Mathematical Modelling of Phenotypic Selection Within Solid Tumours

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

Research output: Contribution to journalArticlepeer-review


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)
Pages (from-to)237-245
Number of pages9
JournalNumerical Mathematics and Advanced Applications ENUMATH 2017
StatePublished - Jan 5 2019

Bibliographical note

KAUST Repository Item: Exported on 2023-01-26
Acknowledged KAUST grant number(s): BAS/1/1648-01-01, BAS/1/1648-01-02
Acknowledgements: CV wishes to acknowledge partial support from the European Union’s Horizon 2020 research and innovation programme under the Marie Sklodowska-Curie grant agreement No 642866. AL was supported by King Abdullah University of Science and Technology (KAUST) baseline and start-up funds (BAS/1/1648-01-01 and BAS/1/1648-01-02). MAJC gratefully acknowledges support of EPSRC grant no. EP/N014642/1.

ASJC Scopus subject areas

  • Engineering(all)
  • Modeling and Simulation
  • Computational Mathematics
  • Discrete Mathematics and Combinatorics
  • Control and Optimization


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