Abstract
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.