The DOI matches its Crossref record; 24 of the 24 references it cites were found in a registry or an index.
Modelling solid tumour growth using the theory of mixtures
Abstract
In this paper the theory of mixtures is used to develop a two-phase model of an avascular tumour, which comprises a solid, cellular, phase and a liquid phase. Mass and momentum balances which are used to derive the governing equations are supplemented by constitutive laws that distinguish the two phases and enable the stresses within the tumour to be calculated. Novel features of the model include the dependence of the cell proliferation rate on the cellular stress and the incorporation of mass exchange between the two phases. A combination of numerical and analytical techniques is used to investigate the sensitivity of equilibrium tumour configurations to changes in the model parameters. Variation of parameters such as the maximum cell proliferation rate and the rate of natural cell death yield results which are consistent with analyses performed on simpler tumour growth models and indicate that the two-phase formulation is a natural extension of the earlier models. New predictions relate to the impact of mechanical effects on the tumour's equilibrium size which decreases under increasing stress and/or external loading. In particular, as a parameter which measures the reduction in cell proliferation due to cell stress is increased a critical value is reached, above which the tumour is eliminated.
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Citations
Cites
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Cited by
The Role of Mechanical Forces in Tumor Growth and Therapy
Jain, R. K., Martin, J. D., & Stylianopoulos, T. (2014) · Annual Review of Biomedical Engineering · doi:10.1146/annurev-bioeng-071813-105259 · Cited by 1,044
Nonlinear modelling of cancer: bridging the gap between cells and tumours
Lowengrub, J. S., Frieboes, H. B., Jin, F., Chuang, Y.-L., Li, X., Macklin, P., Wise, S. M., & Cristini, V (2010) · Nonlinearity · doi:10.1088/0951-7715/23/1/r01 · Cited by 553
Three-dimensional multispecies nonlinear tumor growth—I
Wise, S. M., Lowengrub, J. S., Frieboes, H. B., & Cristini, V. (2008) · Journal of Theoretical Biology · doi:10.1016/j.jtbi.2008.03.027 · Cited by 484
ON THE FOUNDATIONS OF CANCER MODELLING: SELECTED TOPICS, SPECULATIONS, AND PERSPECTIVES
BELLOMO, N., LI, N. K., & MAINI, P. K. (2008) · Mathematical Models and Methods in Applied Sciences · doi:10.1142/s0218202508002796 · Cited by 420
Multiscale modelling and nonlinear simulation of vascular tumour growth
Macklin, P., McDougall, S., Anderson, A. R. A., Chaplain, M. A. J., Cristini, V., & Lowengrub, J. (2009) · Journal of Mathematical Biology · doi:10.1007/s00285-008-0216-9 · Cited by 363
Metadata
- Authors
- Byrne, H.
- Venue
- Mathematical Medicine and Biology
- Publisher
- Oxford University Press (OUP)
- Published
- 2003-12-01
- Volume
- 20
- Issue
- 4
- Pages
- 341-366
- ISSN
- 1477-8599 (ISSN-L)
- 1477-8602
- OpenAlex
- W2047016831
- Cited by
- 437
- References
- 24
- FWCI
- 9.71
- Type
- journal article
- Language
- en
- Open access
- closed
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Data sources
Bibliographic data: Semantic Scholar, OpenAlex, Crossref.
Contains information from the Semantic Scholar Academic Graph Datasets, made available under the ODC Attribution License (ODC-BY 1.0).
Semantic Scholar’s data is described in: Kinney, R., et al. (2023). The Semantic Scholar Open Data Platform. arXiv:2301.10140.
