Skip to content

Research at St Andrews

Evolutionary dynamics in vascularised tumours under chemotherapy: mathematical modelling, asymptotic analysis and numerical simulations

Research output: Contribution to journalArticlepeer-review

Abstract

We consider a mathematical model for the evolutionary dynamics of tumour cells in vascularised tumours under chemotherapy. The model comprises a system of coupled partial integro-differential equations for the phenotypic distribution of tumour cells, the concentration of oxygen and the concentration of a chemotherapeutic agent. In order to disentangle the impact of different evolutionary parameters on the emergence of intra-tumour phenotypic heterogeneity and the development of resistance to chemotherapy, we construct explicit solutions to the equation for the phenotypic distribution of tumour cells and provide a detailed quantitative characterisation of the long-time asymptotic behaviour of such solutions. Analytical results are integrated with numerical simulations of a calibrated version of the model based on biologically consistent parameter values. The results obtained provide a theoretical explanation for the observation that the phenotypic properties of tumour cells in vascularised tumours vary with the distance from the blood vessels. Moreover, we demonstrate that lower oxygen levels may correlate with higher levels of phenotypic variability, which suggests that the presence of hypoxic regions supports intra-tumour phenotypic heterogeneity. Finally, the results of our analysis put on a rigorous mathematical basis the idea, previously suggested by formal asymptotic results and numerical simulations, that hypoxia favours the selection for chemoresistant phenotypic variants prior to treatment. Consequently, this facilitates the development of resistance following chemotherapy.
Close

Details

Original languageEnglish
JournalVietnam Journal of Mathematics
VolumeFirst Online
Early online date6 Oct 2020
DOIs
Publication statusE-pub ahead of print - 6 Oct 2020

    Research areas

  • Vascularised tumours, Evolutionary dynamics, Intra-tumour heterogeneity, Resistance to chemotherapy, Mathematical oncology, Non-local partial differential equations

Discover related content
Find related publications, people, projects and more using interactive charts.

View graph of relations

Related by author

  1. Development of a coupled simulation toolkit for computational radiation biology based on Geant4 and CompuCell3D

    Liu, R., Higley, K., Swat, M., Chaplain, M. A. J., Powathil, G. & Glazier, J., 10 Feb 2021, In: Physics in Medicine and Biology. 66, 4, 20 p., 045026.

    Research output: Contribution to journalArticlepeer-review

  2. A hybrid discrete-continuum approach to model Turing pattern formation

    Macfarlane, F. R., Chaplain, M. A. J. & Lorenzi, T., 29 Oct 2020, In: Mathematical Biosciences and Engineering. 17, 6, p. 7442-7479

    Research output: Contribution to journalArticlepeer-review

  3. A mathematical multi-organ model for bidirectional epithelial-mesenchymal transitions in the metastatic spread of cancer

    Franßen, L. C. & Chaplain, M. A. J., Oct 2020, In: IMA Journal of Applied Mathematics. 85, 5, p. 724-761

    Research output: Contribution to journalArticlepeer-review

Related by journal

  1. Fibonacci length of automorphism groups involving Tribonacci numbers

    Doostie, H. & Campbell, C. M., 2000, In: Vietnam Journal of Mathematics. 28, p. 57 - 66

    Research output: Contribution to journalArticlepeer-review

ID: 269967305

Top