalities of cancer. This includes drug scheduling and the effect of combination therapy to avoid the evolution of resistance.
8. The key role of mathematical modelling in the future will not only be to describe what is known, but also to point to gaps in our understanding of which complex interactions drive tumour growth, treatment dynamics and resistance evolution.

要点翻译：

1. 数学模型已成为癌症生物学不可或缺的组成部分。它们是推导癌症动态过程机制化认知的有效工具。
2. 体细胞进化过程既能维持组织稳态又可能诱发癌症，这一特性已成为肿瘤数学描述的标志性特征。数学模型有助于理解驱动肿瘤发生的稳态机制、环境因素与突变积累之间的相互作用。
3. 基于细胞层级组织结构模型的理论研究，推动了人类癌症起源细胞的预测，这可能深化对转移机制和治疗反应的理解。
4. 肿瘤发展过程中的事件时序可通过数学模型与基因组学数据联合重构。
5. 数学模型亦被用于探索肿瘤微环境在癌症进展中的作用。这类模型有助于阐明影响癌症有效治疗的关键微环境障碍及其突破路径。
6. 转移演进与免疫治疗虽日益受到关注，仍为数学模型研究提供了广阔空间。
7. 结合药理学考量，定量模型在探索癌症新型治疗模式中具有决定性作用，包括药物时序安排与联合疗法避免耐药性演化的效应。
8. 未来数学模型的关键作用不仅在于描述已知现象，更在于揭示哪些复杂相互作用驱动肿瘤生长、治疗动态与耐药演化等认知空白领域。

英文摘要：

Mathematical modelling approaches have become increasingly abundant in cancer research. The complexity of cancer is well suited to quantitative approaches as it provides challenges and opportunities for new developments. In turn, mathematical modelling contributes to cancer research by helping to elucidate mechanisms and by providing quantitative predictions that can be validated. The recent expansion of quantitative models addresses many questions regarding tumour initiation, progression and metastases as well as intra-tumour heterogeneity, treatment responses and resistance. Mathematical models can complement experimental and clinical studies, but also challenge current paradigms, redefine our understanding of mechanisms driving tumorigenesis and shape future research in cancer biology.

摘要翻译： 

数学建模方法在癌症研究中日益增多。癌症的复杂性非常适合定量研究，这既带来了挑战，也为新发展提供了机遇。反过来，数学建模通过阐明机制并提供可验证的定量预测，为癌症研究做出了贡献。近年来，定量模型的扩展解决了许多关于肿瘤起始、进展和转移以及肿瘤内异质性、治疗反应和耐药性的问题。数学模型可以补充实验和临床研究，也可以挑战当前的范式，重新定义我们对肿瘤发生机制的理解，并塑造未来癌症生物学研究的方向。

原文链接：

The mathematics of cancer: integrating quantitative models