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Dissecting cancer through mathematics: from the cell to the animal model

Nature Reviews Cancer volume 10, pages 221–230 (2010)Cite this article

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Abstract

This Timeline article charts progress in mathematical modelling of cancer over the past 50 years, highlighting the different theoretical approaches that have been used to dissect the disease and the insights that have arisen. Although most of this research was conducted with little involvement from experimentalists or clinicians, there are signs that the tide is turning and that increasing numbers of those involved in cancer research and mathematical modellers are recognizing that by working together they might more rapidly advance our understanding of cancer and improve its treatment.

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Figure 1: From biological hypothesis to testable prediction by mathematical modelling.
Figure 2: Alternative approaches for modelling the growth of multicellular spheroids (MCS).
Figure 3: Multi-scale modelling of vascular tumour growth.
Figure 4: A mathematical model of vascularized tumour growth.
Figure 5: Changes in tumour cell growth after drug exposure.

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Acknowledgements

H.M.B. would like to thank M. Owen (University of Nottingham, UK) for generating the multi-scale numerical simulations and also C. Lewis and G. Tozer (University of Sheffield, UK) for providing images from their laboratories. H.M.B. is also grateful to S. McElwain and D. Hutmacher (Queensland University of Technology, Australia) for their helpful and constructive comments on the Timeline.

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  1. Helen M. Byrne is at the Centre for Mathematical Medicine and Biology, School of Mathematical Sciences, University of Nottingham, Nottingham NG7 2RD, UK. Helen.byrne@nottingham.ac.uk,

    Helen M. Byrne

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Supplementary information

Supplementary Information S1

Simulation showing the control case of untreated tumour growth, generated using a multiscale model of vascular tumour growth (owen et al., 2009) and accompany FIGS 4 and 5. (MOV 1731 kb)

Supplementary Information S2

Simulation showing the response of the tumour in (i) to chemotherapy, generated using a multiscale model of vascular tumour growth (owen et al., 2009) and accompany FIGS 4 and 5. (MOV 1823 kb)

Supplementary Information S3

Simulation showing the response of the tumour in (i) to immunotherapy, generated using a multiscale model of vascular tumour growth (owen et al., 2009) and accompany FIGS 4 and 5. (MOV 1624 kb)

Supplementary Information S4

Simulation showing the response of the tumour in (i) to combined chemo-and immuno-therapy, generated using a multiscale model of vascular tumour growth (owen et al., 2009) and accompany FIGS 4 and 5. (MOV 1785 kb)

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Byrne, H. Dissecting cancer through mathematics: from the cell to the animal model. Nat Rev Cancer 10, 221–230 (2010). https://doi.org/10.1038/nrc2808

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