用数学能更好地治疗癌症？

诸平

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据加拿大滑铁卢大学（University of Waterloo）2022年11月28日报道，滑铁卢大学的研究人员与加拿大渥太华大学（University of Ottawa, Canada）的研究人员合作，开发了针对异质性肿瘤（heterogeneous tumours）的治疗时序安排方法（treatment scheduling method）。研究人员已经确定了一种安排放射治疗（scheduling radiation therapy）的新方法（Using math to better treat cancer），与目前的标准放射治疗方案相比，这种方法在杀死癌细胞方面的效率可能高出22%。相关研究结果于2022年10月13日已经在《数学生物学杂志》（Journal of Mathematical Biology）网站发表——Cameron Meaney, Mohammad Kohandel, Arian Novruzi. Temporal optimization of radiation therapy to heterogeneous tumour populations and cancer stem cells. Journal of Mathematical Biology, Published: 13 October 2022, Volume 85, Article number: 51. DOI: 10.1007/s00285-022-01819-y. https://link.springer.com/article/10.1007/s00285-022-01819-y

虽然许多数学研究已经研究了如何优化放射治疗的时间安排以获得最大的抗癌效果，但大多数这些研究都假设“瘤内同质性”("intratumoral homogeneity")——也就是说，所有的癌细胞都是相同的。然而，近年来，科学家们已经意识到肿瘤是由许多不同种类的细胞组成的。最重要的是，它们包括癌症干细胞，它们比其他类型的细胞更能抵抗辐射。

上述研究论文的第一作者、滑铁卢大学应用数学博士候选人卡梅伦·米尼（Cameron Meaney） 说：“任何涉及癌症的计算的问题在于很难获得准确值，因为癌症类型与癌症类型之间、患者与患者之间的情况各不相同，即使在肿瘤内部也是如此。”

这种新算法可以概括干细胞和非干细胞的不同抗辐射力，使医生能够在收集有关个体癌症的确切数据之前预测肿瘤对放射治疗的反应。

卡梅伦·米尼解释说，该模型有局限性，因为肿瘤包含的细胞远远不止两种。然而，它的作用是为临床研究人员提供更好的治疗研究起点。

“该算法的结果很重要，因为它们阐明了肿瘤的异质性对于规划治疗很重要的想法，”卡梅伦·米尼说。

研究人员希望看到的下一步是将他们的算法应用于临床研究：他们建议的治疗计划是否会在实验室试验中优于现有的计划实践？

本研究得到加拿大自然科学与工程研究理事会（Natural Science and Engineering Research Council of Canada）的资助。

上述介绍，仅供参考。欲了解更多信息，敬请注意浏览原文或者相关报道。

Abstract

External beam radiation therapy is a key part of modern cancer treatments which uses high doses of radiation to destroy tumour cells. Despite its widespread usage and extensive study in theoretical, experimental, and clinical works, many questions still remain about how best to administer it. Many mathematical studies have examined optimal scheduling of radiotherapy, and most come to similar conclusions. Importantly though, these studies generally assume intratumoral homogeneity. But in recent years, it has become clear that tumours are not homogeneous masses of cancerous cells, but wildly heterogeneous masses with various subpopulations which grow and respond to treatment differently. One subpopulation of particular importance is cancer stem cells (CSCs) which are known to exhibit higher radioresistence compared with non-CSCs. Knowledge of these differences between cell types could theoretically lead to changes in optimal treatment scheduling. Only a few studies have examined this question, and interestingly, they arrive at apparent conflicting results. However, an understanding of their assumptions reveals a key difference which leads to their differing conclusions. In this paper, we generalize the problem of temporal optimization of dose distribution of radiation therapy to a two cell type model. We do so by creating a mathematical model and a numerical optimization algorithm to find the distribution of dose which leads to optimal cell kill. We then create a data set of optimization solutions and use data analysis tools to learn the relationships between model parameters and the qualitative behaviour of optimization results. Analysis of the model and discussion of biological importance are provided throughout. We find that the key factor in predicting the behaviour of the optimal distribution of radiation is the ratio between the radiosensitivities of the present cell types. These results can provide guidance for treatment in cases where clinicians have knowledge of tumour heterogeneity and of the abundance of CSCs.