Mathematical Modelling of Phenotypic Selection Within Solid Tumours

Mark A. J. Chaplain, Tommaso Lorenzi, ALEXANDER LORZ, Chandrasekhar Venkataraman

Research output: Chapter in Book/Report/Conference proceedingConference contribution


We present a space- and phenotype-structured model of selection dynamics between cancer cells within a solid tumour. In the framework of this model, we combine formal analyses with numerical simulations to investigate in silico the role played by the spatial distribution of oxygen and therapeutic agents in mediating phenotypic selection of cancer cells. Numerical simulations are performed on the 3D geometry of an in vivo human hepatic tumour, which was imaged using computerised tomography. Our modelling extends our previous work in the area through the inclusion of multiple therapeutic agents, one that is cytostatic, whilst the other is cytotoxic. In agreement with our previous work, the results show that spatial inhomogeneities in oxygen and therapeutic agent concentrations, which emerge spontaneously in solid tumours, can promote the creation of distinct local niches and lead to the selection of different phenotypic variants within the same tumour. A novel conclusion we infer from the simulations and analysis is that, for the same total dose, therapeutic protocols based on a combination of cytotoxic and cytostatic agents can be more effective than therapeutic protocols relying solely on cytotoxic agents in reducing the number of viable cancer cells.
Original languageEnglish (US)
Title of host publicationNumerical Mathematics and Advanced Applications ENUMATH 2017
PublisherSpringer Nature
Number of pages9
ISBN (Print)9783319964140
StatePublished - Jan 5 2019


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