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Models for the Growth of a Solid Tumor by Diffusion
Abstract
A simple mathematical model of tumor growth by diffusion is constructed in order to examine and evaluate different hypotheses concerning the evolution of a solid carcinoma. A primary objective is to infer the chemical source of growth inhibition from the most easily obtained data, namely, the outer radius of the nodule as a function of time and a histological examination of the final dormant state. In section 6 some of the conclusions of this study relating to a prototype experiment and described with as little mathematics as possible.
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Cited by
Dissecting cancer through mathematics: From the cell to the animal model
Byrne, H. M. (2010) · Nature reviews. Cancer · doi:10.1038/nrc2808 · Cited by 442
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
Nonlinear simulation of tumor growth
Cristini, V., Lowengrub, J., & Nie, Q. (2003) · Journal of Mathematical Biology · doi:10.1007/s00285-002-0174-6 · Cited by 294
Oxygen consumption dynamics in steady-state tumour models
Grimes, D. R., Fletcher, A. G., & Partridge, M. (2014) · Royal Society Open Science · doi:10.1098/rsos.140080 · Cited by 84
Properties of Tumor Spheroid Growth Exhibited by Simple Mathematical Models
Wallace, D. I., & Guo, X. (2013) · Frontiers in Oncology · doi:10.3389/fonc.2013.00051 · Cited by 77
Metadata
- Authors
- Greenspan, H. P.
- Venue
- Studies in Applied Mathematics
- Publisher
- Wiley
- Published
- 1972-12
- Volume
- 51
- Issue
- 4
- Pages
- 317-340
- ISSN
- 0022-2526 (ISSN-L)
- 1467-9590
- OpenAlex
- W200447247
- Cited by
- 581
- References
- 0
- FWCI
- 1.18
- Type
- journal article
- Language
- en
- Open access
- closed
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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.
