Mathematical Modelling of Phenotypic Selection Within Solid Tumours

Conference paper
Part of the Lecture Notes in Computational Science and Engineering book series (LNCSE, volume 126)


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.



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.


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© Springer Nature Switzerland AG 2019

Authors and Affiliations

  1. 1.School of Mathematics and StatisticsUniversity of St AndrewsSt AndrewsUK
  2. 2.Department of MathematicsSchool of Mathematical and Physical Sciences, University of SussexBrightonUK
  3. 3.CEMSE Division, King Abdullah University of Science and Technology (KAUST)ThuwalSaudi Arabia
  4. 4.Sorbonne Universités, UPMC Univ Paris 06, UMR 7598, Laboratoire Jacques-Louis LionsParisFrance

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