Singh Khimeer, Jacobs Byron A
School of Computational and Applied Mathematics, University of the Witwatersrand, 1 Jan Smuts Avenue, Johannesburg, 2017, Gauteng, South Africa.
Department of Mathematics and Applied Mathematics, University of Johannesburg, Auckland Park, PO Box 524, Johannesburg, 2006, Gauteng, South Africa.
Bull Math Biol. 2025 Apr 9;87(5):65. doi: 10.1007/s11538-025-01441-1.
Metastatic cancer is reported to have a mortality rate of 90%. Understanding the underlying principles of metastasis and quantifying them through mathematical modelling provides insights into potential treatment regimes. This work presents a partial differential equation based mathematical model embedded on a network, representing the organs and the blood vessels between them, with the aim of predicting likely secondary metastatic sites. Through this framework the relationship between metastasis and blood flow and between metastasis and the diffusive behaviour of cancer is explored. An analysis of the model predictions showed a good correlation with clinical data for some cancer types, particularly for cancers originating in the gut and liver. The model also predicts an inverse relationship between blood velocity and the concentration of cancer cells in secondary organs. Finally, for anisotropic diffusive behaviour, where the cancer experiences greater diffusivity in one direction, metastatic efficiency decreased. This is aligned with the clinical observation that gliomas of the brain, which typically show anisotropic diffusive behaviour, exhibit fewer metastases. The investigation yields some valuable results for clinical practitioners and researchers-as it clarifies some aspects of cancer that have hitherto been difficult to study, such as the impact of differing diffusive behaviours and blood flow rates on the global spread of cancer. The model provides a good framework for studying cancer progression using cancer-specific information when simulating metastasis.
据报道，转移性癌症的死亡率为90%。了解转移的潜在原理并通过数学建模对其进行量化，有助于深入了解潜在的治疗方案。这项工作提出了一个基于偏微分方程的数学模型，该模型嵌入在一个网络上，代表器官及其之间的血管，旨在预测可能的继发性转移部位。通过这个框架，探索了转移与血流之间以及转移与癌症扩散行为之间的关系。对模型预测的分析表明，对于某些癌症类型，特别是起源于肠道和肝脏的癌症，模型预测与临床数据具有良好的相关性。该模型还预测了血流速度与继发性器官中癌细胞浓度之间的反比关系。最后，对于各向异性扩散行为，即癌症在一个方向上具有更大的扩散率，转移效率会降低。这与临床观察结果一致，即通常表现出各向异性扩散行为的脑胶质瘤转移较少。这项研究为临床医生和研究人员提供了一些有价值的结果，因为它阐明了一些迄今为止难以研究的癌症方面，例如不同的扩散行为和血流速度对癌症全球扩散的影响。该模型为在模拟转移时使用癌症特异性信息研究癌症进展提供了一个良好的框架。
